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348
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score
int64
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2.35k
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int64
-14,827
666,262,453B
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1999-12-11 03:00:00
2025-07-19 00:40:46
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A356201
a(n) is the first component x of the distance vector (x,y), x >= y >= 0, between two nodes of an infinite square lattice of one-ohm resistors, such that the resistance R between the two nodes is as close as possible to n ohms, i.e., abs(R - n) is minimized. y is A356202(n).
[ "0", "4", "106", "2384", "51196", "958170", "24341911", "636875169", "14536767750", "285039411789", "6322647312660", "202105291334913" ]
[ "nonn", "hard", "more" ]
18
0
2
[ "A355565", "A355566", "A355567", "A355953", "A355955", "A356201", "A356203", "A356204" ]
null
Hugo Pfoertner, Aug 01 2022
2022-09-09T14:50:44
oeisdata/seq/A356/A356201.seq
c25c57a3d866962893e1085d558809c6
A356202
a(n) is the second component y of the distance vector (x,y), x >= y >= 0, between two nodes of an infinite square lattice of one-ohm resistors, such that the resistance R between the two nodes is as close as possible to n ohms, i.e., abs(R - n) is minimized. x is A356201(n).
[ "0", "2", "8", "606", "24881", "903855", "18345919", "303176603", "7423167971", "247828120179", "6034957650107", "7948827377158" ]
[ "nonn", "hard", "more" ]
11
0
2
[ "A355565", "A355566", "A355567", "A355953", "A355955", "A356202" ]
null
Hugo Pfoertner, Aug 01 2022
2022-09-09T14:50:38
oeisdata/seq/A356/A356202.seq
d13a622d0d5971cf398dbf28feef719a
A356203
a(n) is the first component x of the distance vector (x,y) in an oblique 120-degree coordinate system, 0 <= y <= x, between two nodes of an infinite triangular lattice of one-ohm resistors, such that the resistance R between the two nodes is as close as possible to n ohms, i.e., abs(R - n) is minimized. y is A356204(n).
[ "0", "43", "9615", "2299822", "507491696", "118805048562", "25315296119626", "5959615271620724" ]
[ "nonn", "hard", "more" ]
9
0
2
[ "A355585", "A355586", "A355587", "A355588", "A355589", "A355954", "A356201", "A356202", "A356203" ]
null
Hugo Pfoertner, Aug 13 2022
2022-08-27T13:47:41
oeisdata/seq/A356/A356203.seq
d716306a275af45a47630fa29a463314
A356204
a(n) is the second component y of the distance vector (x,y) in an oblique 120-degree coordinate system, 0 <= y <= x, between two nodes of an infinite triangular lattice of one-ohm resistors, such that the resistance R between the two nodes is as close as possible to n ohms, i.e., abs(R - n) is minimized. x is A356203(n).
[ "0", "18", "2536", "1136101", "119227930", "33636581266", "1774960492720", "685318499093455" ]
[ "nonn", "hard", "more" ]
8
0
2
[ "A355585", "A355586", "A355587", "A355588", "A355589", "A355954", "A356201", "A356202", "A356204" ]
null
Hugo Pfoertner, Aug 13 2022
2022-08-27T13:47:48
oeisdata/seq/A356/A356204.seq
edbddbdab6fcca1a94d6eb33b59f79a7
A356205
T(n,k) are the numerators of the coefficients of the Legendre polynomials of degree n, with increasing exponents, where T(n,k) is a triangle read by rows.
