christopher/oeis · Datasets at Hugging Face

sequence_id stringlengths 7 7	sequence_name stringlengths 4 573	sequence sequencelengths 1 348	keywords sequencelengths 1 8	score int64 1 2.31k	offset_a int64 -14,827 666,262,453B	offset_b int64 0 635M ⌀	cross_references sequencelengths 1 128 ⌀	former_ids sequencelengths 1 3 ⌀	author stringlengths 7 231 ⌀	timestamp timestamp[us]date 1999-12-11 03:00:00 2025-04-28 00:58:08	filename stringlengths 29 29	hash stringlengths 32 32
A359301	Least k such that {1, ..., k} contains an n-element set of positive integers satisfying the Lucier-Sárközy difference set condition.	[ "1", "4", "9", "12", "33", "36", "49", "52", "65", "68", "105", "108", "133", "136", "153", "156", "209", "212", "217", "220", "243", "246", "299", "302", "489", "492" ]	[ "nonn", "more", "nice" ]	21	1	2	[ "A174911", "A359301" ]	null	Charles R Greathouse IV, Dec 24 2022	2023-02-19T18:45:27	oeisdata/seq/A359/A359301.seq	bfc4e6c92a49261a12a5fa74beaf1cb7
A359302	Dirichlet g.f.: zeta(s)^2/zeta(3*s-2).	[ "1", "2", "2", "3", "2", "4", "2", "0", "3", "4", "2", "6", "2", "4", "4", "-3", "2", "6", "2", "6", "4", "4", "2", "0", "3", "4", "-5", "6", "2", "8", "2", "-6", "4", "4", "4", "9", "2", "4", "4", "0", "2", "8", "2", "6", "6", "4", "2", "-6", "3", "6", "4", "6", "2", "-10", "4", "0", "4", "4", "2", "12", "2", "4", "6", "-9", "4", "8", "2", "6", "4", "8", "2", "0", "2", "4", "6", "6", "4", "8", "2", "-6", "-13", "4", "2", "12" ]	[ "sign", "easy", "mult" ]	8	1	2	[ "A344326", "A359302" ]	null	Vaclav Kotesovec, Dec 25 2022	2023-09-15T05:52:45	oeisdata/seq/A359/A359302.seq	22375c2d2e33518f94e5cb5323aaa605
A359303	Bitwise encoding of the state of a 1D cellular automaton after n steps from ...111000... where adjacent cells swap 01 <-> 10 when within triples 110 or 011.	[ "1", "3", "5", "11", "13", "39", "43", "45", "103", "155", "171", "173", "359", "411", "619", "669", "1367", "1371", "1387", "1437", "3287", "4923", "5339", "5467", "5483", "5533", "11479", "13115", "19675", "21339", "21739", "21853", "43735", "43835", "44251", "45915", "52459", "78685", "170455", "173755", "174555", "174811", "174939", "175339", "176989", "367063", "419515", "629211" ]	[ "nonn", "easy" ]	96	1	2	[ "A030101", "A035327", "A053644", "A359303", "A360141", "A360142" ]	null	Raphael J. F. Berger, Dec 25 2022	2024-04-01T12:09:17	oeisdata/seq/A359/A359303.seq	2453353c72d8ec686cea2f3ce73c2908
A359304	Oblong numbers which are products of five distinct primes.	[ "4290", "4830", "6006", "11130", "12210", "13110", "16770", "23870", "27390", "33306", "34410", "34782", "37830", "44310", "49062", "56406", "60762", "64770", "66822", "70490", "71022", "74802", "82082", "84390", "95790", "101442", "103362", "104006", "109230", "119370", "125670", "127806", "133590", "137270", "148610", "151710", "158802" ]	[ "nonn" ]	11	1	1	[ "A002378", "A046387", "A359304" ]	null	Massimo Kofler, Dec 25 2022	2023-01-14T17:35:31	oeisdata/seq/A359/A359304.seq	432c85845a1228f7f1ff7482d3483228
A359305	Number of divisors of 6n-1 of form 6k+1.	[ "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "2", "1", "2", "2", "1", "1", "1", "2", "1", "1", "2", "2", "2", "2", "1", "1", "1", "3", "1", "1", "1", "1", "3", "1", "2", "1", "2", "2", "1", "1", "2", "2", "2", "2", "1", "1", "1", "2", "2", "2", "1", "1", "2", "1", "2", "2", "1", "3", "1", "2", "1", "1", "4", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "2", "3" ]	[ "nonn", "easy" ]	21	1	6	[ "A000005", "A001620", "A016969", "A078703", "A279060", "A319995", "A359211", "A359233", "A359305", "A359306", "A359307", "A359308", "A359309", "A359324", "A359325", "A359326", "A359327" ]	null	Seiichi Manyama, Dec 25 2022	2022-12-27T07:08:28	oeisdata/seq/A359/A359305.seq	09df164a0a086518b732c4ac78697913
A359306	Number of divisors of 6n-2 of form 6k+1.	[ "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "2", "2", "1", "1", "1", "2", "1", "2", "1", "2", "2", "1", "1", "2", "2", "1", "1", "2", "1", "1", "2", "3", "1", "2", "1", "2", "1", "1", "2", "2", "2", "1", "1", "2", "1", "2", "2", "2", "1", "2", "2", "2", "2", "1", "1", "2", "1", "1", "1", "4", "2", "1", "1", "2", "1", "2", "2", "2", "2", "1", "2", "2", "2", "2", "1", "2", "1", "1", "1", "2", "3", "2", "1", "2", "1", "2", "1", "4", "1" ]	[ "nonn", "easy" ]	16	1	5	[ "A279060", "A359305", "A359306", "A359307", "A359308", "A359309" ]	null	Seiichi Manyama, Dec 25 2022	2023-08-16T02:26:51	oeisdata/seq/A359/A359306.seq	9e2f947065c6cd9c43363ff8874509f9
A359307	Number of divisors of 6n-3 of form 6k+1.	[ "1", "1", "1", "2", "1", "1", "2", "1", "1", "2", "2", "1", "2", "1", "1", "2", "1", "2", "2", "2", "1", "2", "1", "1", "3", "1", "1", "2", "2", "1", "2", "2", "2", "2", "1", "1", "2", "2", "2", "2", "1", "1", "2", "1", "1", "4", "2", "2", "2", "1", "1", "2", "2", "1", "2", "2", "1", "2", "2", "2", "2", "1", "2", "2", "2", "1", "4", "1", "1", "2", "1", "2", "2", "3", "1", "2", "1", "2", "2", "1", "2", "2", "2", "1", "3", "2", "1", "4", "1", "1" ]	[ "nonn", "easy" ]	14	1	4	[ "A279060", "A359305", "A359306", "A359307", "A359308", "A359309" ]	null	Seiichi Manyama, Dec 25 2022	2023-08-16T02:26:54	oeisdata/seq/A359/A359307.seq	9749fcc62059a5e5a4c678201f455077
A359308	Number of divisors of 6n-4 of form 6k+1.	[ "1", "1", "2", "1", "2", "1", "2", "1", "2", "2", "2", "1", "2", "1", "2", "1", "3", "2", "2", "1", "2", "1", "2", "2", "2", "2", "2", "1", "2", "1", "4", "1", "2", "2", "2", "1", "2", "2", "2", "1", "2", "2", "2", "2", "4", "1", "2", "1", "2", "2", "2", "2", "2", "1", "2", "1", "3", "2", "4", "1", "2", "1", "2", "2", "2", "3", "2", "1", "2", "2", "2", "1", "4", "2", "2", "1", "2", "1", "2", "2", "2", "2", "4", "2", "2", "1", "4", "1", "2", "2" ]	[ "nonn", "easy" ]	15	1	3	[ "A279060", "A359305", "A359306", "A359307", "A359308", "A359309" ]	null	Seiichi Manyama, Dec 25 2022	2023-08-16T02:26:57	oeisdata/seq/A359/A359308.seq	ed225d5769560a55f48df4f4116ca19d
A359309	Number of divisors of 6n-5 of form 6k+1.	[ "1", "2", "2", "2", "2", "2", "2", "2", "3", "2", "2", "2", "2", "2", "2", "4", "2", "2", "2", "2", "2", "2", "4", "2", "2", "2", "2", "2", "3", "4", "2", "2", "2", "2", "2", "2", "4", "2", "2", "2", "2", "4", "2", "4", "2", "2", "2", "2", "2", "2", "4", "2", "2", "2", "4", "2", "2", "4", "2", "2", "3", "2", "2", "2", "4", "2", "2", "4", "2", "2", "2", "4", "2", "2", "2", "2", "2", "2", "4", "4", "4", "2", "2", "2", "2", "4", "2", "2", "2", "2" ]	[ "nonn", "easy" ]	15	1	2	[ "A279060", "A359305", "A359306", "A359307", "A359308", "A359309" ]	null	Seiichi Manyama, Dec 25 2022	2023-08-16T02:27:01	oeisdata/seq/A359/A359309.seq	87f22c36748e7f20b0db13162c1ae1dd
A359310	Cyclic cubic conductors associated with closed Andozhskii groups.	[ "59031", "209853", "247437", "263017", "271737", "329841", "377923", "407851", "412909", "415597", "416241", "416727", "462573", "474561", "487921", "493839", "547353", "586963", "612747", "613711", "615663", "622063", "648427", "651829", "689347", "690631", "753787", "796779", "811069", "818217", "869611", "914263", "915439", "922167", "936747", "977409", "997087" ]	[ "nonn" ]	45	1	1	null	null	Daniel Constantin Mayer, Dec 25 2022	2023-09-24T12:16:31	oeisdata/seq/A359/A359310.seq	0fbaeaff0fcd9e0bdd8a356c274b4d88
A359311	Number of Catalan paths (nonnegative, starting and ending at 0, step +/-1) of 2*n steps which reach at least 6 at some point.	[ "0", "0", "0", "0", "0", "0", "1", "12", "89", "528", "2755", "13244", "60214", "263121", "1116791", "4637476", "18936940", "76327705", "304520286", "1205152900", "4738962369", "18540020091", "72240167011", "280579954028", "1087033982059", "4203231136230", "16228518078010", "62588797371361", "241198478726775" ]	[ "nonn", "easy" ]	124	0	8	[ "A000108", "A080936", "A080937", "A289419", "A359311" ]	null	Greg Dresden, Jan 21 2023	2023-01-25T09:09:26	oeisdata/seq/A359/A359311.seq	6f961ae15c3ea76b9e4d5ea2159135f7
A359312	a(1) = 1; for n >= 1, a(2n) = A000005(a(n)), a(2n + 1) = A000005(a(n)) + 1.	[ "1", "1", "2", "1", "2", "2", "3", "1", "2", "2", "3", "2", "3", "2", "3", "1", "2", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "1", "2", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "1", "2", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2" ]	[ "nonn" ]	20	1	3	[ "A000005", "A131051", "A359312" ]	null	Ctibor O. Zizka, Dec 25 2022	2022-12-31T15:16:24	oeisdata/seq/A359/A359312.seq	281902b5f72e716a60ddb4c07c76c590
A359313	Triangular array read by rows. T(n,k) is the number of Green's H-classes contained in the D-class of rank k matrices in the semigroup Mat_n(F_2) of n X n matrices over the field F_2. n>=0, 0<=k<=n.	[ "1", "1", "1", "1", "9", "1", "1", "49", "49", "1", "1", "225", "1225", "225", "1", "1", "961", "24025", "24025", "961", "1", "1", "3969", "423801", "1946025", "423801", "3969", "1", "1", "16129", "7112889", "139499721", "139499721", "7112889", "16129", "1", "1", "65025", "116532025", "9439094025", "40315419369", "9439094025", "116532025", "65025", "1" ]	[ "nonn", "tabl" ]	15	0	5	[ "A002416", "A002884", "A005329", "A022166", "A243950", "A296548", "A359313" ]	null	Geoffrey Critzer, Dec 25 2022	2022-12-28T04:59:48	oeisdata/seq/A359/A359313.seq	9cd9860cba0c64f74433eb63029aee18
A359314	Three-column table T(n,k) read by rows where the elements in the pair of two adjacent rows, starting with the odd-indexed row T(2j-1,k) and followed by the even-indexed one T(2j,k), are such that they are not multiples of the elements presented in the previous rows and that Sum_{k=1..3} T(2j-1,k)^2 = Sum_{k=1..3} T(2j,k)^2 and Sum_{k=1..3} T(2j-1,k)^6 = Sum_{k=1..3} T(2j,k)^6 for j > 0 and k = 1, 2, 3.	[ "3", "19", "22", "10", "15", "23", "15", "52", "65", "36", "37", "67", "23", "54", "73", "33", "47", "74", "3", "55", "80", "32", "43", "81", "11", "65", "78", "37", "50", "81" ]	[ "nonn", "tabf", "more" ]	45	1	1	null	null	Alexander R. Povolotsky, Dec 25 2022	2023-12-10T09:12:25	oeisdata/seq/A359/A359314.seq	210ea127c45c348c409dcd9260f83ece
A359315	a(n) is the smallest centered triangular number with binary weight n.	[ "1", "10", "19", "46", "31", "235", "631", "1786", "1999", "7669", "7039", "12286", "16381", "180094", "114679", "949231", "2086831", "2883574", "4175839", "12480511", "50329585", "62898151", "132638719", "234618814", "771743710", "2883510271", "4269733885", "8254119871", "17045499901", "33214168831" ]	[ "nonn", "base" ]	9	1	2	[ "A000120", "A005448", "A089999", "A358932", "A359315", "A359316" ]	null	Ilya Gutkovskiy, Dec 25 2022	2025-02-16T08:34:04	oeisdata/seq/A359/A359315.seq	e8bc5d58533ec3aafb082071294cec4e
A359316	a(n) is the smallest centered square number with binary weight n.	[ "1", "5", "13", "85", "61", "221", "761", "1013", "2813", "12013", "23545", "54781", "16381", "196565", "425965", "770041", "3137513", "7663613", "13629421", "20962813", "63946741", "121602013", "192805885", "499122013", "989724541", "2411720701", "6435110905", "17162301181", "29929502461", "63753420281" ]	[ "nonn", "base" ]	8	1	2	[ "A000120", "A001844", "A089998", "A358932", "A359315", "A359316" ]	null	Ilya Gutkovskiy, Dec 25 2022	2025-02-16T08:34:04	oeisdata/seq/A359/A359316.seq	e23ebd9dfba61087ac10d777d63837d2
A359317	a(n) is the smallest tetrahedral number with binary weight n.	[ "0", "1", "10", "35", "120", "220", "455", "2024", "1771", "4060", "14190", "16215", "129766", "32509", "1414910", "1823471", "5159805", "8171255", "4192244", "24117100", "30865405", "334985911", "192937325", "1610599145", "1048440315", "4261347265", "4244012991", "63828916911", "213588635511", "133110357279" ]	[ "nonn", "base" ]	9	0	3	[ "A000120", "A000292", "A089999", "A358931", "A359317", "A359318" ]	null	Ilya Gutkovskiy, Dec 25 2022	2025-02-16T08:34:04	oeisdata/seq/A359/A359317.seq	d22ad15619e46ce0db1732983b36d9bd
A359318	a(n) is the smallest square pyramidal number with binary weight n.	[ "0", "1", "5", "14", "30", "55", "819", "506", "1785", "1015", "16206", "51039", "98021", "81375", "1113775", "964535", "2607099", "5494655", "1048061", "6029275", "50331190", "356343295", "534555645", "516941815", "4021378559", "2143222510", "12842950505", "34091142526", "68651299705", "124545644405", "273736383990" ]	[ "nonn", "base" ]	10	0	3	[ "A000120", "A000330", "A089998", "A358931", "A359317", "A359318" ]	null	Ilya Gutkovskiy, Dec 25 2022	2025-02-16T08:34:04	oeisdata/seq/A359/A359318.seq	500e7ac44cc2f0f1c59573f91e75c9a4
A359319	Maximal coefficient of (1 + x) * (1 + x^8) * (1 + x^27) * ... * (1 + x^(n^3)).	[ "1", "1", "1", "1", "1", "1", "2", "2", "2", "3", "4", "5", "7", "10", "14", "18", "27", "36", "62", "95", "140", "241", "370", "607", "1014", "1646", "2751", "4863", "8260", "13909", "24870", "41671", "73936", "131257", "228204", "411128", "737620", "1292651", "2324494", "4253857", "7487549", "13710736", "25291179", "44938191", "82814603" ]	[ "nonn" ]	31	0	7	[ "A000537", "A000578", "A001405", "A025591", "A160235", "A279329", "A359319", "A359320" ]	null	Ilya Gutkovskiy, Dec 25 2022	2022-12-31T12:46:16	oeisdata/seq/A359/A359319.seq	6b3bc3fd1a9917d01522aebe30809b79
A359320	Maximal coefficient of (1 + x) * (1 + x^16) * (1 + x^81) * ... * (1 + x^(n^4)).	[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "3", "3", "4", "5", "5", "6", "9", "13", "17", "24", "34", "53", "84", "130", "177", "290", "500", "797", "1300", "2066", "3591", "6090", "10298", "17330", "29888", "50811", "88358", "153369", "280208", "481289", "845090", "1474535", "2703811", "4808816", "8329214", "14806743", "27529781", "48859783", "87674040", "156471632" ]	[ "nonn" ]	20	0	10	[ "A000538", "A000583", "A025591", "A160235", "A298859", "A359319", "A359320" ]	null	Ilya Gutkovskiy, Dec 25 2022	2024-01-31T14:12:16	oeisdata/seq/A359/A359320.seq	9ac204d92fde25130d3f1ec481ec9bca
A359321	a(n) is the smallest n-gonal pyramidal number which can be represented as the sum of n distinct nonzero n-gonal pyramidal numbers in exactly n ways, or -1 if none exists.	[ "2300", "6201", "8125", "6391" ]	[ "nonn", "more" ]	5	3	1	[ "A080851", "A350210", "A350397", "A350423", "A359321" ]	null	Ilya Gutkovskiy, Dec 25 2022	2025-02-16T08:34:04	oeisdata/seq/A359/A359321.seq	9326bc64993bc5ce6feab56a90a9c4c3
A359322	a(n) is the first prime p such that the average of the squares of n consecutive primes starting with p is prime.	[ "3", "7", "7", "1627", "83", "7", "23", "7", "19", "17", "73", "281", "179", "257", "5", "43", "73", "43", "19", "67", "911", "193", "7", "1613", "139", "383", "7", "719", "113", "967", "31", "19", "211", "769", "149", "173", "13", "13", "59", "137", "23", "47", "89", "607", "61", "127", "61", "317", "1049", "1277", "547", "281", "317", "4157", "199", "107", "373", "149", "229", "367", "1489", "643", "563", "587", "263" ]	[ "nonn" ]	13	2	1	null	null	Robert Israel, Dec 25 2022	2023-01-06T10:42:19	oeisdata/seq/A359/A359322.seq	4efc5ed92b726a008b96094a4408bab4
A359323	a(n) is the first prime p such that the average of the n-th powers of n consecutive primes starting with p is prime.	[ "2", "3", "1531", "19", "631", "37", "41", "13", "670231", "614333", "11699", "11", "2447", "3049", "223", "13", "8353", "2531", "2203", "241", "3209", "5023", "52631", "461", "26723", "3307" ]	[ "nonn", "more" ]	22	1	1	[ "A359322", "A359323" ]	null	Robert Israel, Dec 25 2022	2025-03-24T05:56:16	oeisdata/seq/A359/A359323.seq	82d84a45fea057d58861da876cd12f21
A359324	Number of divisors of 6n-2 of form 6k+5.	[ "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "0", "2", "0", "1", "1", "1", "1", "1", "0", "1", "0", "2", "1", "1", "0", "2", "1", "1", "0", "1", "1", "2", "0", "1", "0", "1", "2", "1", "1", "2", "0", "2", "0", "1", "0", "1", "2", "2", "0", "1", "0", "2", "0", "2", "1", "1", "2", "1", "1", "1", "0", "2", "1", "1", "0", "1", "1", "2", "0", "2", "1", "2", "0", "2", "0", "1", "2", "1", "1", "1", "1", "3", "0", "1", "0", "1", "2", "1", "0", "1" ]	[ "nonn", "easy" ]	18	1	12	[ "A319995", "A359239", "A359269", "A359290", "A359305", "A359324", "A359325", "A359326", "A359327" ]	null	Seiichi Manyama, Dec 25 2022	2023-08-14T01:59:23	oeisdata/seq/A359/A359324.seq	6e0d7bb5460018259f88a13af69a62a4
A359325	Number of divisors of 6n-3 of form 6k+5.	[ "0", "0", "1", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "1", "0", "1", "2", "0", "0", "1", "0", "1", "1", "0", "1", "1", "2", "0", "1", "0", "0", "2", "0", "1", "1", "0", "1", "2", "0", "0", "1", "2", "1", "1", "0", "0", "2", "0", "1", "1", "0", "2", "1", "0", "0", "1", "2", "0", "2", "1", "1", "2", "0", "0", "1", "0", "1", "1", "0", "1", "2", "2", "0", "1", "0", "1", "2", "0", "1", "2", "0", "2", "1", "0", "0", "1", "2", "1", "1" ]	[ "nonn", "easy" ]	16	1	18	[ "A319995", "A359305", "A359324", "A359325", "A359326", "A359327" ]	null	Seiichi Manyama, Dec 25 2022	2023-08-16T02:27:04	oeisdata/seq/A359/A359325.seq	f6194838219e42cd8d44a3365398b828