[ "1", "0", "1", "-1", "0", "3", "0", "-3", "0", "5", "3", "0", "-15", "0", "35", "0", "15", "0", "-35", "0", "63", "-5", "0", "105", "0", "-315", "0", "231", "0", "-35", "0", "315", "0", "-693", "0", "429", "35", "0", "-315", "0", "3465", "0", "-3003", "0", "6435", "0", "315", "0", "-1155", "0", "9009", "0", "-6435", "0", "12155", "-63", "0", "3465", "0", "-15015", "0", "45045", "0", "-109395", "0", "46189" ]
[ "sign", "tabl", "frac" ]
5
0
6
[ "A005187", "A100258", "A356205", "A356206" ]
null
Hugo Pfoertner, Jul 29 2022
2022-07-29T14:14:36
oeisdata/seq/A356/A356205.seq
cd491e9dce7de22bc656ee2d324c7568
A356206
T(n,k) are the denominators of the coefficients of the Legendre polynomials of degree n, with increasing exponents, where T(n,k) is a triangle read by rows.
[ "1", "1", "1", "2", "1", "2", "1", "2", "1", "2", "8", "1", "4", "1", "8", "1", "8", "1", "4", "1", "8", "16", "1", "16", "1", "16", "1", "16", "1", "16", "1", "16", "1", "16", "1", "16", "128", "1", "32", "1", "64", "1", "32", "1", "128", "1", "128", "1", "32", "1", "64", "1", "32", "1", "128", "256", "1", "256", "1", "128", "1", "128", "1", "256", "1", "256", "1", "256", "1", "256", "1", "128", "1", "128", "1", "256", "1", "256" ]
[ "nonn", "frac", "tabl" ]
4
0
4
[ "A356205", "A356206" ]
null
Hugo Pfoertner, Jul 29 2022
2022-07-29T14:14:21
oeisdata/seq/A356/A356206.seq
c18c8d357250ccab9d185ec1600fb754
A356207
a(n) is the difference between n! and the next smaller odd squarefree semiprime (A046388).
[ "3", "1", "3", "7", "1", "7", "1", "5", "3", "1", "19", "11", "1", "19", "19", "11", "1", "19", "23", "1", "1", "47", "1", "1", "29", "3", "29", "31", "59", "73", "1", "43", "1", "13", "17", "41", "1", "5", "5", "3", "53", "79", "7", "1", "53", "23", "1", "13", "13", "61", "7", "59", "61", "7", "31", "1", "89", "107", "103", "67", "47", "103", "19", "43", "1", "71", "11", "7", "83", "79", "67", "71", "29" ]
[ "nonn" ]
14
4
1
[ "A000142", "A046388", "A131057", "A356207" ]
null
Hugo Pfoertner, Aug 28 2022
2022-08-29T10:22:48
oeisdata/seq/A356/A356207.seq
cd3d27d5322bc4d5f0709a3886271a65
A356208
a(n) is the number of occurrences of n in A133388.
[ "2", "3", "4", "4", "5", "7", "6", "8", "8", "9", "9", "10", "10", "12", "13", "12", "12", "15", "14", "17", "16", "16", "17", "18", "19", "18", "19", "20", "18", "24", "20", "22", "25", "22", "27", "26", "23", "25", "25", "29", "26", "30", "27", "31", "32", "32", "24", "33", "33", "34", "32", "32", "35", "37", "36", "37", "38", "32", "35", "44", "36", "41", "41", "40", "42", "45", "39", "43", "42" ]
[ "nonn" ]
11
1
1
[ "A000161", "A001481", "A133388", "A356208", "A356209" ]
null
Hugo Pfoertner, Sep 07 2022
2023-11-22T21:34:06
oeisdata/seq/A356/A356208.seq
d5eff6629695a1b96cd6be3fe72b6328
A356209
a(n) is the position of the latest occurrence of n in A133388.
[ "2", "8", "18", "32", "41", "72", "98", "128", "162", "181", "242", "288", "313", "392", "421", "512", "514", "648", "722", "761", "882", "968", "1058", "1152", "1201", "1301", "1458", "1568", "1466", "1741", "1922", "2048", "2178", "2056", "2381", "2592", "2594", "2888", "2817", "3121", "3202", "3528", "3698", "3872", "3789", "4232", "4418", "4608", "4802", "4804", "5101" ]
[ "nonn" ]
10
1
1
[ "A000161", "A001481", "A009003", "A356208", "A356209" ]
null
Hugo Pfoertner, Sep 07 2022
2022-09-09T02:31:06
oeisdata/seq/A356/A356209.seq
9f49c3287a4a3876768de8c5c8ba74f0
A356210
a(n) is the number of tuples (t_1, ..., t_n) with integers 2 <= t_1 <= ... <= t_n such that 2^n + 1 = Product_{i = 1..n} (2 + 1/t_i).
[ "0", "1", "11", "430", "364693" ]
[ "nonn", "hard", "more" ]
12
1
3
[ "A355243", "A355516", "A355626", "A355629", "A356210", "A356211" ]
null
Hugo Pfoertner and Markus Sigg, Aug 27 2022
2024-08-02T12:04:29
oeisdata/seq/A356/A356210.seq
46fa832031e5fc50dc2caca8094e7833
A356211
Odd numbers that cannot be written as a product of an arbitrary number of rational factors of the form 2 + 1/t_k with integers t_k > 1.
[ "3", "7", "13", "15", "27", "29", "31", "53", "57", "59", "61", "63", "107", "123", "127" ]
[ "nonn", "more" ]
12
1
1
[ "A355243", "A355516", "A355626", "A356211" ]
null
Hugo Pfoertner and Markus Sigg, Aug 16 2022
2022-08-24T09:23:16
oeisdata/seq/A356/A356211.seq
7bf62b92ad5fce1f14f7dd98ac5624ed
A356212
Number of edge covers in the n-cycle complement graph bar C_n.
[ "0", "1", "11", "263", "10965", "828185", "117206551", "31833062131", "16861895760945", "17600261657295445", "36430086149957824355", "150088723046184226003199", "1233420904097181936354336237", "20242863089169097481278428598961", "663925026643212111959892436105140751", "43532228537929216561827941013608880940843" ]
[ "nonn" ]
8
3
3
[ "A351587", "A356212", "A377652", "A378862" ]
null
Eric W. Weisstein, Jul 29 2022
2024-12-13T09:31:50
oeisdata/seq/A356/A356212.seq
297edee981652c2cb5c014d3cc041125
A356213
Number of edge covers in the n-trapezohedral graph.
[ "4", "104", "1699", "23904", "317044", "4101107", "52473796", "668177568", "8490113467", "107776172264", "1367566963756", "17349734444643", "220090218116188", "2791852592070632", "35414167120396459", "449219270600324928", "5698208011194600148", "72279907017666274643", "916846410588661477204" ]
[ "nonn" ]
34
1
1
[ "A297047", "A356213" ]
null
Eric W. Weisstein, Jul 29 2022
2024-08-11T22:08:16
oeisdata/seq/A356/A356213.seq
17c517967520eeb2e97ff4d5d8c5e820
A356214
Number of edge covers in the n-Sierpinski gasket graph.
[ "4", "198", "31257772", "119663504378704719130518", "6713329439711345431716916679280868301022936622514475069583264989008212" ]
[ "nonn" ]
11
1
1
null
null
Eric W. Weisstein, Jul 29 2022
2024-12-09T11:03:21
oeisdata/seq/A356/A356214.seq
4c78b171353863ed793d0e9ad51b3a62
A356215
The binary expansion of a(n) is obtained by applying the elementary cellular automaton with rule (2*n) mod 16 to the binary expansion of n.