A359326	Number of divisors of 6n-4 of form 6k+5.	[ "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "1", "0", "1", "0", "0", "2", "1", "0", "0", "0", "2", "0", "0", "0", "1", "2", "1", "0", "1", "0", "1", "0", "1", "0", "0", "2", "1", "1", "0", "0", "2", "0", "1", "0", "1", "2", "0", "0", "2", "0", "1", "0", "1", "0", "0", "2", "1", "0", "1", "2", "2", "0", "0", "0", "1", "2", "0", "0", "1", "0", "2", "0", "1", "0", "1", "2", "2", "0", "0", "0", "2", "2", "0", "0", "1", "2", "0" ]	[ "nonn", "easy" ]	18	1	19	[ "A319995", "A359305", "A359324", "A359325", "A359326", "A359327" ]	null	Seiichi Manyama, Dec 25 2022	2023-08-14T01:59:19	oeisdata/seq/A359/A359326.seq	b487c66b729698c6541bac49b2811756
A359327	Number of divisors of 6n-5 of form 6k+5.	[ "0", "0", "0", "0", "1", "0", "0", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "0", "0", "2", "1", "0", "0", "0", "2", "0", "0", "0", "0", "2", "0", "2", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "2", "0", "2", "0", "0", "0", "1", "2", "0", "0", "0", "2", "2", "0", "0", "0", "0", "2", "0", "0", "0", "0", "4", "2", "0", "0", "0", "2", "0", "0", "0", "0", "2", "2", "0", "0", "0", "2", "0", "0", "2", "0", "2", "0", "2", "0", "1", "2" ]	[ "nonn", "easy" ]	18	1	10	[ "A319995", "A359239", "A359240", "A359241", "A359305", "A359324", "A359325", "A359326", "A359327" ]	null	Seiichi Manyama, Dec 25 2022	2023-08-14T01:59:32	oeisdata/seq/A359/A359327.seq	3f758d1ada64b1335a0c00e6adb395e4
A359328	Maximal coefficient of x^2(x^2 + x^3)(x^2 + x^3 + x^5)...(x^2 + x^3 + x^5 + ... + x^prime(n)).	[ "1", "1", "1", "2", "4", "12", "46", "251", "1576", "11578", "94933", "875134", "8900088", "99276703", "1214131109", "16107824706", "229757728186", "3499486564517", "56862172844198", "980725126968577", "17899265342632635", "345197504845310134", "7005723403640260805", "149261757412790940113", "3329108788695272565243" ]	[ "nonn" ]	35	0	4	[ "A000040", "A326178", "A350457", "A359328", "A359337", "A359338", "A359339" ]	null	Stefano Spezia, Dec 26 2022	2024-02-01T16:24:09	oeisdata/seq/A359/A359328.seq	6a722b43576cce1059e61625a92eccb9
A359329	Number of diagonals in a regular polygon with n sides not passing through the center.	[ "0", "0", "5", "6", "14", "16", "27", "30", "44", "48", "65", "70", "90", "96", "119", "126", "152", "160", "189", "198", "230", "240", "275", "286", "324", "336", "377", "390", "434", "448", "495", "510", "560", "576", "629", "646", "702", "720", "779", "798", "860", "880", "945", "966", "1034", "1056", "1127", "1150", "1224", "1248", "1325", "1350", "1430", "1456", "1539", "1566", "1652", "1680" ]	[ "nonn", "easy" ]	30	3	3	[ "A000096", "A014106", "A054000", "A142150", "A359329" ]	null	Luk De Clercq, Dec 26 2022	2024-10-02T07:40:09	oeisdata/seq/A359/A359329.seq	a13739fa4a59310af9a634d93f63e739
A359330	Composite k for which phi(k) + phi(k') = k, where k' is the arithmetic derivative of k (A003415).	[ "4", "6", "8", "10", "12", "18", "22", "28", "34", "58", "60", "72", "82", "84", "88", "108", "112", "118", "124", "132", "140", "142", "202", "204", "214", "216", "220", "228", "260", "274", "298", "324", "340", "358", "372", "382", "394", "444", "454", "478", "492", "508", "538", "562", "564", "572", "580", "620", "622", "644", "694", "708", "740", "804", "812", "820" ]	[ "nonn" ]	18	1	1	[ "A000010", "A001359", "A002808", "A003415", "A023221", "A051953", "A066938", "A190402", "A359330" ]	null	Marius A. Burtea, Jan 28 2023	2023-02-17T22:05:35	oeisdata/seq/A359/A359330.seq	e07eb72a8842f89a0bac6bc9c59d162a
A359331	Nonprime numbers k for which k*k' is a palindrome, where k' is the arithmetic derivative of k (A003415).	[ "1", "34", "44", "49", "121", "476", "524", "533", "1808", "6797", "7326", "10016", "10201", "10403", "10817", "16019", "17831", "26322", "33898", "55198", "57247", "74711", "87241", "131395", "148753", "156029", "239593", "240021", "289831", "295022", "423758", "441691", "595777", "725754", "900009", "2568543", "2910271", "2981619" ]	[ "nonn", "base" ]	18	1	2	[ "A002113", "A003415", "A018252", "A190116", "A359331" ]	null	Marius A. Burtea, Jan 29 2023	2023-02-17T22:07:43	oeisdata/seq/A359/A359331.seq	9f4768d21938685723bcdd3a782d03a8
A359332	Numbers with arithmetic derivative which is a palindromic prime number (A002385).	[ "6", "10", "114", "130", "174", "182", "222", "231", "255", "273", "286", "298", "357", "358", "455", "574", "622", "870", "1015", "1309", "1335", "1677", "1695", "12594", "13630", "13686", "15258", "18534", "18654", "19082", "19114", "19522", "19626", "19922", "19986", "20998", "21558", "22178", "22882", "22930", "23062", "23262", "23709", "24338" ]	[ "nonn", "base" ]	22	1	1	[ "A001097", "A002113", "A002385", "A003415", "A157037", "A359332" ]	null	Marius A. Burtea, Jan 29 2023	2025-03-24T06:02:28	oeisdata/seq/A359/A359332.seq	e3a36211257eaaaa12d7dbeb5b3859c0
A359333	a(1) = 0, and for any n > 1, a(n) is chosen among 0 and 1 so as to minimize the length of the longest sequence of distinct integers in arithmetic progression in the interval 1..n and containing n where the sequence is constant; in case of a tie, maximize the least common difference in those longest arithmetic progressions.	[ "0", "1", "0", "1", "1", "0", "1", "0", "0", "1", "1", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "1", "1", "1", "1", "0", "1", "0", "0", "0", "1", "1", "0", "1", "0", "1", "0", "0", "0", "1", "1", "1", "0", "1", "1", "0", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "0", "0", "1", "1", "1", "0", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "1", "1" ]	[ "nonn" ]	32	1	null	[ "A038219", "A359333" ]	null	Rémy Sigrist, Jan 23 2023	2023-01-26T16:13:57	oeisdata/seq/A359/A359333.seq	dc19ce9dd653c76805ef64fbc71fb148
A359334	Amicable numbers k that can be expressed as a sum k = x+y = A001065(x) + A001065(y) and a sum k = z+t = A001065(z) + A001065(t) where (x, y, z, t) are parts of two amicable pairs and A001065(i) is the sum of the aliquot parts of i.	[ "67212", "1296000", "20528640", "37739520", "75479040", "321408000", "348364800", "556839360", "579156480", "638668800", "661893120", "761177088", "796340160", "883872000", "1181174400", "1282417920", "2068416000", "2395008000", "2682408960", "3155023872", "3599769600", "4049740800", "4606156800", "4716601344" ]	[ "nonn" ]	83	1	1	[ "A001065", "A002025", "A036471", "A063990", "A066539", "A180164", "A259180", "A259933", "A359334" ]	null	Zoltan Galantai, Dec 26 2022	2025-02-16T08:34:04	oeisdata/seq/A359/A359334.seq	7ae0c4beda86c033b82f3f3dbe55ddc6
A359335	Square root of determinant of skew-symmetric 2n X 2n matrix with entries i XOR j for i < j, i=1..2n, j=1..2n.	[ "1", "3", "14", "84", "360", "2160", "10080", "60480", "249984", "1499904", "6999552", "41997312", "179988480", "1079930880", "5039677440", "30238064640", "122903101440", "737418608640", "3441286840320", "20647721041920", "88490233036800", "530941398220800", "2477726525030400", "14866359150182400" ]	[ "nonn" ]	13	0	2	[ "A006519", "A359335" ]	null	Andrey Zabolotskiy, Dec 26 2022	2022-12-28T09:04:29	oeisdata/seq/A359/A359335.seq	3f06fef36966d95649410b6945d9d422
A359336	Irregular triangle read by rows: the n-th row lists the values 0..2^n-1 representing all subsets of a set of n elements. When its elements are linearly ordered, the subsets are sorted first by their size and then lexicographically.	[ "0", "0", "1", "0", "2", "1", "3", "0", "4", "2", "1", "6", "5", "3", "7", "0", "8", "4", "2", "1", "12", "10", "9", "6", "5", "3", "14", "13", "11", "7", "15", "0", "16", "8", "4", "2", "1", "24", "20", "18", "17", "12", "10", "9", "6", "5", "3", "28", "26", "25", "22", "21", "19", "14", "13", "11", "7", "30", "29", "27", "23", "15", "31", "0", "32", "16", "8", "4", "2", "1", "48", "40", "36", "34", "33", "24", "20", "18", "17", "12", "10", "9", "6", "5", "3", "56", "52", "50", "49" ]	[ "nonn", "tabf" ]	35	0	5	[ "A000004", "A000012", "A000225", "A006516", "A294648", "A351939", "A356028", "A359336" ]	null	Valentin Bakoev, Dec 27 2022	2023-03-01T14:51:49	oeisdata/seq/A359/A359336.seq	7b5ccf0d59fd3ddcb08b2551179805f5
A359337	Irregular triangle read by rows: the n-th row gives the exponents of the powers of x corresponding to the maximal coefficient of the product x^2(x^2 + x^3)(x^2 + x^3 + x^5)...(x^2 + x^3 + x^5 + ... + x^prime(n)).	[ "0", "2", "4", "5", "7", "12", "16", "17", "22", "24", "32", "42", "53", "65", "79", "96", "114", "134", "155", "180", "205", "233", "263", "294", "329", "364", "403", "442", "485", "529", "576", "625", "676", "729", "785", "842", "902", "964", "1029", "1097", "1167", "1238", "1313", "1390", "1469", "1552", "1636", "1723", "1813", "1904", "1999", "2096", "2195", "2298" ]	[ "nonn", "tabf" ]	11	0	2	[ "A000040", "A359328", "A359337", "A359338", "A359339" ]	null	Stefano Spezia, Dec 27 2022	2022-12-31T15:18:15	oeisdata/seq/A359/A359337.seq	9e1fbd4a6d0ba2cee8df04c3a00df48d
A359338	Minimal exponent of the powers of x corresponding to the maximal coefficient of the product x^2(x^2 + x^3)(x^2 + x^3 + x^5)...(x^2 + x^3 + x^5 + ... + x^prime(n)).	[ "0", "2", "4", "7", "12", "16", "22", "32", "42", "53", "65", "79", "96", "114", "134", "155", "180", "205", "233", "263", "294", "329", "364", "403", "442", "485", "529", "576", "625", "676", "729", "785", "842", "902", "964", "1029", "1097", "1167", "1238", "1313", "1390", "1469", "1552", "1636", "1723", "1813", "1904", "1999", "2096", "2195", "2298", "2402", "2510" ]	[ "nonn" ]	8	0	2	[ "A000040", "A359328", "A359337", "A359338", "A359339" ]	null	Stefano Spezia, Dec 27 2022	2022-12-31T15:18:36	oeisdata/seq/A359/A359338.seq	671ea0c3d02ce41f4eb1958d481e6a68
A359339	Maximal exponent of the powers of x corresponding to the maximal coefficient of the product x^2(x^2 + x^3)(x^2 + x^3 + x^5)...(x^2 + x^3 + x^5 + ... + x^prime(n)).	[ "0", "2", "5", "7", "12", "17", "24", "32", "42", "53", "65", "79", "96", "114", "134", "155", "180", "205", "233", "263", "294", "329", "364", "403", "442", "485", "529", "576", "625", "676", "729", "785", "842", "902", "964", "1029", "1097", "1167", "1238", "1313", "1390", "1469", "1552", "1636", "1723", "1813", "1904", "1999", "2096", "2195", "2298", "2402", "2510" ]	[ "nonn" ]	8	0	2	[ "A000040", "A359328", "A359337", "A359338", "A359339" ]	null	Stefano Spezia, Dec 27 2022	2022-12-31T15:18:48	oeisdata/seq/A359/A359339.seq	288ea43ac0d3f7cf403d683d2b28c94d
A359340	The primes associated with A339174.	[ "2", "3", "7", "43", "3613", "65250781", "38318979202732621", "8810065002836730577256726488782121", "6131762382982476362788562753503495060507087787406616806191258317645081" ]	[ "nonn" ]	7	1	1	[ "A061092", "A071580", "A339174", "A359340" ]	null	Jeppe Stig Nielsen, Dec 27 2022	2023-01-02T09:01:05	oeisdata/seq/A359/A359340.seq	00b306e212b9a753758ba8535a08565b
A359341	Number of pandigital squares with n digits.	[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "87", "504", "4275", "29433", "179235", "955818", "4653802", "21034628", "89834238", "366490378", "1440743933", "5493453262" ]	[ "nonn", "base" ]	10	1	10	[ "A036745", "A225218", "A359341" ]	null	Martin Renner, Dec 27 2022	2022-12-31T02:12:22	oeisdata/seq/A359/A359341.seq	e8de94746c9ac9d7cd41b7d845ec4067
A359342	Least pandigital square with n digits.	[ "1026753849", "10057482369", "100549873216", "1000574082369", "10000938205476", "100005740082369", "1000000973875264", "10000057400082369", "100000030347218596", "1000000574000082369", "10000000365759287524", "100000005740000082369", "1000000003751486308921", "10000000057400000082369" ]	[ "nonn", "base" ]	12	10	1	[ "A225218", "A359342", "A359343", "A359344" ]	null	Martin Renner, Dec 27 2022	2022-12-31T02:12:45	oeisdata/seq/A359/A359342.seq	74967ac054a33e08d59e2e052c7fc586
A359343	Square roots of least pandigital squares with n digits.	[ "32043", "100287", "317096", "1000287", "3162426", "10000287", "31622792", "100000287", "316227814", "1000000287", "3162277718", "10000000287", "31622776661", "100000000287", "316227766026", "1000000000287", "3162277660177", "10000000000287", "31622776601685", "100000000000287", "316227766016843" ]	[ "nonn", "base" ]	15	10	1	[ "A359342", "A359343", "A359345" ]	null	Martin Renner, Dec 27 2022	2023-01-05T18:59:39	oeisdata/seq/A359/A359343.seq	7cb3138d2c25b5e4bf403c49df7aa6ba
A359344	Largest pandigital square with n digits.	[ "9814072356", "99853472016", "998732401956", "9998490637521", "99992580137641", "999984024130576", "9999925800137641", "99999987340240516", "999999258000137641", "9999999562540763281", "99999992580000137641", "999999991102375684521", "9999999925800000137641", "99999999986188478340025" ]	[ "nonn", "base" ]	8	10	1	[ "A225218", "A359342", "A359344", "A359345" ]	null	Martin Renner, Dec 27 2022	2022-12-31T02:12:55	oeisdata/seq/A359/A359344.seq	d18c786eb4ceb85c3f372a46d4a37ce8
A359345	Roots of largest pandigital squares with n digits.	[ "99066", "315996", "999366", "3162039", "9999629", "31622524", "99999629", "316227746", "999999629", "3162277591", "9999999629", "31622776461", "99999999629", "316227765995", "999999999629", "3162277660155", "9999999999629", "31622776601681", "99999999999629", "316227766016811", "999999999999629" ]	[ "nonn", "base" ]	8	10	1	[ "A359343", "A359344", "A359345" ]	null	Martin Renner, Dec 27 2022	2022-12-31T02:13:03	oeisdata/seq/A359/A359345.seq	d251723303a2a02fd0e9a9cc2df65538
A359346	Reversible pandigital square numbers.	[ "1234549876609", "9066789454321", "123452587690084", "123454387666009", "123454987660900", "123456987654400", "123458987664100", "123478988652100", "125688987432100", "146678985432100", "445678965432100", "480096785254321", "900666783454321", "906678945432100", "10223418547690084" ]	[ "nonn", "base" ]	20	1	1	[ "A036745", "A061457", "A156977", "A225218", "A359346", "A359347" ]	null	Martin Renner, Dec 27 2022	2023-01-23T13:13:09	oeisdata/seq/A359/A359346.seq	813e8aa3648dd295dd1d62869a2b0a74
A359347	Roots of reversible pandigital square numbers.	[ "1111103", "3011111", "11110922", "11111003", "11111030", "11111120", "11111210", "11112110", "11211110", "12111110", "21111110", "21911111", "30011111", "30111110", "101110922", "101111112", "101111121", "101111211", "102111111", "110109212", "110911211", "110921111", "111109220", "111110030", "111110103" ]	[ "nonn", "base" ]	21	1	1	[ "A102859", "A359346", "A359347" ]	null	Martin Renner, Dec 27 2022	2023-01-21T18:12:43	oeisdata/seq/A359/A359347.seq	c6bbdfa8c963dc2a919ccccc4a51812c
A359348	Maximal coefficient of (1 + x) * (1 + x^3) * (1 + x^6) * ... * (1 + x^(n*(n+1)/2)).	[ "1", "1", "1", "1", "2", "2", "3", "4", "5", "7", "12", "18", "27", "44", "73", "122", "210", "362", "620", "1050", "1857", "3290", "5949", "10665", "19086", "34330", "62252", "113643", "209460", "383888", "706457", "1300198", "2407535", "4468367", "8331820", "15525814", "28987902", "54180854", "101560631", "190708871", "358969426" ]	[ "nonn" ]	16	0	5	[ "A000217", "A024940", "A025591", "A158380", "A160235", "A359348" ]	null	Seiichi Manyama, Dec 27 2022	2022-12-29T03:04:34	oeisdata/seq/A359/A359348.seq	b311e14f9a525b2d5bac51ec39036ce8
A359349	The initial bits, written from left to right, in the 2-adic limit of the mod 2^e value of the odd factor of (2^e)!.	[ "1", "1", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "1", "0", "0", "0", "1", "0", "1", "1", "1", "0", "1", "1", "0", "0", "0", "1", "1", "1", "0", "1", "1", "0", "1", "0", "1", "0", "0", "1", "0" ]	[ "nonn", "more" ]	85	1	null	[ "A000722", "A067667", "A359349" ]	null	Donald M Davis, Jul 05 2023	2023-08-20T21:55:12	oeisdata/seq/A359/A359349.seq	42ca54bb12b4350ddc5ed9c67b0b6545
A359350	Irregular triangle T(n,k) (n >= 1, k >= 1) read by rows: row n is constructed by replacing A336811(n,k) with the largest partition into consecutive parts of A000217(A336811(n,k)).	[ "1", "2", "1", "3", "2", "1", "1", "4", "3", "2", "1", "2", "1", "1", "5", "4", "3", "2", "1", "3", "2", "1", "2", "1", "1", "1", "6", "5", "4", "3", "2", "1", "4", "3", "2", "1", "3", "2", "1", "2", "1", "2", "1", "1", "1", "7", "6", "5", "4", "3", "2", "1", "5", "4", "3", "2", "1", "4", "3", "2", "1", "3", "2", "1", "3", "2", "1", "2", "1", "2", "1", "1", "1", "1", "1", "8", "7", "6", "5", "4", "3", "2", "1", "6", "5", "4", "3", "2", "1", "5", "4", "3", "2", "1", "4", "3", "2", "1", "4", "3", "2", "1", "3", "2", "1" ]	[ "nonn", "tabf" ]	39	1	2	[ "A000027", "A000041", "A000070", "A000217", "A014153", "A176206", "A299779", "A336811", "A336812", "A338156", "A359279", "A359280", "A359350" ]	null	Omar E. Pol, Dec 27 2022	2023-09-01T14:16:44	oeisdata/seq/A359/A359350.seq	5638c330dd2bd368fbb096b02c54295e
A359351	a(n) = A001952(A003151(n)).	[ "6", "13", "23", "30", "40", "47", "54", "64", "71", "81", "88", "95", "105", "112", "122", "129", "139", "146", "153", "163", "170", "180", "187", "194", "204", "211", "221", "228", "238", "245", "252", "262", "269", "279", "286", "293", "303", "310", "320", "327", "334", "344", "351", "361", "368", "378", "385", "392", "402", "409", "419", "426", "433", "443" ]	[ "nonn", "easy" ]	4	1	1	[ "A001951", "A001952", "A003151", "A003152", "A184922", "A188376", "A188396", "A341239", "A356136", "A359351" ]	null	Clark Kimberling, Dec 27 2022	2023-01-08T11:45:10	oeisdata/seq/A359/A359351.seq	6e97d9c8187e53ddec423ef7a54be654
A359352	a(n) = A026430(1 + A026430(n)).	[ "3", "6", "9", "10", "14", "15", "16", "19", "23", "24", "26", "28", "30", "33", "36", "37", "41", "42", "44", "46", "48", "51", "54", "55", "57", "60", "63", "65", "68", "69", "70", "73", "77", "78", "80", "82", "84", "87", "90", "91", "93", "96", "99", "100", "103", "105", "107", "109", "111", "114", "117", "118", "121", "123", "125", "128", "130", "132", "134", "136", "138" ]	[ "nonn", "easy" ]	17	1	1	[ "A026530", "A285953", "A285954", "A359277", "A359352", "A359353", "A360139" ]	null	Clark Kimberling, Jan 26 2023	2023-03-01T14:28:32	oeisdata/seq/A359/A359352.seq	14b5b4c2a08bb8f5b64dc49229c825cb
A359353	a(n) = A026430(A285953(n+1)).	[ "1", "5", "8", "12", "18", "21", "27", "31", "35", "39", "45", "50", "52", "59", "61", "66", "72", "75", "81", "86", "88", "95", "98", "102", "108", "113", "116", "120", "126", "129", "135", "139", "143", "147", "153", "158", "160", "167", "170", "174", "180", "185", "188", "192", "198", "201", "207", "212", "214", "221", "224", "228", "234", "237", "243", "248", "250" ]	[ "nonn", "easy" ]	8	1	2	[ "A026530", "A285953", "A285954", "A359277", "A359352", "A359353", "A360134", "A360139" ]	null	Clark Kimberling, Jan 30 2023	2023-01-31T08:33:35	oeisdata/seq/A359/A359353.seq	10038268f5d53daac8362eb92939a288
A359354	Position of the first subsequence of n primes that differs from the first n primes, but where the relative distances among their elements coincide with those of the subsequence of first n primes except for a scale factor.	[ "2", "2", "3", "238", "28495", "576169", "24635028" ]	[ "nonn", "hard", "more" ]	20	1	1	[ "A001223", "A272863", "A274225", "A274263", "A359354" ]	null	Andres Cicuttin, Dec 27 2022	2023-02-10T20:14:46	oeisdata/seq/A359/A359354.seq	892f76a2ce9e68a74974a965bbcaea00
A359355	a(n) = A359107(2n, n) = Sum_{j=0..n} Stirling2(2n, j) = Sum_{j=0..n} A048993(2*n, j).	[ "1", "1", "8", "122", "2795", "86472", "3403127", "164029595", "9433737120", "635182667816", "49344452550230", "4371727233798927", "437489737355466560", "49048715505983309703", "6116937802946210183545", "843220239072837883168510", "127757559136845878072576947", "21166434937698025552654090472" ]	[ "nonn" ]	16	0	3	[ "A048993", "A102661", "A359107", "A359355" ]	null	Peter Luschny, Dec 27 2022	2023-06-13T15:21:48	oeisdata/seq/A359/A359355.seq	490532f94f1ca067544bc1dd64f54096
A359356	a(n-1) + a(n) has only digits also in a(n); lexicographically earliest such sequence of distinct nonnegative integers.	[ "0", "1", "10", "12", "179", "132", "1048", "416", "135", "126", "125", "1025", "136", "15", "146", "82", "31", "302", "53", "128", "183", "130", "14", "157", "1254", "139", "304", "73", "41", "403", "74", "208", "103", "152", "1028", "91", "21", "201", "32", "159", "506", "160", "17", "124", "1036", "104", "51", "504", "95", "16", "204", "62", "129", "203", "52", "503" ]	[ "nonn", "base" ]	23	0	3	[ "A359356", "A359517" ]	null	M. F. Hasler and Eric Angelini, Dec 27 2022	2023-01-06T14:12:00	oeisdata/seq/A359/A359356.seq	b0134e571a053becf268644298ef3656
A359357	Number of different ratios between consecutive prime gaps among the first n primes.	[ "1", "2", "2", "3", "3", "3", "3", "4", "5", "6", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "8", "8", "8", "8", "8", "8", "9", "10", "10", "10", "11", "12", "12", "12", "12", "12", "12", "12", "12", "12", "12", "12", "13", "13", "13", "13", "13", "13", "13", "13", "14", "14", "14", "14", "14", "14", "14", "14", "15", "15", "15", "15", "15", "16", "17", "17", "17", "17", "17", "18", "18", "18", "18", "18", "18", "18", "19", "19", "19", "19" ]	[ "nonn" ]	26	3	2	[ "A001223", "A272863", "A274225", "A274263", "A275785", "A359357" ]	null	Andres Cicuttin, Dec 27 2022	2023-02-07T12:43:07	oeisdata/seq/A359/A359357.seq	71c34b0b9bacd011d7fbdfff85ecd8ba
A359358	Let y be the integer partition with Heinz number n. Then a(n) is the size of the Young diagram of y after removing a rectangle of the same length as y and width equal to the smallest part of y.	[ "0", "0", "0", "0", "0", "1", "0", "0", "0", "2", "0", "1", "0", "3", "1", "0", "0", "2", "0", "2", "2", "4", "0", "1", "0", "5", "0", "3", "0", "3", "0", "0", "3", "6", "1", "2", "0", "7", "4", "2", "0", "4", "0", "4", "1", "8", "0", "1", "0", "4", "5", "5", "0", "3", "2", "3", "6", "9", "0", "3", "0", "10", "2", "0", "3", "5", "0", "6", "7", "5", "0", "2", "0", "11", "2", "7", "1", "6", "0", "2", "0", "12", "0", "4", "4", "13" ]	[ "nonn" ]	8	1	10	[ "A001222", "A055396", "A056239", "A061395", "A112798", "A124010", "A241916", "A243055", "A243503", "A246277", "A268192", "A316413", "A325351", "A325352", "A326836", "A326837", "A326844", "A326846", "A355534", "A356958", "A358172", "A358195", "A359358", "A359360" ]	null	Gus Wiseman, Dec 27 2022	2022-12-28T09:05:02	oeisdata/seq/A359/A359358.seq	632f60dc1e4a6a85695d044a6d53bb94
A359359	Sum of positions of zeros in the binary expansion of n, where positions are read starting with 1 from the left (big-endian).	[ "1", "0", "2", "0", "5", "2", "3", "0", "9", "5", "6", "2", "7", "3", "4", "0", "14", "9", "10", "5", "11", "6", "7", "2", "12", "7", "8", "3", "9", "4", "5", "0", "20", "14", "15", "9", "16", "10", "11", "5", "17", "11", "12", "6", "13", "7", "8", "2", "18", "12", "13", "7", "14", "8", "9", "3", "15", "9", "10", "4", "11", "5", "6", "0", "27", "20", "21", "14", "22", "15", "16", "9", "23", "16", "17", "10" ]	[ "nonn", "base" ]	14	0	3	[ "A000120", "A003714", "A023416", "A029931", "A030190", "A039004", "A048793", "A059015", "A065359", "A069010", "A070939", "A073642", "A083652", "A230877", "A328594", "A328595", "A345927", "A359359", "A359400", "A359402", "A359495" ]	null	Gus Wiseman, Jan 03 2023	2023-01-05T18:30:39	oeisdata/seq/A359/A359359.seq	f6eb432f618a3210d4c59078f34b0b34
A359360	Length times minimum part of the integer partition with Heinz number n. Least prime index of n times number of prime indices of n.	[ "0", "1", "2", "2", "3", "2", "4", "3", "4", "2", "5", "3", "6", "2", "4", "4", "7", "3", "8", "3", "4", "2", "9", "4", "6", "2", "6", "3", "10", "3", "11", "5", "4", "2", "6", "4", "12", "2", "4", "4", "13", "3", "14", "3", "6", "2", "15", "5", "8", "3", "4", "3", "16", "4", "6", "4", "4", "2", "17", "4", "18", "2", "6", "6", "6", "3", "19", "3", "4", "3", "20", "5", "21", "2", "6", "3", "8", "3", "22", "5", "8", "2" ]	[ "nonn" ]	8	1	3	[ "A001222", "A006141", "A055396", "A056239", "A061395", "A112798", "A124010", "A241916", "A243055", "A246277", "A268192", "A316413", "A325352", "A326836", "A326837", "A326844", "A326846", "A355534", "A356958", "A358172", "A358195", "A359358", "A359360" ]	null	Gus Wiseman, Dec 28 2022	2022-12-28T15:42:39	oeisdata/seq/A359/A359360.seq	be59f693024248aa52e8376d2c37b9e1
A359361	Irregular triangle read by rows whose n-th row lists the partial sums of the integer partition with Heinz number n.	[ "1", "2", "1", "2", "3", "2", "3", "4", "1", "2", "3", "2", "4", "3", "4", "5", "2", "3", "4", "6", "4", "5", "3", "5", "1", "2", "3", "4", "7", "2", "4", "5", "8", "3", "4", "5", "4", "6", "5", "6", "9", "2", "3", "4", "5", "3", "6", "6", "7", "2", "4", "6", "4", "5", "6", "10", "3", "5", "6", "11", "1", "2", "3", "4", "5", "5", "7", "7", "8", "4", "7", "2", "4", "5", "6", "12", "8", "9", "6", "8", "3", "4", "5", "6", "13" ]	[ "nonn", "tabf" ]	13	2	2	[ "A000009", "A000041", "A000720", "A001221", "A001222", "A003963", "A048793", "A055396", "A056239", "A061395", "A112798", "A261079", "A296150", "A304818", "A318283", "A325362", "A355536", "A358134", "A358136", "A358137", "A359361", "A359397" ]	null	Gus Wiseman, Dec 30 2022	2023-03-31T05:51:08	oeisdata/seq/A359/A359361.seq	60583a0ed5bbe5445109d7ea3920702c
A359362	a(n) = (A001222(n) + 1) * A056239(n), where A001222 counts prime indices and A056239 adds them up.	[ "0", "2", "4", "6", "6", "9", "8", "12", "12", "12", "10", "16", "12", "15", "15", "20", "14", "20", "16", "20", "18", "18", "18", "25", "18", "21", "24", "24", "20", "24", "22", "30", "21", "24", "21", "30", "24", "27", "24", "30", "26", "28", "28", "28", "28", "30", "30", "36", "24", "28", "27", "32", "32", "35", "24", "35", "30", "33", "34", "35", "36", "36", "32", "42", "27", "32", "38" ]	[ "nonn" ]	11	1	2	[ "A001222", "A055396", "A056239", "A061395", "A112798", "A261079", "A316413", "A326836", "A326837", "A326844", "A326846", "A359358", "A359362" ]	null	Gus Wiseman, Dec 31 2022	2023-01-02T02:17:16	oeisdata/seq/A359/A359362.seq	860f93b3eca5f05fd8ae5922deaac126
A359363	Triangle read by rows. The coefficients of the Baxter polynomials p(0, x) = 1 and p(n, x) = x*hypergeom([-1 - n, -n, 1 - n], [2, 3], -x) for n >= 1.	[ "1", "0", "1", "0", "1", "1", "0", "1", "4", "1", "0", "1", "10", "10", "1", "0", "1", "20", "50", "20", "1", "0", "1", "35", "175", "175", "35", "1", "0", "1", "56", "490", "980", "490", "56", "1", "0", "1", "84", "1176", "4116", "4116", "1176", "84", "1", "0", "1", "120", "2520", "14112", "24696", "14112", "2520", "120", "1", "0", "1", "165", "4950", "41580", "116424", "116424", "41580", "4950", "165", "1" ]	[ "nonn", "tabl" ]	36	0	9	[ "A000178", "A000292", "A001181", "A006542", "A046996", "A047819", "A056939", "A056940", "A056941", "A090181", "A097805", "A142465", "A217800", "A342889", "A359363" ]	null	Peter Luschny, Dec 28 2022	2024-01-04T08:57:55	oeisdata/seq/A359/A359363.seq	bd4880281aa41a6b7ee927287280ca75
A359364	Triangle read by rows. The Motzkin triangle, the coefficients of the Motzkin polynomials. M(n, k) = binomial(n, k) * CatalanNumber(k/2) if k is even, otherwise 0.	[ "1", "1", "0", "1", "0", "1", "1", "0", "3", "0", "1", "0", "6", "0", "2", "1", "0", "10", "0", "10", "0", "1", "0", "15", "0", "30", "0", "5", "1", "0", "21", "0", "70", "0", "35", "0", "1", "0", "28", "0", "140", "0", "140", "0", "14", "1", "0", "36", "0", "252", "0", "420", "0", "126", "0", "1", "0", "45", "0", "420", "0", "1050", "0", "630", "0", "42", "1", "0", "55", "0", "660", "0", "2310", "0", "2310", "0", "462", "0" ]	[ "nonn", "tabl" ]	37	0	9	[ "A000012", "A000108", "A000217", "A000910", "A001006", "A002457", "A002522", "A014531", "A023426", "A025179", "A025235", "A026300", "A034827", "A055151", "A056107", "A080159", "A088625", "A088626", "A091147", "A097610", "A107131", "A107587", "A126120", "A138364", "A189912", "A213380", "A343386", "A343773", "A359364", "A359647", "A359649" ]	null	Peter Luschny, Jan 09 2023	2023-01-10T13:05:07	oeisdata/seq/A359/A359364.seq	1ddf52afefcbcbfc75288d8532512098
A359365	a(n) = lcm([ n!*binomial(n-1, m-1) / m! for m = 1..n ]) with a(0) = 1.	[ "1", "1", "2", "6", "72", "240", "3600", "75600", "1411200", "10160640", "457228800", "4191264000", "184415616000", "2054916864000", "12466495641600", "1308982042368000", "314155690168320000", "14241724620963840000", "2178983867007467520000", "37260624125827694592000", "337119932567012474880000" ]	[ "nonn" ]	14	0	3	[ "A103505", "A271703", "A359365" ]	null	Peter Luschny, Dec 30 2022	2022-12-30T11:23:53	oeisdata/seq/A359/A359365.seq	c5c6448bc3bd82c710160b6f865c49b1
A359366	a(n) = (1/8)(((3n + 1) + (n - 1)(-1)^n)(n + 1)).	[ "0", "1", "3", "4", "10", "9", "21", "16", "36", "25", "55", "36", "78", "49", "105", "64", "136", "81", "171", "100", "210", "121", "253", "144", "300", "169", "351", "196", "406", "225", "465", "256", "528", "289", "595", "324", "666", "361", "741", "400", "820", "441", "903", "484", "990", "529", "1081", "576", "1176", "625", "1275", "676", "1378", "729", "1485" ]	[ "nonn" ]	13	0	3	[ "A000290", "A014105", "A056136", "A106465", "A359366" ]	null	Peter Luschny, Dec 30 2022	2022-12-30T15:44:21	oeisdata/seq/A359/A359366.seq	14393a03ff747864cc750fb8a744af02
A359367	a(n) = number of regular polytopes of rank m-n with group S_m, up to isomorphism and duality (this is independent of m if m >= 2n+3).	[ "1", "1", "7", "9", "35", "48", "135" ]	[ "nonn", "hard", "more" ]	18	1	3	null	null	Peter J. Cameron, Dec 28 2022	2023-01-28T11:58:14	oeisdata/seq/A359/A359367.seq	8a4a2a19b693407ebb2cc2081217e343
A359368	Sequence begins 1, 1, 1; for even n > 3, a(n) = a(n/2 - 1) + a(n/2 + 1); for odd n > 3, a(n) = -a((n-1)/2).	[ "1", "1", "1", "2", "-1", "3", "-1", "0", "-2", "5", "1", "-2", "-3", "3", "1", "-3", "0", "5", "2", "-1", "-5", "3", "-1", "-2", "2", "1", "3", "-2", "-3", "0", "-1", "1", "3", "2", "0", "2", "-5", "4", "-2", "-3", "1", "2", "5", "-6", "-3", "1", "1", "1", "2", "-1", "-2", "5", "-1", "-1", "-3", "0", "2", "-2", "3", "-4", "0", "1", "1", "2", "-1", "3", "-3", "3", "-2", "4", "0", "-5", "-2", "6", "5", "-7", "-4", "1", "2", "-1" ]	[ "sign", "easy" ]	27	1	4	null	null	Eden Lippmann, Dec 28 2022	2024-12-19T11:46:19	oeisdata/seq/A359/A359368.seq	1566a2a21899b8c6f0d68b9d5ec642e9
A359369	a(1) = 1. Thereafter a(n) = Sum_{j=1..n} {b(a(j)), where b(a(j)) = b(a(n))}, and b is A000120.	[ "1", "1", "2", "3", "2", "4", "5", "4", "6", "6", "8", "7", "3", "10", "12", "14", "6", "16", "8", "9", "18", "20", "22", "9", "24", "26", "12", "28", "15", "4", "10", "30", "8", "11", "18", "32", "12", "34", "36", "38", "21", "24", "40", "42", "27", "12", "44", "30", "16", "13", "33", "46", "20", "48", "50", "36", "52", "39", "24", "54", "28", "42", "45", "32", "14", "48", "56", "51", "36", "58", "40", "60", "44", "54", "48", "62", "5" ]	[ "nonn" ]	21	1	3	[ "A000005", "A000120", "A000225", "A359369" ]	null	David James Sycamore, Dec 28 2022	2023-01-16T09:04:44	oeisdata/seq/A359/A359369.seq	a8f0487beac450340c2fd2b574ae1dba
A359370	a(n) = 1 if n is not a multiple of 4 and has an even number of prime factors (with multiplicity), otherwise a(n) = 0.	[ "1", "0", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1", "1", "0", "1" ]	[ "nonn" ]	11	1	null	[ "A001222", "A166486", "A358839", "A359170", "A359370", "A359371", "A359372" ]	null	Antti Karttunen, Dec 28 2022	2022-12-30T16:14:47	oeisdata/seq/A359/A359370.seq	46fce55787dcc5a4ed16a8f9104ea0bb
A359371	Nonmultiples of 4 that have an even number of prime factors (with multiplicity).	[ "1", "6", "9", "10", "14", "15", "21", "22", "25", "26", "33", "34", "35", "38", "39", "46", "49", "51", "54", "55", "57", "58", "62", "65", "69", "74", "77", "81", "82", "85", "86", "87", "90", "91", "93", "94", "95", "106", "111", "115", "118", "119", "121", "122", "123", "126", "129", "133", "134", "135", "141", "142", "143", "145", "146", "150", "155", "158", "159", "161", "166", "169", "177", "178", "183", "185", "187", "189" ]	[ "nonn" ]	14	1	2	[ "A001222", "A008836", "A010873", "A028260", "A042968", "A046337", "A166486", "A358839", "A359370", "A359371", "A359373" ]	null	Antti Karttunen, Dec 28 2022	2022-12-29T09:09:21	oeisdata/seq/A359/A359371.seq	213e4f0807774c6f86b81f5434053cce
A359372	a(n) = 1 if n is not a multiple of 4 and has an odd number of prime factors (with multiplicity), otherwise a(n) = 0.	[ "0", "1", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "1", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "1", "0", "1", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "1", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1" ]	[ "nonn" ]	8	1	null	[ "A001222", "A166486", "A358839", "A359372", "A359373" ]	null	Antti Karttunen, Dec 28 2022	2022-12-29T15:11:46	oeisdata/seq/A359/A359372.seq	f983587a715b8f72e36e76f16d7155b1
A359373	Nonmultiples of 4 that have an odd number of prime factors (with multiplicity).	[ "2", "3", "5", "7", "11", "13", "17", "18", "19", "23", "27", "29", "30", "31", "37", "41", "42", "43", "45", "47", "50", "53", "59", "61", "63", "66", "67", "70", "71", "73", "75", "78", "79", "83", "89", "97", "98", "99", "101", "102", "103", "105", "107", "109", "110", "113", "114", "117", "125", "127", "130", "131", "137", "138", "139", "147", "149", "151", "153", "154", "157", "162", "163", "165", "167", "170", "171", "173", "174" ]	[ "nonn" ]	11	1	1	[ "A001222", "A008836", "A010873", "A026424", "A042968", "A067019", "A166486", "A358839", "A359371", "A359372", "A359373" ]	null	Antti Karttunen, Dec 28 2022	2022-12-29T09:16:26	oeisdata/seq/A359/A359373.seq	cdc13f3c07df31efc53183d77cceceb9
A359374	Parity of A252463(n).	[ "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1" ]	[ "nonn" ]	14	1	null	[ "A000035", "A064989", "A252463", "A359374", "A359375", "A359376", "A359379" ]	null	Antti Karttunen, Dec 31 2022	2023-01-24T02:50:57	oeisdata/seq/A359/A359374.seq	dc217d5456d848dd7c0cedf8ae73e53a