[ "0", "1", "1", "2", "0", "5", "3", "7", "0", "9", "5", "14", "4", "13", "7", "15", "0", "17", "9", "26", "0", "21", "11", "31", "0", "17", "5", "22", "12", "29", "15", "31", "0", "33", "17", "50", "0", "37", "19", "55", "0", "41", "21", "62", "4", "45", "23", "63", "0", "33", "9", "42", "16", "53", "27", "63", "0", "33", "5", "38", "28", "61", "31", "63", "0", "65", "33", "98", "0", "69", "35", "103" ]
[ "nonn", "base" ]
10
0
4
[ "A352528", "A356195", "A356215" ]
null
Rémy Sigrist, Jul 29 2022
2022-07-31T19:54:45
oeisdata/seq/A356/A356215.seq
8bb43d7816611a43805b44185c6536a2
A356216
Decimal expansion of the real part of the first nontrivial zero of zeta'.
[ "2", "4", "6", "3", "1", "6", "1", "8", "6", "9", "4", "5", "4", "3", "2", "1", "2", "8", "5", "8", "7", "4", "3", "9", "5", "0", "5", "3", "3", "0", "6", "3", "2", "9", "1", "4", "4", "9", "2", "0", "7", "9", "3", "1", "3", "4", "5", "6", "7", "3", "2", "3", "4", "7", "5", "0", "2", "2", "2", "1", "7", "3", "7", "0", "7", "2", "7", "1", "1", "7", "5", "0", "8", "6", "7", "1", "0", "2", "6", "3", "7", "1", "1", "9", "4", "8", "2", "4", "6", "8", "6", "1", "3", "2", "8", "3", "5", "5", "4", "2", "6", "7", "0", "5", "4", "1", "5", "5", "1", "0", "4", "1", "7", "8", "8", "8", "6", "1", "9", "2", "3", "5", "0", "7", "4", "0", "4" ]
[ "nonn", "cons" ]
89
1
1
[ "A356092", "A356216" ]
null
Benoit Cloitre, Aug 13 2022
2022-09-23T17:19:18
oeisdata/seq/A356/A356216.seq
350f91ef35a0014fc68c2a7f820a2943
A356217
a(n) = A022839(A000201(n)).
[ "2", "6", "8", "13", "17", "20", "24", "26", "31", "35", "38", "42", "46", "49", "53", "55", "60", "64", "67", "71", "73", "78", "82", "84", "89", "93", "96", "100", "102", "107", "111", "114", "118", "122", "125", "129", "131", "136", "140", "143", "147", "149", "154", "158", "160", "165", "169", "172", "176", "178", "183", "187", "190", "194", "196", "201", "205", "207" ]
[ "nonn", "easy" ]
22
1
1
[ "A000201", "A001950", "A022839", "A108598", "A190509", "A351415", "A356104", "A356217", "A356218", "A356220" ]
null
Clark Kimberling, Oct 02 2022
2025-03-23T18:24:08
oeisdata/seq/A356/A356217.seq
4cc1c30c6cf235dc840d51659ba072b5
A356218
a(n) = A108598(A000201(n)).
[ "1", "5", "7", "10", "14", "16", "19", "21", "25", "28", "30", "34", "37", "39", "43", "45", "48", "52", "54", "57", "59", "63", "66", "68", "72", "75", "77", "81", "83", "86", "90", "92", "95", "99", "101", "104", "106", "110", "113", "115", "119", "121", "124", "128", "130", "133", "137", "139", "142", "144", "148", "151", "153", "157", "159", "162", "166", "168", "171" ]
[ "nonn", "easy" ]
17
1
2
[ "A000201", "A001950", "A022839", "A108598", "A190509", "A351415", "A356104", "A356217", "A356218", "A356220" ]
null
Clark Kimberling, Oct 02 2022
2025-03-23T18:39:53
oeisdata/seq/A356/A356218.seq
f308b2d18efa1a987dbd8674735e8bc1
A356219
Intersection of A001952 and A003151.