A359375	Numbers that are neither multiples of 4 nor of the form 6u+3.	[ "1", "2", "5", "6", "7", "10", "11", "13", "14", "17", "18", "19", "22", "23", "25", "26", "29", "30", "31", "34", "35", "37", "38", "41", "42", "43", "46", "47", "49", "50", "53", "54", "55", "58", "59", "61", "62", "65", "66", "67", "70", "71", "73", "74", "77", "78", "79", "82", "83", "85", "86", "89", "90", "91", "94", "95", "97", "98", "101", "102", "103", "106", "107", "109", "110", "113", "114", "115", "118", "119", "121", "122", "125" ]	[ "nonn", "easy" ]	16	1	2	[ "A000035", "A064989", "A252463", "A359374", "A359375", "A359376", "A359380" ]	null	Antti Karttunen, Dec 31 2022	2023-01-24T02:50:23	oeisdata/seq/A359/A359375.seq	f8b7db5110ea84967828776053be51b6
A359376	Numbers that are either odd multiples of 3 or multiples of 4. Numbers k such that A252463(k) is even.	[ "0", "3", "4", "8", "9", "12", "15", "16", "20", "21", "24", "27", "28", "32", "33", "36", "39", "40", "44", "45", "48", "51", "52", "56", "57", "60", "63", "64", "68", "69", "72", "75", "76", "80", "81", "84", "87", "88", "92", "93", "96", "99", "100", "104", "105", "108", "111", "112", "116", "117", "120", "123", "124", "128", "129", "132", "135", "136", "140", "141", "144", "147", "148", "152", "153", "156", "159", "160", "164", "165" ]	[ "nonn", "easy" ]	16	1	2	[ "A000035", "A008586", "A016945", "A064989", "A252463", "A359374", "A359375", "A359376", "A359379" ]	null	Antti Karttunen, Dec 31 2022	2023-01-24T02:50:30	oeisdata/seq/A359/A359376.seq	486dad525bce1b237083a9bd64c82792
A359377	a(n) = 1 if 3*n is squarefree, otherwise 0.	[ "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0" ]	[ "nonn", "mult" ]	28	1	null	[ "A000035", "A008966", "A011655", "A055615", "A088245", "A156277", "A261034", "A323239", "A349125", "A353627", "A359377", "A359378", "A365428" ]	null	Antti Karttunen, Dec 29 2022	2023-09-16T16:03:07	oeisdata/seq/A359/A359377.seq	9912afcb24ef3885baca500555ee2bca
A359378	Dirichlet inverse of A359377, where A359377(n) = 1 if 3*n is squarefree, otherwise 0.	[ "1", "-1", "0", "1", "-1", "0", "-1", "-1", "0", "1", "-1", "0", "-1", "1", "0", "1", "-1", "0", "-1", "-1", "0", "1", "-1", "0", "1", "1", "0", "-1", "-1", "0", "-1", "-1", "0", "1", "1", "0", "-1", "1", "0", "1", "-1", "0", "-1", "-1", "0", "1", "-1", "0", "1", "-1", "0", "-1", "-1", "0", "1", "1", "0", "1", "-1", "0", "-1", "1", "0", "1", "1", "0", "-1", "-1", "0", "-1", "-1", "0", "-1", "1", "0", "-1", "1", "0", "-1", "-1", "0", "1", "-1", "0", "1", "1", "0", "1", "-1", "0", "1", "-1", "0", "1", "1", "0", "-1", "-1", "0", "1", "-1", "0", "-1", "1", "0", "1" ]	[ "sign", "mult" ]	20	1	null	[ "A001651", "A008585", "A008836", "A011655", "A156277", "A166698", "A358839", "A359170", "A359171", "A359172", "A359377", "A359378", "A359381" ]	null	Antti Karttunen, Dec 29 2022	2023-01-03T09:21:28	oeisdata/seq/A359/A359378.seq	6c2fa52be6585fee146bd12e6fcc3988
A359379	a(n) = 1 if n is either a multiple of 4, or an odd multiple of 3, otherwise 0.	[ "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1" ]	[ "nonn", "easy" ]	17	0	null	[ "A079979", "A121262", "A359374", "A359375", "A359376", "A359379" ]	null	Antti Karttunen, Dec 31 2022	2023-01-24T02:50:36	oeisdata/seq/A359/A359379.seq	224b39d39c38a433b3c0ac532ee3032c
A359380	Numbers that are neither multiples of 3 nor of the form 4u+2.	[ "1", "4", "5", "7", "8", "11", "13", "16", "17", "19", "20", "23", "25", "28", "29", "31", "32", "35", "37", "40", "41", "43", "44", "47", "49", "52", "53", "55", "56", "59", "61", "64", "65", "67", "68", "71", "73", "76", "77", "79", "80", "83", "85", "88", "89", "91", "92", "95", "97", "100", "101", "103", "104", "107", "109", "112", "113", "115", "116", "119", "121", "124", "125", "127", "128", "131", "133", "136", "137", "139", "140" ]	[ "nonn", "easy" ]	18	1	2	[ "A010892", "A057079", "A187074", "A359375", "A359380" ]	null	Antti Karttunen, Dec 31 2022	2024-07-10T16:48:13	oeisdata/seq/A359/A359380.seq	d50b203641cf643e3d248bad1b66dcb8
A359381	Nonmultiples of 3 that have an odd number of prime factors (with multiplicity).	[ "2", "5", "7", "8", "11", "13", "17", "19", "20", "23", "28", "29", "31", "32", "37", "41", "43", "44", "47", "50", "52", "53", "59", "61", "67", "68", "70", "71", "73", "76", "79", "80", "83", "89", "92", "97", "98", "101", "103", "107", "109", "110", "112", "113", "116", "124", "125", "127", "128", "130", "131", "137", "139", "148", "149", "151", "154", "157", "163", "164", "167", "170", "172", "173", "175", "176", "179", "181", "182" ]	[ "nonn" ]	12	1	1	[ "A001651", "A008836", "A010872", "A026424", "A359171", "A359172", "A359373", "A359378", "A359381" ]	null	Antti Karttunen, Dec 30 2022	2023-02-23T09:43:38	oeisdata/seq/A359/A359381.seq	91d9b5f2a2b67d4bf42d0e54387e51c1
A359382	a(n) = number of k < t such that rad(k) = rad(t) and k does not divide t, where t = A360768(n) and rad(k) = A007947(k).	[ "1", "1", "1", "2", "2", "4", "2", "1", "1", "1", "4", "2", "2", "4", "1", "1", "1", "1", "3", "1", "3", "2", "8", "1", "2", "1", "7", "2", "1", "2", "5", "2", "1", "1", "3", "3", "1", "6", "1", "1", "5", "5", "4", "5", "1", "1", "4", "8", "3", "3", "1", "2", "1", "4", "2", "3", "5", "10", "2", "1", "3", "3", "1", "1", "1", "6", "1", "3", "7", "1", "1", "7", "3", "14", "3", "6", "3", "2", "1", "1", "2", "7", "2", "1", "1", "2", "2", "8", "4", "6", "4", "8", "1", "1", "2", "1", "6", "9", "2", "1" ]	[ "nonn" ]	16	1	4	[ "A007947", "A010846", "A013929", "A020639", "A024619", "A027750", "A126706", "A162306", "A243822", "A272618", "A355432", "A359382", "A359929", "A360589", "A360768" ]	null	Michael De Vlieger, Mar 29 2023	2023-04-01T13:29:08	oeisdata/seq/A359/A359382.seq	deda77c221d4456470a1fe4f78dbaf89
A359383	Allan W. Johnson, Jr.'s 4 X 4 magic square of squares.	[ "900", "60516", "29584", "2025", "8649", "13456", "4356", "66564", "15876", "19044", "56169", "1936", "67600", "9", "2916", "22500" ]	[ "nonn", "fini", "full" ]	19	1	1	[ "A271580", "A359383" ]	null	Robert C. Lyons, Dec 28 2022	2024-02-12T08:39:17	oeisdata/seq/A359/A359383.seq	5714ed75b9e5ad0f059e1171cb9e3e38
A359384	a(1) = 0. If a(n-1) is a first occurrence, a(n) = A000120(a(n-1)). Otherwise, if a(n-1) is a repeat of a prior terms, a(n) = number of indices j < n such that a(j) = a(n-1).	[ "0", "0", "2", "1", "1", "2", "2", "3", "2", "4", "1", "3", "2", "5", "2", "6", "2", "7", "3", "3", "4", "2", "8", "1", "4", "3", "5", "2", "9", "2", "10", "2", "11", "3", "6", "2", "12", "2", "13", "3", "7", "2", "14", "3", "8", "2", "15", "4", "4", "5", "3", "9", "2", "16", "1", "5", "4", "6", "3", "10", "2", "17", "2", "18", "2", "19", "3", "11", "2", "20", "2", "21", "3", "12", "2", "22", "3", "13", "2", "23", "4" ]	[ "nonn" ]	15	1	3	[ "A000120", "A359384" ]	null	David James Sycamore, Dec 27 2022	2023-01-14T08:44:57	oeisdata/seq/A359/A359384.seq	62d40720152f4fbf93c206fda6d6c9d1
A359385	The lexicographically earliest "Increasing Term Fractal Jump Sequence" that does not use the digit 0 in any terms.	[ "1", "2", "21", "22", "23", "112", "122", "132", "133", "134", "141", "221", "311", "2112", "2113", "3111", "21111", "31113", "31114", "31124", "31131", "34111", "41121", "42111", "43111", "111121", "111122", "112111", "112311", "131111", "211112", "211113", "1111311", "1111312", "3111311", "3111312", "4111131", "4111132", "4141111" ]	[ "nonn", "base" ]	15	1	2	[ "A105395", "A105396", "A105397", "A105398", "A105647", "A359385" ]	null	Tyler Busby, Dec 29 2022	2022-12-31T10:49:54	oeisdata/seq/A359/A359385.seq	917f6d3761e862f86f4399b41c0b14f0
A359386	a(n) is the least positive integer that can be expressed as the sum of one or more consecutive prime powers (not including 1) in exactly n ways.	[ "1", "2", "5", "9", "29", "1027", "6659", "13560", "2149512", "38239583" ]	[ "nonn", "more" ]	24	0	2	[ "A054859", "A246655", "A359386" ]	null	Ilya Gutkovskiy, Mar 13 2023	2023-03-14T09:27:44	oeisdata/seq/A359/A359386.seq	f1dc8bf881983e34513bc46efc17ce5b
A359387	Primes p such that the smallest prime factor of (2^(p-1)-1)/(3*p) is greater than p.	[ "11", "23", "47", "59", "83", "107", "167", "179", "227", "263", "347", "359", "383", "443", "467", "479", "503", "563", "587", "647", "719", "839", "863", "887", "983", "1019", "1187", "1283", "1307", "1319", "1367", "1439", "1487", "1523", "1619", "1823", "1847", "1907", "2027", "2039", "2063", "2099", "2207", "2243", "2447", "2459", "2579", "2687", "2699" ]	[ "nonn" ]	45	1	1	[ "A068231", "A096060", "A358527", "A359387" ]	null	Alain Rocchelli, Dec 29 2022	2023-01-21T02:40:31	oeisdata/seq/A359/A359387.seq	dc90ef7ed138a2b53b95cacd8140863a
A359388	a(n) is the number of compositions of n into prime parts, with the 1st part equal to 2, the 2nd part less than or equal to 3, ..., and the k-th part less than or equal to prime(k), and so on.	[ "1", "0", "1", "0", "1", "1", "1", "2", "2", "4", "5", "7", "11", "15", "24", "33", "50", "73", "105", "159", "229", "342", "501", "738", "1094", "1604", "2378", "3499", "5166", "7627", "11243", "16610", "24494", "36165", "53376", "78775", "116301", "171642", "253398", "374034", "552139", "815079", "1203166", "1776174", "2621938", "3870572", "5713798", "8434744" ]	[ "nonn" ]	33	0	8	[ "A000040", "A004526", "A023360", "A078974", "A326178", "A359328", "A359388" ]	null	Stefano Spezia, Dec 29 2022	2023-01-01T14:49:39	oeisdata/seq/A359/A359388.seq	d1b026fbfbb2209101617d873537ea5f
A359389	Maximal coefficient of Product_{k=1..n} (1 + 2*x^k).	[ "1", "2", "4", "8", "16", "32", "72", "176", "384", "976", "2496", "6560", "17152", "45952", "123520", "336640", "920832", "2526976", "6979584", "19379712", "53966336", "150892544", "423132160", "1190260736", "3356964864", "9491228672", "26889519104", "76351971328", "217229369344", "619159953408", "1767696515072", "5054679908352" ]	[ "nonn" ]	11	0	2	[ "A025591", "A032302", "A160235", "A359389" ]	null	Vaclav Kotesovec, Dec 29 2022	2022-12-30T01:14:35	oeisdata/seq/A359/A359389.seq	c1d79d9e928bf2853f20d9a4e18521f6
A359390	Sequence lists the numbers k such that bottom entry is an integer in the ratio d(i+1)/d(i) triangle of the elements in the divisors of n, where d(1) < d(2) < ... < d(q) denote the divisors of k.	[ "1", "2", "3", "4", "5", "7", "8", "9", "11", "13", "16", "17", "19", "23", "25", "27", "29", "31", "32", "36", "37", "41", "43", "47", "49", "53", "59", "61", "64", "67", "71", "73", "79", "81", "83", "89", "97", "100", "101", "103", "107", "109", "113", "121", "125", "127", "128", "131", "137", "139", "144", "149", "151", "157", "163", "167", "169", "173", "179", "181", "191", "193" ]	[ "nonn" ]	54	1	2	[ "A000290", "A000961", "A323306", "A359390" ]	null	Michel Lagneau, Jan 03 2023	2023-01-28T12:17:00	oeisdata/seq/A359/A359390.seq	97048064cd39c25337292f0fecb178fb
A359391	a(n) is the smallest number which can be represented as the sum of n distinct positive Fibonacci numbers (1 is allowed twice as a part) in exactly n ways, or -1 if no such number exists.	[ "1", "2", "3", "16", "27", "71", "116", "278", "451", "818", "1305", "2169", "3925", "8119", "13117", "23252", "37858", "62999", "101939", "178088", "298357", "484576", "813710", "1613509", "2610739", "4224275", "6845969", "11280196", "19772533", "32524576", "53157802", "85936132" ]	[ "nonn", "more" ]	25	0	2	[ "A000045", "A000121", "A013583", "A083853", "A359391" ]	null	Ilya Gutkovskiy, Dec 29 2022	2023-01-07T11:05:50	oeisdata/seq/A359/A359391.seq	00ffa82bbeccf9c41c872be687ffb581
A359392	Number of trees on n unlabeled nodes with all nodes of degree <= 7.	[ "1", "1", "1", "1", "2", "3", "6", "11", "23", "46", "104", "230", "539", "1270", "3081", "7536", "18785", "47207", "120074", "307739", "795426", "2069248", "5418014", "14263084", "37742929", "100331646", "267854040", "717863832", "1930888297", "5210968114", "14106844554" ]	[ "nonn" ]	18	0	5	[ "A036722", "A144528", "A359392" ]	null	Robert A. Russell, Dec 29 2022	2023-02-12T10:23:31	oeisdata/seq/A359/A359392.seq	ff8659b6f7ca11e8f0d39d3f84e9661a
A359393	a(n) is the number of times A025581(n-1) (runs of k..0) occur among terms a(1..n-1).	[ "0", "0", "2", "1", "1", "2", "0", "2", "2", "3", "0", "1", "4", "3", "4", "0", "2", "2", "6", "3", "5", "1", "1", "2", "3", "7", "5", "5", "1", "1", "3", "2", "5", "8", "7", "5", "1", "2", "1", "5", "2", "5", "10", "9", "5", "1", "1", "2", "1", "8", "2", "5", "12", "12", "5", "1", "1", "2", "2", "1", "10", "2", "5", "15", "15", "5", "0", "2", "1", "2", "2", "1", "12", "2", "5", "19", "17", "6", "3", "0", "2", "1", "2", "2", "2", "13" ]	[ "nonn", "easy" ]	21	1	3	[ "A025581", "A032531", "A342585", "A359393" ]	null	Tamas Sandor Nagy, Dec 29 2022	2024-12-19T11:46:19	oeisdata/seq/A359/A359393.seq	b0acfd9be1b9574ee4350916dee2576b
A359394	Numbers k such that the average of the squares of k consecutive primes starting with 7 is a prime.	[ "3", "4", "7", "9", "24", "28", "3872", "15172", "23440", "1390100", "7031920" ]	[ "nonn", "more" ]	9	1	1	[ "A359322", "A359394" ]	null	Robert Israel, Dec 29 2022	2022-12-31T15:23:03	oeisdata/seq/A359/A359394.seq	cdac477fa5696f74604bb3959afdff4d
A359395	Least odd prime p in position n in the prime factorization of M(p) = 2^(p - 1) - 1.	[ "3", "5", "17", "13", "71", "37", "157", "61", "211", "313", "1289", "241", "337", "181", "577", "601", "541", "1381", "421", "1201", "1009", "1621", "1873", "3433", "4561", "1801", "3301", "2161", "3061", "5281", "3361", "2521", "7393", "6481", "4201", "4621", "8737", "9181", "6301", "19501", "7561", "16633", "12241", "26881", "15601", "9241", "21001", "14281", "12601", "53551" ]	[ "nonn" ]	34	1	1	[ "A098102", "A358527", "A359395" ]	null	Jean-Marc Rebert, Dec 31 2022	2023-01-14T12:41:17	oeisdata/seq/A359/A359395.seq	31c12d3794114a381f975a2153d72103
A359396	a(n) is the least k such that k^j+2 is prime for j = 1 to n but not n+1.	[ "5", "9", "105", "3", "909", "4995825", "28212939" ]	[ "nonn", "more" ]	15	1	1	[ "A087576", "A359396" ]	null	Robert Israel, Dec 29 2022	2023-01-11T08:48:08	oeisdata/seq/A359/A359396.seq	b621793e032a98e9a532f7390bfb2986
A359397	Squarefree numbers with weakly decreasing first differences of 0-prepended prime indices.	[ "1", "2", "3", "5", "6", "7", "11", "13", "15", "17", "19", "21", "23", "29", "30", "31", "35", "37", "41", "43", "47", "53", "55", "59", "61", "65", "67", "71", "73", "77", "79", "83", "89", "91", "97", "101", "103", "105", "107", "109", "113", "119", "127", "131", "133", "137", "139", "143", "149", "151", "157", "163", "167", "173", "179", "181", "187", "191", "193", "197" ]	[ "nonn" ]	7	1	2	[ "A000009", "A000720", "A001221", "A001222", "A005117", "A056239", "A112798", "A253566", "A261079", "A287352", "A296150", "A304818", "A318283", "A325362", "A355536", "A358136", "A358137", "A358169", "A359361", "A359397" ]	null	Gus Wiseman, Dec 31 2022	2023-01-01T19:30:36	oeisdata/seq/A359/A359397.seq	01f8cdbeea2c7990a95ac2fa4f5eefd7
A359398	Number of unlabeled trees covering 2n nodes, half of which are leaves.	[ "0", "1", "2", "8", "32", "158", "833", "4755", "28389", "176542", "1131055", "7432876", "49873477", "340658595", "2362652648", "16605707901", "118082160358", "848399575321", "6152038125538", "44981009272740", "331344933928536", "2457372361637286", "18337490246234464", "137612955519565773", "1038076541372187991" ]	[ "nonn" ]	11	1	3	[ "A000055", "A000088", "A000272", "A001187", "A001349", "A001433", "A002494", "A006125", "A006129", "A014068", "A055290", "A055314", "A163395", "A185650", "A358107", "A358732", "A359398" ]	null	Gus Wiseman, Jan 01 2023	2023-01-02T00:06:07	oeisdata/seq/A359/A359398.seq	d6e942ac6c2f73eb1d8d03e3f662afcf
A359399	a(1) = 1; a(n) = Sum_{k=2..n} k * a(floor(n/k)).	[ "1", "2", "5", "11", "16", "31", "38", "62", "80", "105", "116", "194", "207", "242", "287", "383", "400", "526", "545", "675", "738", "793", "816", "1200", "1250", "1315", "1423", "1605", "1634", "1979", "2010", "2394", "2493", "2578", "2683", "3475", "3512", "3607", "3724", "4364", "4405", "4888", "4931", "5217", "5577", "5692", "5739", "7563", "7661", "8011" ]	[ "nonn" ]	16	1	2	[ "A022825", "A359399" ]	null	Seiichi Manyama, Mar 31 2023	2023-04-01T11:23:52	oeisdata/seq/A359/A359399.seq	c9bc9631f6a219c7f824b9c29e44bc3a
A359400	Sum of positions of zeros in the reversed binary expansion of n, where positions in a sequence are read starting with 1 from the left.	[ "1", "0", "1", "0", "3", "2", "1", "0", "6", "5", "4", "3", "3", "2", "1", "0", "10", "9", "8", "7", "7", "6", "5", "4", "6", "5", "4", "3", "3", "2", "1", "0", "15", "14", "13", "12", "12", "11", "10", "9", "11", "10", "9", "8", "8", "7", "6", "5", "10", "9", "8", "7", "7", "6", "5", "4", "6", "5", "4", "3", "3", "2", "1", "0", "21", "20", "19", "18", "18", "17", "16", "15", "17", "16", "15", "14", "14", "13" ]	[ "nonn", "base" ]	47	0	5	[ "A000120", "A003714", "A023416", "A029931", "A030190", "A030308", "A039004", "A048793", "A059015", "A069010", "A070939", "A073642", "A230877", "A328594", "A328595", "A344618", "A345927", "A359359", "A359400", "A359402", "A359495", "A368494" ]	null	Gus Wiseman, Jan 05 2023	2024-03-23T20:26:12	oeisdata/seq/A359/A359400.seq	3c199ac4c63c0e02de2706a3c570d179

A359301

Least k such that {1, ..., k} contains an n-element set of positive integers satisfying the Lucier-Sárközy difference set condition.

[ "1", "4", "9", "12", "33", "36", "49", "52", "65", "68", "105", "108", "133", "136", "153", "156", "209", "212", "217", "220", "243", "246", "299", "302", "489", "492" ]

[ "nonn", "more", "nice" ]

21

1

2

[ "A174911", "A359301" ]

null

Charles R Greathouse IV, Dec 24 2022

2023-02-19T18:45:27

oeisdata/seq/A359/A359301.seq

bfc4e6c92a49261a12a5fa74beaf1cb7

A359302

Dirichlet g.f.: zeta(s)^2/zeta(3*s-2).

[ "1", "2", "2", "3", "2", "4", "2", "0", "3", "4", "2", "6", "2", "4", "4", "-3", "2", "6", "2", "6", "4", "4", "2", "0", "3", "4", "-5", "6", "2", "8", "2", "-6", "4", "4", "4", "9", "2", "4", "4", "0", "2", "8", "2", "6", "6", "4", "2", "-6", "3", "6", "4", "6", "2", "-10", "4", "0", "4", "4", "2", "12", "2", "4", "6", "-9", "4", "8", "2", "6", "4", "8", "2", "0", "2", "4", "6", "6", "4", "8", "2", "-6", "-13", "4", "2", "12" ]

[ "sign", "easy", "mult" ]

8

1

2

[ "A344326", "A359302" ]

null

Vaclav Kotesovec, Dec 25 2022

2023-09-15T05:52:45

oeisdata/seq/A359/A359302.seq

22375c2d2e33518f94e5cb5323aaa605

A359303

Bitwise encoding of the state of a 1D cellular automaton after n steps from ...111000... where adjacent cells swap 01 <-> 10 when within triples 110 or 011.

[ "1", "3", "5", "11", "13", "39", "43", "45", "103", "155", "171", "173", "359", "411", "619", "669", "1367", "1371", "1387", "1437", "3287", "4923", "5339", "5467", "5483", "5533", "11479", "13115", "19675", "21339", "21739", "21853", "43735", "43835", "44251", "45915", "52459", "78685", "170455", "173755", "174555", "174811", "174939", "175339", "176989", "367063", "419515", "629211" ]

[ "nonn", "easy" ]

96

1

2

[ "A030101", "A035327", "A053644", "A359303", "A360141", "A360142" ]

null

Raphael J. F. Berger, Dec 25 2022

2024-04-01T12:09:17

oeisdata/seq/A359/A359303.seq

2453353c72d8ec686cea2f3ce73c2908

A359304

Oblong numbers which are products of five distinct primes.

[ "4290", "4830", "6006", "11130", "12210", "13110", "16770", "23870", "27390", "33306", "34410", "34782", "37830", "44310", "49062", "56406", "60762", "64770", "66822", "70490", "71022", "74802", "82082", "84390", "95790", "101442", "103362", "104006", "109230", "119370", "125670", "127806", "133590", "137270", "148610", "151710", "158802" ]

[ "nonn" ]

11

1

[ "A002378", "A046387", "A359304" ]

null

Massimo Kofler, Dec 25 2022

2023-01-14T17:35:31

oeisdata/seq/A359/A359304.seq

432c85845a1228f7f1ff7482d3483228

A359305

Number of divisors of 6*n-1 of form 6*k+1.

[ "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "2", "1", "2", "2", "1", "1", "1", "2", "1", "1", "2", "2", "2", "2", "1", "1", "1", "3", "1", "1", "1", "1", "3", "1", "2", "1", "2", "2", "1", "1", "2", "2", "2", "2", "1", "1", "1", "2", "2", "2", "1", "1", "2", "1", "2", "2", "1", "3", "1", "2", "1", "1", "4", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "1", "2", "2", "3" ]

[ "nonn", "easy" ]

21

1

6

[ "A000005", "A001620", "A016969", "A078703", "A279060", "A319995", "A359211", "A359233", "A359305", "A359306", "A359307", "A359308", "A359309", "A359324", "A359325", "A359326", "A359327" ]

null

Seiichi Manyama, Dec 25 2022

2022-12-27T07:08:28

oeisdata/seq/A359/A359305.seq

09df164a0a086518b732c4ac78697913

A359306

Number of divisors of 6*n-2 of form 6*k+1.

[ "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "2", "2", "1", "1", "1", "2", "1", "2", "1", "2", "2", "1", "1", "2", "2", "1", "1", "2", "1", "1", "2", "3", "1", "2", "1", "2", "1", "1", "2", "2", "2", "1", "1", "2", "1", "2", "2", "2", "1", "2", "2", "2", "2", "1", "1", "2", "1", "1", "1", "4", "2", "1", "1", "2", "1", "2", "2", "2", "2", "1", "2", "2", "2", "2", "1", "2", "1", "1", "1", "2", "3", "2", "1", "2", "1", "2", "1", "4", "1" ]

[ "nonn", "easy" ]

16

1

5

[ "A279060", "A359305", "A359306", "A359307", "A359308", "A359309" ]

null

Seiichi Manyama, Dec 25 2022

2023-08-16T02:26:51

oeisdata/seq/A359/A359306.seq

9e2f947065c6cd9c43363ff8874509f9

A359307

Number of divisors of 6*n-3 of form 6*k+1.

[ "1", "1", "1", "2", "1", "1", "2", "1", "1", "2", "2", "1", "2", "1", "1", "2", "1", "2", "2", "2", "1", "2", "1", "1", "3", "1", "1", "2", "2", "1", "2", "2", "2", "2", "1", "1", "2", "2", "2", "2", "1", "1", "2", "1", "1", "4", "2", "2", "2", "1", "1", "2", "2", "1", "2", "2", "1", "2", "2", "2", "2", "1", "2", "2", "2", "1", "4", "1", "1", "2", "1", "2", "2", "3", "1", "2", "1", "2", "2", "1", "2", "2", "2", "1", "3", "2", "1", "4", "1", "1" ]

[ "nonn", "easy" ]

14

1

4

[ "A279060", "A359305", "A359306", "A359307", "A359308", "A359309" ]

null

Seiichi Manyama, Dec 25 2022

2023-08-16T02:26:54

oeisdata/seq/A359/A359307.seq

9749fcc62059a5e5a4c678201f455077

A359308

Number of divisors of 6*n-4 of form 6*k+1.

[ "1", "1", "2", "1", "2", "1", "2", "1", "2", "2", "2", "1", "2", "1", "2", "1", "3", "2", "2", "1", "2", "1", "2", "2", "2", "2", "2", "1", "2", "1", "4", "1", "2", "2", "2", "1", "2", "2", "2", "1", "2", "2", "2", "2", "4", "1", "2", "1", "2", "2", "2", "2", "2", "1", "2", "1", "3", "2", "4", "1", "2", "1", "2", "2", "2", "3", "2", "1", "2", "2", "2", "1", "4", "2", "2", "1", "2", "1", "2", "2", "2", "2", "4", "2", "2", "1", "4", "1", "2", "2" ]

[ "nonn", "easy" ]

15

1

3

[ "A279060", "A359305", "A359306", "A359307", "A359308", "A359309" ]

null

Seiichi Manyama, Dec 25 2022

2023-08-16T02:26:57

oeisdata/seq/A359/A359308.seq

ed225d5769560a55f48df4f4116ca19d

A359309

Number of divisors of 6*n-5 of form 6*k+1.

[ "1", "2", "2", "2", "2", "2", "2", "2", "3", "2", "2", "2", "2", "2", "2", "4", "2", "2", "2", "2", "2", "2", "4", "2", "2", "2", "2", "2", "3", "4", "2", "2", "2", "2", "2", "2", "4", "2", "2", "2", "2", "4", "2", "4", "2", "2", "2", "2", "2", "2", "4", "2", "2", "2", "4", "2", "2", "4", "2", "2", "3", "2", "2", "2", "4", "2", "2", "4", "2", "2", "2", "4", "2", "2", "2", "2", "2", "2", "4", "4", "4", "2", "2", "2", "2", "4", "2", "2", "2", "2" ]

[ "nonn", "easy" ]

15

1

2

[ "A279060", "A359305", "A359306", "A359307", "A359308", "A359309" ]

null

Seiichi Manyama, Dec 25 2022

2023-08-16T02:27:01

oeisdata/seq/A359/A359309.seq

87f22c36748e7f20b0db13162c1ae1dd

A359310

Cyclic cubic conductors associated with closed Andozhskii groups.

[ "59031", "209853", "247437", "263017", "271737", "329841", "377923", "407851", "412909", "415597", "416241", "416727", "462573", "474561", "487921", "493839", "547353", "586963", "612747", "613711", "615663", "622063", "648427", "651829", "689347", "690631", "753787", "796779", "811069", "818217", "869611", "914263", "915439", "922167", "936747", "977409", "997087" ]

[ "nonn" ]

45

1

null

Daniel Constantin Mayer, Dec 25 2022

2023-09-24T12:16:31

oeisdata/seq/A359/A359310.seq

0fbaeaff0fcd9e0bdd8a356c274b4d88

A359311

Number of Catalan paths (nonnegative, starting and ending at 0, step +/-1) of 2*n steps which reach at least 6 at some point.

[ "0", "0", "0", "0", "0", "0", "1", "12", "89", "528", "2755", "13244", "60214", "263121", "1116791", "4637476", "18936940", "76327705", "304520286", "1205152900", "4738962369", "18540020091", "72240167011", "280579954028", "1087033982059", "4203231136230", "16228518078010", "62588797371361", "241198478726775" ]

[ "nonn", "easy" ]

124

0

8

[ "A000108", "A080936", "A080937", "A289419", "A359311" ]

null

Greg Dresden, Jan 21 2023

2023-01-25T09:09:26

oeisdata/seq/A359/A359311.seq

6f961ae15c3ea76b9e4d5ea2159135f7

A359312

a(1) = 1; for n >= 1, a(2*n) = A000005(a(n)), a(2*n + 1) = A000005(a(n)) + 1.

[ "1", "1", "2", "1", "2", "2", "3", "1", "2", "2", "3", "2", "3", "2", "3", "1", "2", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "1", "2", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "1", "2", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2" ]

[ "nonn" ]

20

1

3

[ "A000005", "A131051", "A359312" ]

null

Ctibor O. Zizka, Dec 25 2022

2022-12-31T15:16:24

oeisdata/seq/A359/A359312.seq

281902b5f72e716a60ddb4c07c76c590

A359313

Triangular array read by rows. T(n,k) is the number of Green's H-classes contained in the D-class of rank k matrices in the semigroup Mat_n(F_2) of n X n matrices over the field F_2. n>=0, 0<=k<=n.

[ "1", "1", "1", "1", "9", "1", "1", "49", "49", "1", "1", "225", "1225", "225", "1", "1", "961", "24025", "24025", "961", "1", "1", "3969", "423801", "1946025", "423801", "3969", "1", "1", "16129", "7112889", "139499721", "139499721", "7112889", "16129", "1", "1", "65025", "116532025", "9439094025", "40315419369", "9439094025", "116532025", "65025", "1" ]

[ "nonn", "tabl" ]

15

0

5

[ "A002416", "A002884", "A005329", "A022166", "A243950", "A296548", "A359313" ]

null

Geoffrey Critzer, Dec 25 2022

2022-12-28T04:59:48

oeisdata/seq/A359/A359313.seq

9cd9860cba0c64f74433eb63029aee18

A359314

Three-column table T(n,k) read by rows where the elements in the pair of two adjacent rows, starting with the odd-indexed row T(2j-1,k) and followed by the even-indexed one T(2j,k), are such that they are not multiples of the elements presented in the previous rows and that Sum_{k=1..3} T(2j-1,k)^2 = Sum_{k=1..3} T(2j,k)^2 and Sum_{k=1..3} T(2j-1,k)^6 = Sum_{k=1..3} T(2j,k)^6 for j > 0 and k = 1, 2, 3.

[ "3", "19", "22", "10", "15", "23", "15", "52", "65", "36", "37", "67", "23", "54", "73", "33", "47", "74", "3", "55", "80", "32", "43", "81", "11", "65", "78", "37", "50", "81" ]

[ "nonn", "tabf", "more" ]

45

1

null

Alexander R. Povolotsky, Dec 25 2022

2023-12-10T09:12:25

oeisdata/seq/A359/A359314.seq

210ea127c45c348c409dcd9260f83ece

A359315

a(n) is the smallest centered triangular number with binary weight n.

[ "1", "10", "19", "46", "31", "235", "631", "1786", "1999", "7669", "7039", "12286", "16381", "180094", "114679", "949231", "2086831", "2883574", "4175839", "12480511", "50329585", "62898151", "132638719", "234618814", "771743710", "2883510271", "4269733885", "8254119871", "17045499901", "33214168831" ]

[ "nonn", "base" ]

9

1

2

[ "A000120", "A005448", "A089999", "A358932", "A359315", "A359316" ]

null

Ilya Gutkovskiy, Dec 25 2022

2025-02-16T08:34:04

oeisdata/seq/A359/A359315.seq

e8bc5d58533ec3aafb082071294cec4e

A359316

a(n) is the smallest centered square number with binary weight n.

[ "1", "5", "13", "85", "61", "221", "761", "1013", "2813", "12013", "23545", "54781", "16381", "196565", "425965", "770041", "3137513", "7663613", "13629421", "20962813", "63946741", "121602013", "192805885", "499122013", "989724541", "2411720701", "6435110905", "17162301181", "29929502461", "63753420281" ]

[ "nonn", "base" ]

8

1

2

[ "A000120", "A001844", "A089998", "A358932", "A359315", "A359316" ]

null

Ilya Gutkovskiy, Dec 25 2022

2025-02-16T08:34:04

oeisdata/seq/A359/A359316.seq

e23ebd9dfba61087ac10d777d63837d2

A359317

a(n) is the smallest tetrahedral number with binary weight n.

[ "0", "1", "10", "35", "120", "220", "455", "2024", "1771", "4060", "14190", "16215", "129766", "32509", "1414910", "1823471", "5159805", "8171255", "4192244", "24117100", "30865405", "334985911", "192937325", "1610599145", "1048440315", "4261347265", "4244012991", "63828916911", "213588635511", "133110357279" ]

[ "nonn", "base" ]

9

0

3

[ "A000120", "A000292", "A089999", "A358931", "A359317", "A359318" ]

null

Ilya Gutkovskiy, Dec 25 2022

2025-02-16T08:34:04

oeisdata/seq/A359/A359317.seq

d22ad15619e46ce0db1732983b36d9bd

A359318

a(n) is the smallest square pyramidal number with binary weight n.

[ "0", "1", "5", "14", "30", "55", "819", "506", "1785", "1015", "16206", "51039", "98021", "81375", "1113775", "964535", "2607099", "5494655", "1048061", "6029275", "50331190", "356343295", "534555645", "516941815", "4021378559", "2143222510", "12842950505", "34091142526", "68651299705", "124545644405", "273736383990" ]

[ "nonn", "base" ]

10

0

3

[ "A000120", "A000330", "A089998", "A358931", "A359317", "A359318" ]

null

Ilya Gutkovskiy, Dec 25 2022

2025-02-16T08:34:04

oeisdata/seq/A359/A359318.seq

500e7ac44cc2f0f1c59573f91e75c9a4

A359319

Maximal coefficient of (1 + x) * (1 + x^8) * (1 + x^27) * ... * (1 + x^(n^3)).

[ "1", "1", "1", "1", "1", "1", "2", "2", "2", "3", "4", "5", "7", "10", "14", "18", "27", "36", "62", "95", "140", "241", "370", "607", "1014", "1646", "2751", "4863", "8260", "13909", "24870", "41671", "73936", "131257", "228204", "411128", "737620", "1292651", "2324494", "4253857", "7487549", "13710736", "25291179", "44938191", "82814603" ]

[ "nonn" ]

31

0

7

[ "A000537", "A000578", "A001405", "A025591", "A160235", "A279329", "A359319", "A359320" ]

null

Ilya Gutkovskiy, Dec 25 2022

2022-12-31T12:46:16

oeisdata/seq/A359/A359319.seq

6b3bc3fd1a9917d01522aebe30809b79

A359320

Maximal coefficient of (1 + x) * (1 + x^16) * (1 + x^81) * ... * (1 + x^(n^4)).

[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "3", "3", "4", "5", "5", "6", "9", "13", "17", "24", "34", "53", "84", "130", "177", "290", "500", "797", "1300", "2066", "3591", "6090", "10298", "17330", "29888", "50811", "88358", "153369", "280208", "481289", "845090", "1474535", "2703811", "4808816", "8329214", "14806743", "27529781", "48859783", "87674040", "156471632" ]

[ "nonn" ]

20

0

10

[ "A000538", "A000583", "A025591", "A160235", "A298859", "A359319", "A359320" ]

null

Ilya Gutkovskiy, Dec 25 2022

2024-01-31T14:12:16

oeisdata/seq/A359/A359320.seq

9ac204d92fde25130d3f1ec481ec9bca

A359321

a(n) is the smallest n-gonal pyramidal number which can be represented as the sum of n distinct nonzero n-gonal pyramidal numbers in exactly n ways, or -1 if none exists.

[ "2300", "6201", "8125", "6391" ]

[ "nonn", "more" ]

5

3

1

[ "A080851", "A350210", "A350397", "A350423", "A359321" ]

null

Ilya Gutkovskiy, Dec 25 2022

2025-02-16T08:34:04

oeisdata/seq/A359/A359321.seq

9326bc64993bc5ce6feab56a90a9c4c3

A359322

a(n) is the first prime p such that the average of the squares of n consecutive primes starting with p is prime.

[ "3", "7", "7", "1627", "83", "7", "23", "7", "19", "17", "73", "281", "179", "257", "5", "43", "73", "43", "19", "67", "911", "193", "7", "1613", "139", "383", "7", "719", "113", "967", "31", "19", "211", "769", "149", "173", "13", "13", "59", "137", "23", "47", "89", "607", "61", "127", "61", "317", "1049", "1277", "547", "281", "317", "4157", "199", "107", "373", "149", "229", "367", "1489", "643", "563", "587", "263" ]

[ "nonn" ]

13

2

1

null

Robert Israel, Dec 25 2022

2023-01-06T10:42:19

oeisdata/seq/A359/A359322.seq

4efc5ed92b726a008b96094a4408bab4

A359323

a(n) is the first prime p such that the average of the n-th powers of n consecutive primes starting with p is prime.

[ "2", "3", "1531", "19", "631", "37", "41", "13", "670231", "614333", "11699", "11", "2447", "3049", "223", "13", "8353", "2531", "2203", "241", "3209", "5023", "52631", "461", "26723", "3307" ]

[ "nonn", "more" ]

22

1

[ "A359322", "A359323" ]

null

Robert Israel, Dec 25 2022

2025-03-24T05:56:16

oeisdata/seq/A359/A359323.seq

82d84a45fea057d58861da876cd12f21

A359324

Number of divisors of 6*n-2 of form 6*k+5.

[ "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "0", "2", "0", "1", "1", "1", "1", "1", "0", "1", "0", "2", "1", "1", "0", "2", "1", "1", "0", "1", "1", "2", "0", "1", "0", "1", "2", "1", "1", "2", "0", "2", "0", "1", "0", "1", "2", "2", "0", "1", "0", "2", "0", "2", "1", "1", "2", "1", "1", "1", "0", "2", "1", "1", "0", "1", "1", "2", "0", "2", "1", "2", "0", "2", "0", "1", "2", "1", "1", "1", "1", "3", "0", "1", "0", "1", "2", "1", "0", "1" ]

[ "nonn", "easy" ]

18

1

12

[ "A319995", "A359239", "A359269", "A359290", "A359305", "A359324", "A359325", "A359326", "A359327" ]

null

Seiichi Manyama, Dec 25 2022

2023-08-14T01:59:23

oeisdata/seq/A359/A359324.seq

6e0d7bb5460018259f88a13af69a62a4

A359325

Number of divisors of 6*n-3 of form 6*k+5.

[ "0", "0", "1", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "1", "0", "1", "2", "0", "0", "1", "0", "1", "1", "0", "1", "1", "2", "0", "1", "0", "0", "2", "0", "1", "1", "0", "1", "2", "0", "0", "1", "2", "1", "1", "0", "0", "2", "0", "1", "1", "0", "2", "1", "0", "0", "1", "2", "0", "2", "1", "1", "2", "0", "0", "1", "0", "1", "1", "0", "1", "2", "2", "0", "1", "0", "1", "2", "0", "1", "2", "0", "2", "1", "0", "0", "1", "2", "1", "1" ]

[ "nonn", "easy" ]

16

1

18

[ "A319995", "A359305", "A359324", "A359325", "A359326", "A359327" ]

null

Seiichi Manyama, Dec 25 2022

2023-08-16T02:27:04

oeisdata/seq/A359/A359325.seq

f6194838219e42cd8d44a3365398b828

A359326

Number of divisors of 6*n-4 of form 6*k+5.