[ "284", "287", "289", "292", "294", "296", "299", "301", "304", "306", "309", "311", "313", "316", "318", "321", "323", "325", "328", "330", "333", "335", "337", "340", "342", "345", "347", "350", "352", "354", "357", "359", "362", "364", "366", "369", "371", "374", "376", "379", "381", "383", "386", "388", "391", "393", "395", "398", "400" ]
[ "nonn", "easy" ]
10
1
1
[ "A001951", "A001952", "A001954", "A003151", "A003152", "A184922", "A341239", "A356219" ]
null
Clark Kimberling, Nov 13 2022
2025-04-13T01:45:55
oeisdata/seq/A356/A356219.seq
a30c740d5772b1aa8c2ef6de07026774
A356220
a(n) = A108598(A001950(n)).
[ "3", "9", "12", "18", "23", "27", "32", "36", "41", "47", "50", "56", "61", "65", "70", "74", "79", "85", "88", "94", "97", "103", "108", "112", "117", "123", "126", "132", "135", "141", "146", "150", "155", "161", "164", "170", "173", "179", "184", "188", "193", "197", "202", "208", "211", "217", "222", "226", "231", "235", "240", "246", "249", "255", "258", "264" ]
[ "nonn", "easy" ]
17
1
1
[ "A000201", "A001950", "A022839", "A108598", "A351415", "A356104", "A356217", "A356218", "A356219", "A356220" ]
null
Clark Kimberling, Nov 13 2022
2025-03-23T18:39:43
oeisdata/seq/A356/A356220.seq
0366d7af438220ef9fff79bf41583532
A356221
Position of second appearance of 2n in the sequence of prime gaps A001223; if 2n does not appear at least twice, a(n) = -1.
[ "3", "6", "11", "72", "42", "47", "62", "295", "180", "259", "297", "327", "446", "462", "650", "1315", "1059", "1532", "4052", "2344", "3732", "3861", "8805", "7234", "4754", "2810", "4231", "14124", "5949", "9834", "17200", "10229", "19724", "25248", "15927", "30765", "42673", "28593", "24554", "50523", "44227", "44390", "29040", "89715", "47350" ]
[ "nonn" ]
8
1
1
[ "A001223", "A028334", "A029709", "A038664", "A066205", "A073491", "A137921", "A193829", "A274121", "A287170", "A328335", "A328457", "A356221", "A356222", "A356223", "A356224", "A356225", "A356226" ]
null
Gus Wiseman, Aug 02 2022
2022-08-08T15:54:44
oeisdata/seq/A356/A356221.seq
bda36e125e424907d0c4b76f465d189e
A356222
Array read by antidiagonals upwards where A(n,k) is the position of the k-th appearance of 2n in the sequence of prime gaps A001223. If A001223 does not contain 2n at least k times, set A(n,k) = -1.
[ "2", "4", "3", "9", "6", "5", "24", "11", "8", "7", "34", "72", "15", "12", "10", "46", "42", "77", "16", "14", "13", "30", "47", "53", "79", "18", "19", "17", "282", "62", "91", "61", "87", "21", "22", "20", "99", "295", "66", "97", "68", "92", "23", "25", "26", "154", "180", "319", "137", "114", "80", "94", "32", "27", "28", "189", "259", "205", "331", "146", "121", "82", "124", "36", "29", "33" ]
[ "nonn", "tabl" ]
9
1
1
[ "A001223", "A028334", "A029707", "A029709", "A038664", "A066205", "A073491", "A119313", "A193829", "A274121", "A287170", "A328457", "A356221", "A356222", "A356223", "A356224", "A356225", "A356226", "A356232" ]
null
Gus Wiseman, Aug 04 2022
2022-08-08T15:54:58
oeisdata/seq/A356/A356222.seq
55c631d21add532b17cc78fffe5e16ab
A356223
Position of n-th appearance of 2n in the sequence of prime gaps (A001223). If 2n does not appear at least n times, set a(n) = -1.