[ "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "1", "0", "1", "0", "0", "2", "1", "0", "0", "0", "2", "0", "0", "0", "1", "2", "1", "0", "1", "0", "1", "0", "1", "0", "0", "2", "1", "1", "0", "0", "2", "0", "1", "0", "1", "2", "0", "0", "2", "0", "1", "0", "1", "0", "0", "2", "1", "0", "1", "2", "2", "0", "0", "0", "1", "2", "0", "0", "1", "0", "2", "0", "1", "0", "1", "2", "2", "0", "0", "0", "2", "2", "0", "0", "1", "2", "0" ]

[ "nonn", "easy" ]

18

1

19

[ "A319995", "A359305", "A359324", "A359325", "A359326", "A359327" ]

null

Seiichi Manyama, Dec 25 2022

2023-08-14T01:59:19

oeisdata/seq/A359/A359326.seq

b487c66b729698c6541bac49b2811756

A359327

Number of divisors of 6*n-5 of form 6*k+5.

[ "0", "0", "0", "0", "1", "0", "0", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "0", "0", "2", "1", "0", "0", "0", "2", "0", "0", "0", "0", "2", "0", "2", "0", "0", "2", "0", "0", "0", "0", "2", "0", "0", "2", "0", "2", "0", "0", "0", "1", "2", "0", "0", "0", "2", "2", "0", "0", "0", "0", "2", "0", "0", "0", "0", "4", "2", "0", "0", "0", "2", "0", "0", "0", "0", "2", "2", "0", "0", "0", "2", "0", "0", "2", "0", "2", "0", "2", "0", "1", "2" ]

[ "nonn", "easy" ]

18

1

10

[ "A319995", "A359239", "A359240", "A359241", "A359305", "A359324", "A359325", "A359326", "A359327" ]

null

Seiichi Manyama, Dec 25 2022

2023-08-14T01:59:32

oeisdata/seq/A359/A359327.seq

3f758d1ada64b1335a0c00e6adb395e4

A359328

Maximal coefficient of x^2*(x^2 + x^3)*(x^2 + x^3 + x^5)*...*(x^2 + x^3 + x^5 + ... + x^prime(n)).

[ "1", "1", "1", "2", "4", "12", "46", "251", "1576", "11578", "94933", "875134", "8900088", "99276703", "1214131109", "16107824706", "229757728186", "3499486564517", "56862172844198", "980725126968577", "17899265342632635", "345197504845310134", "7005723403640260805", "149261757412790940113", "3329108788695272565243" ]

[ "nonn" ]

35

0

4

[ "A000040", "A326178", "A350457", "A359328", "A359337", "A359338", "A359339" ]

null

Stefano Spezia, Dec 26 2022

2024-02-01T16:24:09

oeisdata/seq/A359/A359328.seq

6a722b43576cce1059e61625a92eccb9

A359329

Number of diagonals in a regular polygon with n sides not passing through the center.

[ "0", "0", "5", "6", "14", "16", "27", "30", "44", "48", "65", "70", "90", "96", "119", "126", "152", "160", "189", "198", "230", "240", "275", "286", "324", "336", "377", "390", "434", "448", "495", "510", "560", "576", "629", "646", "702", "720", "779", "798", "860", "880", "945", "966", "1034", "1056", "1127", "1150", "1224", "1248", "1325", "1350", "1430", "1456", "1539", "1566", "1652", "1680" ]

[ "nonn", "easy" ]

30

3

[ "A000096", "A014106", "A054000", "A142150", "A359329" ]

null

Luk De Clercq, Dec 26 2022

2024-10-02T07:40:09

oeisdata/seq/A359/A359329.seq

a13739fa4a59310af9a634d93f63e739

A359330

Composite k for which phi(k) + phi(k') = k, where k' is the arithmetic derivative of k (A003415).

[ "4", "6", "8", "10", "12", "18", "22", "28", "34", "58", "60", "72", "82", "84", "88", "108", "112", "118", "124", "132", "140", "142", "202", "204", "214", "216", "220", "228", "260", "274", "298", "324", "340", "358", "372", "382", "394", "444", "454", "478", "492", "508", "538", "562", "564", "572", "580", "620", "622", "644", "694", "708", "740", "804", "812", "820" ]

[ "nonn" ]

18

1

[ "A000010", "A001359", "A002808", "A003415", "A023221", "A051953", "A066938", "A190402", "A359330" ]

null

Marius A. Burtea, Jan 28 2023

2023-02-17T22:05:35

oeisdata/seq/A359/A359330.seq

e07eb72a8842f89a0bac6bc9c59d162a

A359331

Nonprime numbers k for which k*k' is a palindrome, where k' is the arithmetic derivative of k (A003415).

[ "1", "34", "44", "49", "121", "476", "524", "533", "1808", "6797", "7326", "10016", "10201", "10403", "10817", "16019", "17831", "26322", "33898", "55198", "57247", "74711", "87241", "131395", "148753", "156029", "239593", "240021", "289831", "295022", "423758", "441691", "595777", "725754", "900009", "2568543", "2910271", "2981619" ]

[ "nonn", "base" ]

18

1

2

[ "A002113", "A003415", "A018252", "A190116", "A359331" ]

null

Marius A. Burtea, Jan 29 2023

2023-02-17T22:07:43

oeisdata/seq/A359/A359331.seq

9f4768d21938685723bcdd3a782d03a8

A359332

Numbers with arithmetic derivative which is a palindromic prime number (A002385).

[ "6", "10", "114", "130", "174", "182", "222", "231", "255", "273", "286", "298", "357", "358", "455", "574", "622", "870", "1015", "1309", "1335", "1677", "1695", "12594", "13630", "13686", "15258", "18534", "18654", "19082", "19114", "19522", "19626", "19922", "19986", "20998", "21558", "22178", "22882", "22930", "23062", "23262", "23709", "24338" ]

[ "nonn", "base" ]

22

1

[ "A001097", "A002113", "A002385", "A003415", "A157037", "A359332" ]

null

Marius A. Burtea, Jan 29 2023

2025-03-24T06:02:28

oeisdata/seq/A359/A359332.seq

e3a36211257eaaaa12d7dbeb5b3859c0

A359333

a(1) = 0, and for any n > 1, a(n) is chosen among 0 and 1 so as to minimize the length of the longest sequence of distinct integers in arithmetic progression in the interval 1..n and containing n where the sequence is constant; in case of a tie, maximize the least common difference in those longest arithmetic progressions.

[ "0", "1", "0", "1", "1", "0", "1", "0", "0", "1", "1", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "1", "1", "1", "1", "0", "1", "0", "0", "0", "1", "1", "0", "1", "0", "1", "0", "0", "0", "1", "1", "1", "0", "1", "1", "0", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "0", "0", "1", "1", "1", "0", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "1", "1" ]

[ "nonn" ]

32

1

null

[ "A038219", "A359333" ]

null

Rémy Sigrist, Jan 23 2023

2023-01-26T16:13:57

oeisdata/seq/A359/A359333.seq

dc19ce9dd653c76805ef64fbc71fb148

A359334

Amicable numbers k that can be expressed as a sum k = x+y = A001065(x) + A001065(y) and a sum k = z+t = A001065(z) + A001065(t) where (x, y, z, t) are parts of two amicable pairs and A001065(i) is the sum of the aliquot parts of i.

[ "67212", "1296000", "20528640", "37739520", "75479040", "321408000", "348364800", "556839360", "579156480", "638668800", "661893120", "761177088", "796340160", "883872000", "1181174400", "1282417920", "2068416000", "2395008000", "2682408960", "3155023872", "3599769600", "4049740800", "4606156800", "4716601344" ]

[ "nonn" ]

83

1

[ "A001065", "A002025", "A036471", "A063990", "A066539", "A180164", "A259180", "A259933", "A359334" ]

null

Zoltan Galantai, Dec 26 2022

2025-02-16T08:34:04

oeisdata/seq/A359/A359334.seq

7ae0c4beda86c033b82f3f3dbe55ddc6

A359335

Square root of determinant of skew-symmetric 2n X 2n matrix with entries i XOR j for i < j, i=1..2n, j=1..2n.

[ "1", "3", "14", "84", "360", "2160", "10080", "60480", "249984", "1499904", "6999552", "41997312", "179988480", "1079930880", "5039677440", "30238064640", "122903101440", "737418608640", "3441286840320", "20647721041920", "88490233036800", "530941398220800", "2477726525030400", "14866359150182400" ]

[ "nonn" ]

13

0

2

[ "A006519", "A359335" ]

null

Andrey Zabolotskiy, Dec 26 2022

2022-12-28T09:04:29

oeisdata/seq/A359/A359335.seq

3f06fef36966d95649410b6945d9d422

A359336

Irregular triangle read by rows: the n-th row lists the values 0..2^n-1 representing all subsets of a set of n elements. When its elements are linearly ordered, the subsets are sorted first by their size and then lexicographically.

[ "0", "0", "1", "0", "2", "1", "3", "0", "4", "2", "1", "6", "5", "3", "7", "0", "8", "4", "2", "1", "12", "10", "9", "6", "5", "3", "14", "13", "11", "7", "15", "0", "16", "8", "4", "2", "1", "24", "20", "18", "17", "12", "10", "9", "6", "5", "3", "28", "26", "25", "22", "21", "19", "14", "13", "11", "7", "30", "29", "27", "23", "15", "31", "0", "32", "16", "8", "4", "2", "1", "48", "40", "36", "34", "33", "24", "20", "18", "17", "12", "10", "9", "6", "5", "3", "56", "52", "50", "49" ]

[ "nonn", "tabf" ]

35

0

5

[ "A000004", "A000012", "A000225", "A006516", "A294648", "A351939", "A356028", "A359336" ]

null

Valentin Bakoev, Dec 27 2022

2023-03-01T14:51:49

oeisdata/seq/A359/A359336.seq

7b5ccf0d59fd3ddcb08b2551179805f5

A359337

Irregular triangle read by rows: the n-th row gives the exponents of the powers of x corresponding to the maximal coefficient of the product x^2*(x^2 + x^3)*(x^2 + x^3 + x^5)*...*(x^2 + x^3 + x^5 + ... + x^prime(n)).

[ "0", "2", "4", "5", "7", "12", "16", "17", "22", "24", "32", "42", "53", "65", "79", "96", "114", "134", "155", "180", "205", "233", "263", "294", "329", "364", "403", "442", "485", "529", "576", "625", "676", "729", "785", "842", "902", "964", "1029", "1097", "1167", "1238", "1313", "1390", "1469", "1552", "1636", "1723", "1813", "1904", "1999", "2096", "2195", "2298" ]

[ "nonn", "tabf" ]

11

0

2

[ "A000040", "A359328", "A359337", "A359338", "A359339" ]

null

Stefano Spezia, Dec 27 2022

2022-12-31T15:18:15

oeisdata/seq/A359/A359337.seq

9e1fbd4a6d0ba2cee8df04c3a00df48d

A359338

Minimal exponent of the powers of x corresponding to the maximal coefficient of the product x^2*(x^2 + x^3)*(x^2 + x^3 + x^5)*...*(x^2 + x^3 + x^5 + ... + x^prime(n)).

[ "0", "2", "4", "7", "12", "16", "22", "32", "42", "53", "65", "79", "96", "114", "134", "155", "180", "205", "233", "263", "294", "329", "364", "403", "442", "485", "529", "576", "625", "676", "729", "785", "842", "902", "964", "1029", "1097", "1167", "1238", "1313", "1390", "1469", "1552", "1636", "1723", "1813", "1904", "1999", "2096", "2195", "2298", "2402", "2510" ]

[ "nonn" ]

8

0

2

[ "A000040", "A359328", "A359337", "A359338", "A359339" ]

null

Stefano Spezia, Dec 27 2022

2022-12-31T15:18:36

oeisdata/seq/A359/A359338.seq

671ea0c3d02ce41f4eb1958d481e6a68

A359339

Maximal exponent of the powers of x corresponding to the maximal coefficient of the product x^2*(x^2 + x^3)*(x^2 + x^3 + x^5)*...*(x^2 + x^3 + x^5 + ... + x^prime(n)).

[ "0", "2", "5", "7", "12", "17", "24", "32", "42", "53", "65", "79", "96", "114", "134", "155", "180", "205", "233", "263", "294", "329", "364", "403", "442", "485", "529", "576", "625", "676", "729", "785", "842", "902", "964", "1029", "1097", "1167", "1238", "1313", "1390", "1469", "1552", "1636", "1723", "1813", "1904", "1999", "2096", "2195", "2298", "2402", "2510" ]

[ "nonn" ]

8

0

2

[ "A000040", "A359328", "A359337", "A359338", "A359339" ]

null

Stefano Spezia, Dec 27 2022

2022-12-31T15:18:48

oeisdata/seq/A359/A359339.seq

288ea43ac0d3f7cf403d683d2b28c94d

A359340

The primes associated with A339174.

[ "2", "3", "7", "43", "3613", "65250781", "38318979202732621", "8810065002836730577256726488782121", "6131762382982476362788562753503495060507087787406616806191258317645081" ]

[ "nonn" ]

7

1

[ "A061092", "A071580", "A339174", "A359340" ]

null

Jeppe Stig Nielsen, Dec 27 2022

2023-01-02T09:01:05

oeisdata/seq/A359/A359340.seq

00b306e212b9a753758ba8535a08565b

A359341

Number of pandigital squares with n digits.

[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "87", "504", "4275", "29433", "179235", "955818", "4653802", "21034628", "89834238", "366490378", "1440743933", "5493453262" ]

[ "nonn", "base" ]

10

1

10

[ "A036745", "A225218", "A359341" ]

null

Martin Renner, Dec 27 2022

2022-12-31T02:12:22

oeisdata/seq/A359/A359341.seq

e8de94746c9ac9d7cd41b7d845ec4067

A359342

Least pandigital square with n digits.

[ "1026753849", "10057482369", "100549873216", "1000574082369", "10000938205476", "100005740082369", "1000000973875264", "10000057400082369", "100000030347218596", "1000000574000082369", "10000000365759287524", "100000005740000082369", "1000000003751486308921", "10000000057400000082369" ]

[ "nonn", "base" ]

12

10

1

[ "A225218", "A359342", "A359343", "A359344" ]

null

Martin Renner, Dec 27 2022

2022-12-31T02:12:45

oeisdata/seq/A359/A359342.seq

74967ac054a33e08d59e2e052c7fc586

A359343

Square roots of least pandigital squares with n digits.

[ "32043", "100287", "317096", "1000287", "3162426", "10000287", "31622792", "100000287", "316227814", "1000000287", "3162277718", "10000000287", "31622776661", "100000000287", "316227766026", "1000000000287", "3162277660177", "10000000000287", "31622776601685", "100000000000287", "316227766016843" ]

[ "nonn", "base" ]

15

10

1

[ "A359342", "A359343", "A359345" ]

null

Martin Renner, Dec 27 2022

2023-01-05T18:59:39

oeisdata/seq/A359/A359343.seq

7cb3138d2c25b5e4bf403c49df7aa6ba

A359344

Largest pandigital square with n digits.

[ "9814072356", "99853472016", "998732401956", "9998490637521", "99992580137641", "999984024130576", "9999925800137641", "99999987340240516", "999999258000137641", "9999999562540763281", "99999992580000137641", "999999991102375684521", "9999999925800000137641", "99999999986188478340025" ]

[ "nonn", "base" ]

8

10

1

[ "A225218", "A359342", "A359344", "A359345" ]

null

Martin Renner, Dec 27 2022

2022-12-31T02:12:55

oeisdata/seq/A359/A359344.seq

d18c786eb4ceb85c3f372a46d4a37ce8

A359345

Roots of largest pandigital squares with n digits.

[ "99066", "315996", "999366", "3162039", "9999629", "31622524", "99999629", "316227746", "999999629", "3162277591", "9999999629", "31622776461", "99999999629", "316227765995", "999999999629", "3162277660155", "9999999999629", "31622776601681", "99999999999629", "316227766016811", "999999999999629" ]

[ "nonn", "base" ]

8

10

1

[ "A359343", "A359344", "A359345" ]

null

Martin Renner, Dec 27 2022

2022-12-31T02:13:03

oeisdata/seq/A359/A359345.seq

d251723303a2a02fd0e9a9cc2df65538

A359346

Reversible pandigital square numbers.

[ "1234549876609", "9066789454321", "123452587690084", "123454387666009", "123454987660900", "123456987654400", "123458987664100", "123478988652100", "125688987432100", "146678985432100", "445678965432100", "480096785254321", "900666783454321", "906678945432100", "10223418547690084" ]

[ "nonn", "base" ]

20

1

[ "A036745", "A061457", "A156977", "A225218", "A359346", "A359347" ]

null

Martin Renner, Dec 27 2022

2023-01-23T13:13:09

oeisdata/seq/A359/A359346.seq

813e8aa3648dd295dd1d62869a2b0a74

A359347

Roots of reversible pandigital square numbers.

[ "1111103", "3011111", "11110922", "11111003", "11111030", "11111120", "11111210", "11112110", "11211110", "12111110", "21111110", "21911111", "30011111", "30111110", "101110922", "101111112", "101111121", "101111211", "102111111", "110109212", "110911211", "110921111", "111109220", "111110030", "111110103" ]

[ "nonn", "base" ]

21

1

[ "A102859", "A359346", "A359347" ]

null

Martin Renner, Dec 27 2022

2023-01-21T18:12:43

oeisdata/seq/A359/A359347.seq

c6bbdfa8c963dc2a919ccccc4a51812c

A359348

Maximal coefficient of (1 + x) * (1 + x^3) * (1 + x^6) * ... * (1 + x^(n*(n+1)/2)).

[ "1", "1", "1", "1", "2", "2", "3", "4", "5", "7", "12", "18", "27", "44", "73", "122", "210", "362", "620", "1050", "1857", "3290", "5949", "10665", "19086", "34330", "62252", "113643", "209460", "383888", "706457", "1300198", "2407535", "4468367", "8331820", "15525814", "28987902", "54180854", "101560631", "190708871", "358969426" ]

[ "nonn" ]

16

0

5

[ "A000217", "A024940", "A025591", "A158380", "A160235", "A359348" ]

null

Seiichi Manyama, Dec 27 2022

2022-12-29T03:04:34

oeisdata/seq/A359/A359348.seq

b311e14f9a525b2d5bac51ec39036ce8

A359349

The initial bits, written from left to right, in the 2-adic limit of the mod 2^e value of the odd factor of (2^e)!.

[ "1", "1", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "1", "0", "0", "0", "1", "0", "1", "1", "1", "0", "1", "1", "0", "0", "0", "1", "1", "1", "0", "1", "1", "0", "1", "0", "1", "0", "0", "1", "0" ]

[ "nonn", "more" ]

85

1

null

[ "A000722", "A067667", "A359349" ]

null

Donald M Davis, Jul 05 2023

2023-08-20T21:55:12

oeisdata/seq/A359/A359349.seq

42ca54bb12b4350ddc5ed9c67b0b6545

A359350

Irregular triangle T(n,k) (n >= 1, k >= 1) read by rows: row n is constructed by replacing A336811(n,k) with the largest partition into consecutive parts of A000217(A336811(n,k)).

[ "1", "2", "1", "3", "2", "1", "1", "4", "3", "2", "1", "2", "1", "1", "5", "4", "3", "2", "1", "3", "2", "1", "2", "1", "1", "1", "6", "5", "4", "3", "2", "1", "4", "3", "2", "1", "3", "2", "1", "2", "1", "2", "1", "1", "1", "7", "6", "5", "4", "3", "2", "1", "5", "4", "3", "2", "1", "4", "3", "2", "1", "3", "2", "1", "3", "2", "1", "2", "1", "2", "1", "1", "1", "1", "1", "8", "7", "6", "5", "4", "3", "2", "1", "6", "5", "4", "3", "2", "1", "5", "4", "3", "2", "1", "4", "3", "2", "1", "4", "3", "2", "1", "3", "2", "1" ]

[ "nonn", "tabf" ]

39

1

2

[ "A000027", "A000041", "A000070", "A000217", "A014153", "A176206", "A299779", "A336811", "A336812", "A338156", "A359279", "A359280", "A359350" ]

null

Omar E. Pol, Dec 27 2022

2023-09-01T14:16:44

oeisdata/seq/A359/A359350.seq

5638c330dd2bd368fbb096b02c54295e

A359351

a(n) = A001952(A003151(n)).

[ "6", "13", "23", "30", "40", "47", "54", "64", "71", "81", "88", "95", "105", "112", "122", "129", "139", "146", "153", "163", "170", "180", "187", "194", "204", "211", "221", "228", "238", "245", "252", "262", "269", "279", "286", "293", "303", "310", "320", "327", "334", "344", "351", "361", "368", "378", "385", "392", "402", "409", "419", "426", "433", "443" ]

[ "nonn", "easy" ]

4

1

[ "A001951", "A001952", "A003151", "A003152", "A184922", "A188376", "A188396", "A341239", "A356136", "A359351" ]

null

Clark Kimberling, Dec 27 2022

2023-01-08T11:45:10

oeisdata/seq/A359/A359351.seq

6e97d9c8187e53ddec423ef7a54be654

A359352

a(n) = A026430(1 + A026430(n)).

[ "3", "6", "9", "10", "14", "15", "16", "19", "23", "24", "26", "28", "30", "33", "36", "37", "41", "42", "44", "46", "48", "51", "54", "55", "57", "60", "63", "65", "68", "69", "70", "73", "77", "78", "80", "82", "84", "87", "90", "91", "93", "96", "99", "100", "103", "105", "107", "109", "111", "114", "117", "118", "121", "123", "125", "128", "130", "132", "134", "136", "138" ]

[ "nonn", "easy" ]

17

1

[ "A026530", "A285953", "A285954", "A359277", "A359352", "A359353", "A360139" ]

null

Clark Kimberling, Jan 26 2023

2023-03-01T14:28:32

oeisdata/seq/A359/A359352.seq

14b5b4c2a08bb8f5b64dc49229c825cb

A359353

a(n) = A026430(A285953(n+1)).

[ "1", "5", "8", "12", "18", "21", "27", "31", "35", "39", "45", "50", "52", "59", "61", "66", "72", "75", "81", "86", "88", "95", "98", "102", "108", "113", "116", "120", "126", "129", "135", "139", "143", "147", "153", "158", "160", "167", "170", "174", "180", "185", "188", "192", "198", "201", "207", "212", "214", "221", "224", "228", "234", "237", "243", "248", "250" ]

[ "nonn", "easy" ]

8

1

2

[ "A026530", "A285953", "A285954", "A359277", "A359352", "A359353", "A360134", "A360139" ]

null

Clark Kimberling, Jan 30 2023

2023-01-31T08:33:35

oeisdata/seq/A359/A359353.seq

10038268f5d53daac8362eb92939a288

A359354

Position of the first subsequence of n primes that differs from the first n primes, but where the relative distances among their elements coincide with those of the subsequence of first n primes except for a scale factor.

[ "2", "2", "3", "238", "28495", "576169", "24635028" ]

[ "nonn", "hard", "more" ]

20

1

[ "A001223", "A272863", "A274225", "A274263", "A359354" ]

null

Andres Cicuttin, Dec 27 2022

2023-02-10T20:14:46

oeisdata/seq/A359/A359354.seq

892f76a2ce9e68a74974a965bbcaea00

A359355

a(n) = A359107(2*n, n) = Sum_{j=0..n} Stirling2(2*n, j) = Sum_{j=0..n} A048993(2*n, j).

[ "1", "1", "8", "122", "2795", "86472", "3403127", "164029595", "9433737120", "635182667816", "49344452550230", "4371727233798927", "437489737355466560", "49048715505983309703", "6116937802946210183545", "843220239072837883168510", "127757559136845878072576947", "21166434937698025552654090472" ]

[ "nonn" ]

16

0

3

[ "A048993", "A102661", "A359107", "A359355" ]

null

Peter Luschny, Dec 27 2022

2023-06-13T15:21:48

oeisdata/seq/A359/A359355.seq

490532f94f1ca067544bc1dd64f54096

A359356

a(n-1) + a(n) has only digits also in a(n); lexicographically earliest such sequence of distinct nonnegative integers.

[ "0", "1", "10", "12", "179", "132", "1048", "416", "135", "126", "125", "1025", "136", "15", "146", "82", "31", "302", "53", "128", "183", "130", "14", "157", "1254", "139", "304", "73", "41", "403", "74", "208", "103", "152", "1028", "91", "21", "201", "32", "159", "506", "160", "17", "124", "1036", "104", "51", "504", "95", "16", "204", "62", "129", "203", "52", "503" ]

[ "nonn", "base" ]

23

0

3

[ "A359356", "A359517" ]

null

M. F. Hasler and Eric Angelini, Dec 27 2022

2023-01-06T14:12:00

oeisdata/seq/A359/A359356.seq

b0134e571a053becf268644298ef3656

A359357

Number of different ratios between consecutive prime gaps among the first n primes.

[ "1", "2", "2", "3", "3", "3", "3", "4", "5", "6", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "7", "8", "8", "8", "8", "8", "8", "9", "10", "10", "10", "11", "12", "12", "12", "12", "12", "12", "12", "12", "12", "12", "12", "13", "13", "13", "13", "13", "13", "13", "13", "14", "14", "14", "14", "14", "14", "14", "14", "15", "15", "15", "15", "15", "16", "17", "17", "17", "17", "17", "18", "18", "18", "18", "18", "18", "18", "19", "19", "19", "19" ]

[ "nonn" ]

26

3

2

[ "A001223", "A272863", "A274225", "A274263", "A275785", "A359357" ]

null

Andres Cicuttin, Dec 27 2022

2023-02-07T12:43:07

oeisdata/seq/A359/A359357.seq

71c34b0b9bacd011d7fbdfff85ecd8ba

A359358

Let y be the integer partition with Heinz number n. Then a(n) is the size of the Young diagram of y after removing a rectangle of the same length as y and width equal to the smallest part of y.

[ "0", "0", "0", "0", "0", "1", "0", "0", "0", "2", "0", "1", "0", "3", "1", "0", "0", "2", "0", "2", "2", "4", "0", "1", "0", "5", "0", "3", "0", "3", "0", "0", "3", "6", "1", "2", "0", "7", "4", "2", "0", "4", "0", "4", "1", "8", "0", "1", "0", "4", "5", "5", "0", "3", "2", "3", "6", "9", "0", "3", "0", "10", "2", "0", "3", "5", "0", "6", "7", "5", "0", "2", "0", "11", "2", "7", "1", "6", "0", "2", "0", "12", "0", "4", "4", "13" ]

[ "nonn" ]

8

1

10

[ "A001222", "A055396", "A056239", "A061395", "A112798", "A124010", "A241916", "A243055", "A243503", "A246277", "A268192", "A316413", "A325351", "A325352", "A326836", "A326837", "A326844", "A326846", "A355534", "A356958", "A358172", "A358195", "A359358", "A359360" ]

null

Gus Wiseman, Dec 27 2022

2022-12-28T09:05:02

oeisdata/seq/A359/A359358.seq

632f60dc1e4a6a85695d044a6d53bb94

A359359

Sum of positions of zeros in the binary expansion of n, where positions are read starting with 1 from the left (big-endian).

[ "1", "0", "2", "0", "5", "2", "3", "0", "9", "5", "6", "2", "7", "3", "4", "0", "14", "9", "10", "5", "11", "6", "7", "2", "12", "7", "8", "3", "9", "4", "5", "0", "20", "14", "15", "9", "16", "10", "11", "5", "17", "11", "12", "6", "13", "7", "8", "2", "18", "12", "13", "7", "14", "8", "9", "3", "15", "9", "10", "4", "11", "5", "6", "0", "27", "20", "21", "14", "22", "15", "16", "9", "23", "16", "17", "10" ]

[ "nonn", "base" ]

14

0

3

[ "A000120", "A003714", "A023416", "A029931", "A030190", "A039004", "A048793", "A059015", "A065359", "A069010", "A070939", "A073642", "A083652", "A230877", "A328594", "A328595", "A345927", "A359359", "A359400", "A359402", "A359495" ]

null

Gus Wiseman, Jan 03 2023

2023-01-05T18:30:39

oeisdata/seq/A359/A359359.seq

f6eb432f618a3210d4c59078f34b0b34

A359360

Length times minimum part of the integer partition with Heinz number n. Least prime index of n times number of prime indices of n.

[ "0", "1", "2", "2", "3", "2", "4", "3", "4", "2", "5", "3", "6", "2", "4", "4", "7", "3", "8", "3", "4", "2", "9", "4", "6", "2", "6", "3", "10", "3", "11", "5", "4", "2", "6", "4", "12", "2", "4", "4", "13", "3", "14", "3", "6", "2", "15", "5", "8", "3", "4", "3", "16", "4", "6", "4", "4", "2", "17", "4", "18", "2", "6", "6", "6", "3", "19", "3", "4", "3", "20", "5", "21", "2", "6", "3", "8", "3", "22", "5", "8", "2" ]

[ "nonn" ]

8

1

3

[ "A001222", "A006141", "A055396", "A056239", "A061395", "A112798", "A124010", "A241916", "A243055", "A246277", "A268192", "A316413", "A325352", "A326836", "A326837", "A326844", "A326846", "A355534", "A356958", "A358172", "A358195", "A359358", "A359360" ]

null

Gus Wiseman, Dec 28 2022

2022-12-28T15:42:39

oeisdata/seq/A359/A359360.seq

be59f693024248aa52e8376d2c37b9e1

A359361

Irregular triangle read by rows whose n-th row lists the partial sums of the integer partition with Heinz number n.

[ "1", "2", "1", "2", "3", "2", "3", "4", "1", "2", "3", "2", "4", "3", "4", "5", "2", "3", "4", "6", "4", "5", "3", "5", "1", "2", "3", "4", "7", "2", "4", "5", "8", "3", "4", "5", "4", "6", "5", "6", "9", "2", "3", "4", "5", "3", "6", "6", "7", "2", "4", "6", "4", "5", "6", "10", "3", "5", "6", "11", "1", "2", "3", "4", "5", "5", "7", "7", "8", "4", "7", "2", "4", "5", "6", "12", "8", "9", "6", "8", "3", "4", "5", "6", "13" ]

[ "nonn", "tabf" ]

13

2

[ "A000009", "A000041", "A000720", "A001221", "A001222", "A003963", "A048793", "A055396", "A056239", "A061395", "A112798", "A261079", "A296150", "A304818", "A318283", "A325362", "A355536", "A358134", "A358136", "A358137", "A359361", "A359397" ]

null

Gus Wiseman, Dec 30 2022

2023-03-31T05:51:08

oeisdata/seq/A359/A359361.seq

60583a0ed5bbe5445109d7ea3920702c

A359362

a(n) = (A001222(n) + 1) * A056239(n), where A001222 counts prime indices and A056239 adds them up.

[ "0", "2", "4", "6", "6", "9", "8", "12", "12", "12", "10", "16", "12", "15", "15", "20", "14", "20", "16", "20", "18", "18", "18", "25", "18", "21", "24", "24", "20", "24", "22", "30", "21", "24", "21", "30", "24", "27", "24", "30", "26", "28", "28", "28", "28", "30", "30", "36", "24", "28", "27", "32", "32", "35", "24", "35", "30", "33", "34", "35", "36", "36", "32", "42", "27", "32", "38" ]

[ "nonn" ]

11

1

2

[ "A001222", "A055396", "A056239", "A061395", "A112798", "A261079", "A316413", "A326836", "A326837", "A326844", "A326846", "A359358", "A359362" ]

null

Gus Wiseman, Dec 31 2022

2023-01-02T02:17:16

oeisdata/seq/A359/A359362.seq

860f93b3eca5f05fd8ae5922deaac126

A359363

Triangle read by rows. The coefficients of the Baxter polynomials p(0, x) = 1 and p(n, x) = x*hypergeom([-1 - n, -n, 1 - n], [2, 3], -x) for n >= 1.

[ "1", "0", "1", "0", "1", "1", "0", "1", "4", "1", "0", "1", "10", "10", "1", "0", "1", "20", "50", "20", "1", "0", "1", "35", "175", "175", "35", "1", "0", "1", "56", "490", "980", "490", "56", "1", "0", "1", "84", "1176", "4116", "4116", "1176", "84", "1", "0", "1", "120", "2520", "14112", "24696", "14112", "2520", "120", "1", "0", "1", "165", "4950", "41580", "116424", "116424", "41580", "4950", "165", "1" ]

[ "nonn", "tabl" ]

36

0

9

[ "A000178", "A000292", "A001181", "A006542", "A046996", "A047819", "A056939", "A056940", "A056941", "A090181", "A097805", "A142465", "A217800", "A342889", "A359363" ]

null

Peter Luschny, Dec 28 2022

2024-01-04T08:57:55

oeisdata/seq/A359/A359363.seq

bd4880281aa41a6b7ee927287280ca75

A359364

Triangle read by rows. The Motzkin triangle, the coefficients of the Motzkin polynomials. M(n, k) = binomial(n, k) * CatalanNumber(k/2) if k is even, otherwise 0.

[ "1", "1", "0", "1", "0", "1", "1", "0", "3", "0", "1", "0", "6", "0", "2", "1", "0", "10", "0", "10", "0", "1", "0", "15", "0", "30", "0", "5", "1", "0", "21", "0", "70", "0", "35", "0", "1", "0", "28", "0", "140", "0", "140", "0", "14", "1", "0", "36", "0", "252", "0", "420", "0", "126", "0", "1", "0", "45", "0", "420", "0", "1050", "0", "630", "0", "42", "1", "0", "55", "0", "660", "0", "2310", "0", "2310", "0", "462", "0" ]

[ "nonn", "tabl" ]

37

0

9

[ "A000012", "A000108", "A000217", "A000910", "A001006", "A002457", "A002522", "A014531", "A023426", "A025179", "A025235", "A026300", "A034827", "A055151", "A056107", "A080159", "A088625", "A088626", "A091147", "A097610", "A107131", "A107587", "A126120", "A138364", "A189912", "A213380", "A343386", "A343773", "A359364", "A359647", "A359649" ]

null

Peter Luschny, Jan 09 2023

2023-01-10T13:05:07

oeisdata/seq/A359/A359364.seq

1ddf52afefcbcbfc75288d8532512098

A359365

a(n) = lcm([ n!*binomial(n-1, m-1) / m! for m = 1..n ]) with a(0) = 1.

[ "1", "1", "2", "6", "72", "240", "3600", "75600", "1411200", "10160640", "457228800", "4191264000", "184415616000", "2054916864000", "12466495641600", "1308982042368000", "314155690168320000", "14241724620963840000", "2178983867007467520000", "37260624125827694592000", "337119932567012474880000" ]

[ "nonn" ]

14

0

3

[ "A103505", "A271703", "A359365" ]

null

Peter Luschny, Dec 30 2022

2022-12-30T11:23:53

oeisdata/seq/A359/A359365.seq

c5c6448bc3bd82c710160b6f865c49b1

A359366

a(n) = (1/8)*(((3*n + 1) + (n - 1)*(-1)^n)*(n + 1)).

[ "0", "1", "3", "4", "10", "9", "21", "16", "36", "25", "55", "36", "78", "49", "105", "64", "136", "81", "171", "100", "210", "121", "253", "144", "300", "169", "351", "196", "406", "225", "465", "256", "528", "289", "595", "324", "666", "361", "741", "400", "820", "441", "903", "484", "990", "529", "1081", "576", "1176", "625", "1275", "676", "1378", "729", "1485" ]

[ "nonn" ]

13

0

3

[ "A000290", "A014105", "A056136", "A106465", "A359366" ]

null

Peter Luschny, Dec 30 2022

2022-12-30T15:44:21

oeisdata/seq/A359/A359366.seq

14393a03ff747864cc750fb8a744af02

A359367

a(n) = number of regular polytopes of rank m-n with group S_m, up to isomorphism and duality (this is independent of m if m >= 2n+3).

[ "1", "1", "7", "9", "35", "48", "135" ]

[ "nonn", "hard", "more" ]

18

1

3

null

Peter J. Cameron, Dec 28 2022

2023-01-28T11:58:14

oeisdata/seq/A359/A359367.seq

8a4a2a19b693407ebb2cc2081217e343

A359368

Sequence begins 1, 1, 1; for even n > 3, a(n) = a(n/2 - 1) + a(n/2 + 1); for odd n > 3, a(n) = -a((n-1)/2).

[ "1", "1", "1", "2", "-1", "3", "-1", "0", "-2", "5", "1", "-2", "-3", "3", "1", "-3", "0", "5", "2", "-1", "-5", "3", "-1", "-2", "2", "1", "3", "-2", "-3", "0", "-1", "1", "3", "2", "0", "2", "-5", "4", "-2", "-3", "1", "2", "5", "-6", "-3", "1", "1", "1", "2", "-1", "-2", "5", "-1", "-1", "-3", "0", "2", "-2", "3", "-4", "0", "1", "1", "2", "-1", "3", "-3", "3", "-2", "4", "0", "-5", "-2", "6", "5", "-7", "-4", "1", "2", "-1" ]

[ "sign", "easy" ]

27

1

4

null

Eden Lippmann, Dec 28 2022

2024-12-19T11:46:19

oeisdata/seq/A359/A359368.seq

1566a2a21899b8c6f0d68b9d5ec642e9

A359369

a(1) = 1. Thereafter a(n) = Sum_{j=1..n} {b(a(j)), where b(a(j)) = b(a(n))}, and b is A000120.

[ "1", "1", "2", "3", "2", "4", "5", "4", "6", "6", "8", "7", "3", "10", "12", "14", "6", "16", "8", "9", "18", "20", "22", "9", "24", "26", "12", "28", "15", "4", "10", "30", "8", "11", "18", "32", "12", "34", "36", "38", "21", "24", "40", "42", "27", "12", "44", "30", "16", "13", "33", "46", "20", "48", "50", "36", "52", "39", "24", "54", "28", "42", "45", "32", "14", "48", "56", "51", "36", "58", "40", "60", "44", "54", "48", "62", "5" ]

[ "nonn" ]

21

1

3

[ "A000005", "A000120", "A000225", "A359369" ]

null

David James Sycamore, Dec 28 2022

2023-01-16T09:04:44

oeisdata/seq/A359/A359369.seq

a8f0487beac450340c2fd2b574ae1dba

A359370

a(n) = 1 if n is not a multiple of 4 and has an even number of prime factors (with multiplicity), otherwise a(n) = 0.

[ "1", "0", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1", "1", "0", "1" ]

[ "nonn" ]

11

1

null

[ "A001222", "A166486", "A358839", "A359170", "A359370", "A359371", "A359372" ]

null

Antti Karttunen, Dec 28 2022

2022-12-30T16:14:47

oeisdata/seq/A359/A359370.seq

46fce55787dcc5a4ed16a8f9104ea0bb

A359371

Nonmultiples of 4 that have an even number of prime factors (with multiplicity).

[ "1", "6", "9", "10", "14", "15", "21", "22", "25", "26", "33", "34", "35", "38", "39", "46", "49", "51", "54", "55", "57", "58", "62", "65", "69", "74", "77", "81", "82", "85", "86", "87", "90", "91", "93", "94", "95", "106", "111", "115", "118", "119", "121", "122", "123", "126", "129", "133", "134", "135", "141", "142", "143", "145", "146", "150", "155", "158", "159", "161", "166", "169", "177", "178", "183", "185", "187", "189" ]

[ "nonn" ]

14

1

2

[ "A001222", "A008836", "A010873", "A028260", "A042968", "A046337", "A166486", "A358839", "A359370", "A359371", "A359373" ]

null

Antti Karttunen, Dec 28 2022

2022-12-29T09:09:21

oeisdata/seq/A359/A359371.seq

213e4f0807774c6f86b81f5434053cce

A359372

a(n) = 1 if n is not a multiple of 4 and has an odd number of prime factors (with multiplicity), otherwise a(n) = 0.

[ "0", "1", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "1", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "1", "0", "1", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "1", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1" ]

[ "nonn" ]

8

1

null

[ "A001222", "A166486", "A358839", "A359372", "A359373" ]

null

Antti Karttunen, Dec 28 2022

2022-12-29T15:11:46

oeisdata/seq/A359/A359372.seq

f983587a715b8f72e36e76f16d7155b1

A359373

Nonmultiples of 4 that have an odd number of prime factors (with multiplicity).

[ "2", "3", "5", "7", "11", "13", "17", "18", "19", "23", "27", "29", "30", "31", "37", "41", "42", "43", "45", "47", "50", "53", "59", "61", "63", "66", "67", "70", "71", "73", "75", "78", "79", "83", "89", "97", "98", "99", "101", "102", "103", "105", "107", "109", "110", "113", "114", "117", "125", "127", "130", "131", "137", "138", "139", "147", "149", "151", "153", "154", "157", "162", "163", "165", "167", "170", "171", "173", "174" ]

[ "nonn" ]

11

1

[ "A001222", "A008836", "A010873", "A026424", "A042968", "A067019", "A166486", "A358839", "A359371", "A359372", "A359373" ]

null

Antti Karttunen, Dec 28 2022

2022-12-29T09:16:26

oeisdata/seq/A359/A359373.seq

cdc13f3c07df31efc53183d77cceceb9

A359374

Parity of A252463(n).

[ "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1" ]

[ "nonn" ]

14

1

null

[ "A000035", "A064989", "A252463", "A359374", "A359375", "A359376", "A359379" ]

null

Antti Karttunen, Dec 31 2022

2023-01-24T02:50:57

oeisdata/seq/A359/A359374.seq

dc217d5456d848dd7c0cedf8ae73e53a

A359375

Numbers that are neither multiples of 4 nor of the form 6u+3.

[ "1", "2", "5", "6", "7", "10", "11", "13", "14", "17", "18", "19", "22", "23", "25", "26", "29", "30", "31", "34", "35", "37", "38", "41", "42", "43", "46", "47", "49", "50", "53", "54", "55", "58", "59", "61", "62", "65", "66", "67", "70", "71", "73", "74", "77", "78", "79", "82", "83", "85", "86", "89", "90", "91", "94", "95", "97", "98", "101", "102", "103", "106", "107", "109", "110", "113", "114", "115", "118", "119", "121", "122", "125" ]

[ "nonn", "easy" ]

16

1

2

[ "A000035", "A064989", "A252463", "A359374", "A359375", "A359376", "A359380" ]

null

Antti Karttunen, Dec 31 2022

2023-01-24T02:50:23

oeisdata/seq/A359/A359375.seq

f8b7db5110ea84967828776053be51b6

A359376

Numbers that are either odd multiples of 3 or multiples of 4. Numbers k such that A252463(k) is even.

[ "0", "3", "4", "8", "9", "12", "15", "16", "20", "21", "24", "27", "28", "32", "33", "36", "39", "40", "44", "45", "48", "51", "52", "56", "57", "60", "63", "64", "68", "69", "72", "75", "76", "80", "81", "84", "87", "88", "92", "93", "96", "99", "100", "104", "105", "108", "111", "112", "116", "117", "120", "123", "124", "128", "129", "132", "135", "136", "140", "141", "144", "147", "148", "152", "153", "156", "159", "160", "164", "165" ]

[ "nonn", "easy" ]

16

1

2

[ "A000035", "A008586", "A016945", "A064989", "A252463", "A359374", "A359375", "A359376", "A359379" ]

null

Antti Karttunen, Dec 31 2022

2023-01-24T02:50:30

oeisdata/seq/A359/A359376.seq

486dad525bce1b237083a9bd64c82792

A359377

a(n) = 1 if 3*n is squarefree, otherwise 0.

[ "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0" ]

[ "nonn", "mult" ]

28

1

null

[ "A000035", "A008966", "A011655", "A055615", "A088245", "A156277", "A261034", "A323239", "A349125", "A353627", "A359377", "A359378", "A365428" ]

null

Antti Karttunen, Dec 29 2022

2023-09-16T16:03:07

oeisdata/seq/A359/A359377.seq

9912afcb24ef3885baca500555ee2bca

A359378

Dirichlet inverse of A359377, where A359377(n) = 1 if 3*n is squarefree, otherwise 0.

[ "1", "-1", "0", "1", "-1", "0", "-1", "-1", "0", "1", "-1", "0", "-1", "1", "0", "1", "-1", "0", "-1", "-1", "0", "1", "-1", "0", "1", "1", "0", "-1", "-1", "0", "-1", "-1", "0", "1", "1", "0", "-1", "1", "0", "1", "-1", "0", "-1", "-1", "0", "1", "-1", "0", "1", "-1", "0", "-1", "-1", "0", "1", "1", "0", "1", "-1", "0", "-1", "1", "0", "1", "1", "0", "-1", "-1", "0", "-1", "-1", "0", "-1", "1", "0", "-1", "1", "0", "-1", "-1", "0", "1", "-1", "0", "1", "1", "0", "1", "-1", "0", "1", "-1", "0", "1", "1", "0", "-1", "-1", "0", "1", "-1", "0", "-1", "1", "0", "1" ]

[ "sign", "mult" ]

20

1

null

[ "A001651", "A008585", "A008836", "A011655", "A156277", "A166698", "A358839", "A359170", "A359171", "A359172", "A359377", "A359378", "A359381" ]

null

Antti Karttunen, Dec 29 2022

2023-01-03T09:21:28

oeisdata/seq/A359/A359378.seq

6c2fa52be6585fee146bd12e6fcc3988

A359379

a(n) = 1 if n is either a multiple of 4, or an odd multiple of 3, otherwise 0.

[ "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1" ]

[ "nonn", "easy" ]

17

0

null

[ "A079979", "A121262", "A359374", "A359375", "A359376", "A359379" ]

null

Antti Karttunen, Dec 31 2022

2023-01-24T02:50:36

oeisdata/seq/A359/A359379.seq

224b39d39c38a433b3c0ac532ee3032c

A359380

Numbers that are neither multiples of 3 nor of the form 4u+2.

[ "1", "4", "5", "7", "8", "11", "13", "16", "17", "19", "20", "23", "25", "28", "29", "31", "32", "35", "37", "40", "41", "43", "44", "47", "49", "52", "53", "55", "56", "59", "61", "64", "65", "67", "68", "71", "73", "76", "77", "79", "80", "83", "85", "88", "89", "91", "92", "95", "97", "100", "101", "103", "104", "107", "109", "112", "113", "115", "116", "119", "121", "124", "125", "127", "128", "131", "133", "136", "137", "139", "140" ]

[ "nonn", "easy" ]

18

1

2

[ "A010892", "A057079", "A187074", "A359375", "A359380" ]

null

Antti Karttunen, Dec 31 2022

2024-07-10T16:48:13

oeisdata/seq/A359/A359380.seq

d50b203641cf643e3d248bad1b66dcb8

A359381

Nonmultiples of 3 that have an odd number of prime factors (with multiplicity).

[ "2", "5", "7", "8", "11", "13", "17", "19", "20", "23", "28", "29", "31", "32", "37", "41", "43", "44", "47", "50", "52", "53", "59", "61", "67", "68", "70", "71", "73", "76", "79", "80", "83", "89", "92", "97", "98", "101", "103", "107", "109", "110", "112", "113", "116", "124", "125", "127", "128", "130", "131", "137", "139", "148", "149", "151", "154", "157", "163", "164", "167", "170", "172", "173", "175", "176", "179", "181", "182" ]

[ "nonn" ]

12

1

[ "A001651", "A008836", "A010872", "A026424", "A359171", "A359172", "A359373", "A359378", "A359381" ]

null

Antti Karttunen, Dec 30 2022

2023-02-23T09:43:38

oeisdata/seq/A359/A359381.seq

91d9b5f2a2b67d4bf42d0e54387e51c1

A359382

a(n) = number of k < t such that rad(k) = rad(t) and k does not divide t, where t = A360768(n) and rad(k) = A007947(k).

[ "1", "1", "1", "2", "2", "4", "2", "1", "1", "1", "4", "2", "2", "4", "1", "1", "1", "1", "3", "1", "3", "2", "8", "1", "2", "1", "7", "2", "1", "2", "5", "2", "1", "1", "3", "3", "1", "6", "1", "1", "5", "5", "4", "5", "1", "1", "4", "8", "3", "3", "1", "2", "1", "4", "2", "3", "5", "10", "2", "1", "3", "3", "1", "1", "1", "6", "1", "3", "7", "1", "1", "7", "3", "14", "3", "6", "3", "2", "1", "1", "2", "7", "2", "1", "1", "2", "2", "8", "4", "6", "4", "8", "1", "1", "2", "1", "6", "9", "2", "1" ]

[ "nonn" ]

16

1

4

[ "A007947", "A010846", "A013929", "A020639", "A024619", "A027750", "A126706", "A162306", "A243822", "A272618", "A355432", "A359382", "A359929", "A360589", "A360768" ]

null

Michael De Vlieger, Mar 29 2023

2023-04-01T13:29:08

oeisdata/seq/A359/A359382.seq

deda77c221d4456470a1fe4f78dbaf89

A359383

Allan W. Johnson, Jr.'s 4 X 4 magic square of squares.

[ "900", "60516", "29584", "2025", "8649", "13456", "4356", "66564", "15876", "19044", "56169", "1936", "67600", "9", "2916", "22500" ]

[ "nonn", "fini", "full" ]

19

1

[ "A271580", "A359383" ]

null

Robert C. Lyons, Dec 28 2022

2024-02-12T08:39:17

oeisdata/seq/A359/A359383.seq

5714ed75b9e5ad0f059e1171cb9e3e38

A359384

a(1) = 0. If a(n-1) is a first occurrence, a(n) = A000120(a(n-1)). Otherwise, if a(n-1) is a repeat of a prior terms, a(n) = number of indices j < n such that a(j) = a(n-1).

[ "0", "0", "2", "1", "1", "2", "2", "3", "2", "4", "1", "3", "2", "5", "2", "6", "2", "7", "3", "3", "4", "2", "8", "1", "4", "3", "5", "2", "9", "2", "10", "2", "11", "3", "6", "2", "12", "2", "13", "3", "7", "2", "14", "3", "8", "2", "15", "4", "4", "5", "3", "9", "2", "16", "1", "5", "4", "6", "3", "10", "2", "17", "2", "18", "2", "19", "3", "11", "2", "20", "2", "21", "3", "12", "2", "22", "3", "13", "2", "23", "4" ]

[ "nonn" ]

15

1

3

[ "A000120", "A359384" ]

null

David James Sycamore, Dec 27 2022

2023-01-14T08:44:57

oeisdata/seq/A359/A359384.seq

62d40720152f4fbf93c206fda6d6c9d1

A359385

The lexicographically earliest "Increasing Term Fractal Jump Sequence" that does not use the digit 0 in any terms.

[ "1", "2", "21", "22", "23", "112", "122", "132", "133", "134", "141", "221", "311", "2112", "2113", "3111", "21111", "31113", "31114", "31124", "31131", "34111", "41121", "42111", "43111", "111121", "111122", "112111", "112311", "131111", "211112", "211113", "1111311", "1111312", "3111311", "3111312", "4111131", "4111132", "4141111" ]

[ "nonn", "base" ]

15

1

2

[ "A105395", "A105396", "A105397", "A105398", "A105647", "A359385" ]

null

Tyler Busby, Dec 29 2022

2022-12-31T10:49:54

oeisdata/seq/A359/A359385.seq

917f6d3761e862f86f4399b41c0b14f0

A359386

a(n) is the least positive integer that can be expressed as the sum of one or more consecutive prime powers (not including 1) in exactly n ways.

[ "1", "2", "5", "9", "29", "1027", "6659", "13560", "2149512", "38239583" ]

[ "nonn", "more" ]

24

0

2

[ "A054859", "A246655", "A359386" ]

null

Ilya Gutkovskiy, Mar 13 2023

2023-03-14T09:27:44

oeisdata/seq/A359/A359386.seq

f1dc8bf881983e34513bc46efc17ce5b

A359387

Primes p such that the smallest prime factor of (2^(p-1)-1)/(3*p) is greater than p.

[ "11", "23", "47", "59", "83", "107", "167", "179", "227", "263", "347", "359", "383", "443", "467", "479", "503", "563", "587", "647", "719", "839", "863", "887", "983", "1019", "1187", "1283", "1307", "1319", "1367", "1439", "1487", "1523", "1619", "1823", "1847", "1907", "2027", "2039", "2063", "2099", "2207", "2243", "2447", "2459", "2579", "2687", "2699" ]

[ "nonn" ]

45

1

[ "A068231", "A096060", "A358527", "A359387" ]

null

Alain Rocchelli, Dec 29 2022

2023-01-21T02:40:31

oeisdata/seq/A359/A359387.seq

dc90ef7ed138a2b53b95cacd8140863a

A359388

a(n) is the number of compositions of n into prime parts, with the 1st part equal to 2, the 2nd part less than or equal to 3, ..., and the k-th part less than or equal to prime(k), and so on.

[ "1", "0", "1", "0", "1", "1", "1", "2", "2", "4", "5", "7", "11", "15", "24", "33", "50", "73", "105", "159", "229", "342", "501", "738", "1094", "1604", "2378", "3499", "5166", "7627", "11243", "16610", "24494", "36165", "53376", "78775", "116301", "171642", "253398", "374034", "552139", "815079", "1203166", "1776174", "2621938", "3870572", "5713798", "8434744" ]

[ "nonn" ]

33

0

8

[ "A000040", "A004526", "A023360", "A078974", "A326178", "A359328", "A359388" ]

null

Stefano Spezia, Dec 29 2022

2023-01-01T14:49:39

oeisdata/seq/A359/A359388.seq

d1b026fbfbb2209101617d873537ea5f

A359389

Maximal coefficient of Product_{k=1..n} (1 + 2*x^k).

[ "1", "2", "4", "8", "16", "32", "72", "176", "384", "976", "2496", "6560", "17152", "45952", "123520", "336640", "920832", "2526976", "6979584", "19379712", "53966336", "150892544", "423132160", "1190260736", "3356964864", "9491228672", "26889519104", "76351971328", "217229369344", "619159953408", "1767696515072", "5054679908352" ]

[ "nonn" ]

11

0

2

[ "A025591", "A032302", "A160235", "A359389" ]

null

Vaclav Kotesovec, Dec 29 2022

2022-12-30T01:14:35

oeisdata/seq/A359/A359389.seq

c1d79d9e928bf2853f20d9a4e18521f6

A359390

Sequence lists the numbers k such that bottom entry is an integer in the ratio d(i+1)/d(i) triangle of the elements in the divisors of n, where d(1) < d(2) < ... < d(q) denote the divisors of k.

[ "1", "2", "3", "4", "5", "7", "8", "9", "11", "13", "16", "17", "19", "23", "25", "27", "29", "31", "32", "36", "37", "41", "43", "47", "49", "53", "59", "61", "64", "67", "71", "73", "79", "81", "83", "89", "97", "100", "101", "103", "107", "109", "113", "121", "125", "127", "128", "131", "137", "139", "144", "149", "151", "157", "163", "167", "169", "173", "179", "181", "191", "193" ]

[ "nonn" ]

54

1

2

[ "A000290", "A000961", "A323306", "A359390" ]

null

Michel Lagneau, Jan 03 2023

2023-01-28T12:17:00

oeisdata/seq/A359/A359390.seq

97048064cd39c25337292f0fecb178fb

A359391

a(n) is the smallest number which can be represented as the sum of n distinct positive Fibonacci numbers (1 is allowed twice as a part) in exactly n ways, or -1 if no such number exists.

[ "1", "2", "3", "16", "27", "71", "116", "278", "451", "818", "1305", "2169", "3925", "8119", "13117", "23252", "37858", "62999", "101939", "178088", "298357", "484576", "813710", "1613509", "2610739", "4224275", "6845969", "11280196", "19772533", "32524576", "53157802", "85936132" ]

[ "nonn", "more" ]

25

0

2

[ "A000045", "A000121", "A013583", "A083853", "A359391" ]

null

Ilya Gutkovskiy, Dec 29 2022

2023-01-07T11:05:50

oeisdata/seq/A359/A359391.seq

00ffa82bbeccf9c41c872be687ffb581

A359392

Number of trees on n unlabeled nodes with all nodes of degree <= 7.

[ "1", "1", "1", "1", "2", "3", "6", "11", "23", "46", "104", "230", "539", "1270", "3081", "7536", "18785", "47207", "120074", "307739", "795426", "2069248", "5418014", "14263084", "37742929", "100331646", "267854040", "717863832", "1930888297", "5210968114", "14106844554" ]

[ "nonn" ]

18

0

5

[ "A036722", "A144528", "A359392" ]

null

Robert A. Russell, Dec 29 2022

2023-02-12T10:23:31

oeisdata/seq/A359/A359392.seq

ff8659b6f7ca11e8f0d39d3f84e9661a

A359393

a(n) is the number of times A025581(n-1) (runs of k..0) occur among terms a(1..n-1).

[ "0", "0", "2", "1", "1", "2", "0", "2", "2", "3", "0", "1", "4", "3", "4", "0", "2", "2", "6", "3", "5", "1", "1", "2", "3", "7", "5", "5", "1", "1", "3", "2", "5", "8", "7", "5", "1", "2", "1", "5", "2", "5", "10", "9", "5", "1", "1", "2", "1", "8", "2", "5", "12", "12", "5", "1", "1", "2", "2", "1", "10", "2", "5", "15", "15", "5", "0", "2", "1", "2", "2", "1", "12", "2", "5", "19", "17", "6", "3", "0", "2", "1", "2", "2", "2", "13" ]

[ "nonn", "easy" ]

21

1

3

[ "A025581", "A032531", "A342585", "A359393" ]

null

Tamas Sandor Nagy, Dec 29 2022

2024-12-19T11:46:19

oeisdata/seq/A359/A359393.seq

b0acfd9be1b9574ee4350916dee2576b

A359394

Numbers k such that the average of the squares of k consecutive primes starting with 7 is a prime.

[ "3", "4", "7", "9", "24", "28", "3872", "15172", "23440", "1390100", "7031920" ]

[ "nonn", "more" ]

9

1

[ "A359322", "A359394" ]

null

Robert Israel, Dec 29 2022

2022-12-31T15:23:03

oeisdata/seq/A359/A359394.seq

cdac477fa5696f74604bb3959afdff4d

A359395

Least odd prime p in position n in the prime factorization of M(p) = 2^(p - 1) - 1.

[ "3", "5", "17", "13", "71", "37", "157", "61", "211", "313", "1289", "241", "337", "181", "577", "601", "541", "1381", "421", "1201", "1009", "1621", "1873", "3433", "4561", "1801", "3301", "2161", "3061", "5281", "3361", "2521", "7393", "6481", "4201", "4621", "8737", "9181", "6301", "19501", "7561", "16633", "12241", "26881", "15601", "9241", "21001", "14281", "12601", "53551" ]

[ "nonn" ]

34

1

[ "A098102", "A358527", "A359395" ]

null

Jean-Marc Rebert, Dec 31 2022

2023-01-14T12:41:17

oeisdata/seq/A359/A359395.seq

31c12d3794114a381f975a2153d72103

A359396

a(n) is the least k such that k^j+2 is prime for j = 1 to n but not n+1.

[ "5", "9", "105", "3", "909", "4995825", "28212939" ]

[ "nonn", "more" ]

15

1

[ "A087576", "A359396" ]

null

Robert Israel, Dec 29 2022

2023-01-11T08:48:08

oeisdata/seq/A359/A359396.seq

b621793e032a98e9a532f7390bfb2986

A359397

Squarefree numbers with weakly decreasing first differences of 0-prepended prime indices.

[ "1", "2", "3", "5", "6", "7", "11", "13", "15", "17", "19", "21", "23", "29", "30", "31", "35", "37", "41", "43", "47", "53", "55", "59", "61", "65", "67", "71", "73", "77", "79", "83", "89", "91", "97", "101", "103", "105", "107", "109", "113", "119", "127", "131", "133", "137", "139", "143", "149", "151", "157", "163", "167", "173", "179", "181", "187", "191", "193", "197" ]

[ "nonn" ]

7

1

2

[ "A000009", "A000720", "A001221", "A001222", "A005117", "A056239", "A112798", "A253566", "A261079", "A287352", "A296150", "A304818", "A318283", "A325362", "A355536", "A358136", "A358137", "A358169", "A359361", "A359397" ]

null

Gus Wiseman, Dec 31 2022

2023-01-01T19:30:36

oeisdata/seq/A359/A359397.seq

01f8cdbeea2c7990a95ac2fa4f5eefd7

A359398

Number of unlabeled trees covering 2n nodes, half of which are leaves.

[ "0", "1", "2", "8", "32", "158", "833", "4755", "28389", "176542", "1131055", "7432876", "49873477", "340658595", "2362652648", "16605707901", "118082160358", "848399575321", "6152038125538", "44981009272740", "331344933928536", "2457372361637286", "18337490246234464", "137612955519565773", "1038076541372187991" ]

[ "nonn" ]

11

1

3

[ "A000055", "A000088", "A000272", "A001187", "A001349", "A001433", "A002494", "A006125", "A006129", "A014068", "A055290", "A055314", "A163395", "A185650", "A358107", "A358732", "A359398" ]

null

Gus Wiseman, Jan 01 2023

2023-01-02T00:06:07

oeisdata/seq/A359/A359398.seq

d6e942ac6c2f73eb1d8d03e3f662afcf

A359399

a(1) = 1; a(n) = Sum_{k=2..n} k * a(floor(n/k)).

[ "1", "2", "5", "11", "16", "31", "38", "62", "80", "105", "116", "194", "207", "242", "287", "383", "400", "526", "545", "675", "738", "793", "816", "1200", "1250", "1315", "1423", "1605", "1634", "1979", "2010", "2394", "2493", "2578", "2683", "3475", "3512", "3607", "3724", "4364", "4405", "4888", "4931", "5217", "5577", "5692", "5739", "7563", "7661", "8011" ]

[ "nonn" ]

16

1

2

[ "A022825", "A359399" ]

null

Seiichi Manyama, Mar 31 2023

2023-04-01T11:23:52

oeisdata/seq/A359/A359399.seq

c9bc9631f6a219c7f824b9c29e44bc3a

A359400

Sum of positions of zeros in the reversed binary expansion of n, where positions in a sequence are read starting with 1 from the left.

[ "1", "0", "1", "0", "3", "2", "1", "0", "6", "5", "4", "3", "3", "2", "1", "0", "10", "9", "8", "7", "7", "6", "5", "4", "6", "5", "4", "3", "3", "2", "1", "0", "15", "14", "13", "12", "12", "11", "10", "9", "11", "10", "9", "8", "8", "7", "6", "5", "10", "9", "8", "7", "7", "6", "5", "4", "6", "5", "4", "3", "3", "2", "1", "0", "21", "20", "19", "18", "18", "17", "16", "15", "17", "16", "15", "14", "14", "13" ]

[ "nonn", "base" ]

47

0

5

[ "A000120", "A003714", "A023416", "A029931", "A030190", "A030308", "A039004", "A048793", "A059015", "A069010", "A070939", "A073642", "A230877", "A328594", "A328595", "A344618", "A345927", "A359359", "A359400", "A359402", "A359495", "A368494" ]

null

Gus Wiseman, Jan 05 2023

2024-03-23T20:26:12

oeisdata/seq/A359/A359400.seq

3c199ac4c63c0e02de2706a3c570d179