[ "2", "6", "15", "79", "68", "121", "162", "445", "416", "971", "836", "987", "2888", "1891", "1650", "5637", "5518", "4834", "9237", "8152", "10045", "21550", "20248", "20179", "29914", "36070", "24237", "53355", "52873", "34206", "103134", "90190", "63755", "147861", "98103", "117467", "209102", "206423", "124954", "237847", "369223" ]
[ "nonn" ]
6
1
1
[ "A000005", "A001223", "A028334", "A029709", "A038664", "A060681", "A073491", "A119313", "A137921", "A193829", "A274121", "A287170", "A356221", "A356222", "A356223", "A356224", "A356225", "A356226" ]
null
Gus Wiseman, Aug 04 2022
2022-08-08T15:55:04
oeisdata/seq/A356/A356223.seq
6f5d9fac388e8eef7e781548fb33790f
A356224
Number of divisors of n whose prime indices cover an initial interval of positive integers.
[ "1", "2", "1", "3", "1", "3", "1", "4", "1", "2", "1", "5", "1", "2", "1", "5", "1", "4", "1", "3", "1", "2", "1", "7", "1", "2", "1", "3", "1", "4", "1", "6", "1", "2", "1", "7", "1", "2", "1", "4", "1", "3", "1", "3", "1", "2", "1", "9", "1", "2", "1", "3", "1", "5", "1", "4", "1", "2", "1", "7", "1", "2", "1", "7", "1", "3", "1", "3", "1", "2", "1", "10", "1", "2", "1", "3", "1", "3", "1", "5", "1", "2", "1", "5", "1", "2", "1" ]
[ "nonn" ]
8
1
2
[ "A000005", "A001222", "A001223", "A028334", "A029709", "A055874", "A055932", "A056239", "A070824", "A073491", "A073492", "A112798", "A119313", "A137921", "A287170", "A289509", "A328338", "A356223", "A356224", "A356225", "A356226" ]
null
Gus Wiseman, Aug 04 2022
2022-08-08T16:02:47
oeisdata/seq/A356/A356224.seq
7656875b8be2cc269ffbbcaa675557e9
A356225
Number of divisors of n whose prime indices do not cover an initial interval of positive integers.
[ "0", "0", "1", "0", "1", "1", "1", "0", "2", "2", "1", "1", "1", "2", "3", "0", "1", "2", "1", "3", "3", "2", "1", "1", "2", "2", "3", "3", "1", "4", "1", "0", "3", "2", "3", "2", "1", "2", "3", "4", "1", "5", "1", "3", "5", "2", "1", "1", "2", "4", "3", "3", "1", "3", "3", "4", "3", "2", "1", "5", "1", "2", "5", "0", "3", "5", "1", "3", "3", "6", "1", "2", "1", "2", "5", "3", "3", "5", "1", "5", "4", "2", "1", "7", "3", "2", "3" ]
[ "nonn" ]
12
1
9
[ "A000005", "A001222", "A001223", "A028334", "A055874", "A055932", "A056239", "A070824", "A073491", "A073492", "A080259", "A112798", "A119313", "A137921", "A287170", "A328338", "A356224", "A356225", "A356226", "A356233", "A356237" ]
null
Gus Wiseman, Aug 13 2022
2024-01-23T16:18:08
oeisdata/seq/A356/A356225.seq
381fe0e67695b5ec6124c00bf8243391
A356226
Irregular triangle giving the lengths of maximal gapless submultisets of the prime indices of n.
[ "1", "1", "2", "1", "2", "1", "3", "2", "1", "1", "1", "3", "1", "1", "1", "2", "4", "1", "3", "1", "2", "1", "1", "1", "1", "1", "1", "4", "2", "1", "1", "3", "2", "1", "1", "3", "1", "5", "1", "1", "1", "1", "2", "4", "1", "1", "1", "1", "1", "3", "1", "1", "2", "1", "1", "2", "1", "3", "1", "1", "1", "5", "2", "1", "2", "1", "1", "2", "1", "1", "4", "1", "1", "3", "1", "1", "1", "1", "1", "1", "4", "1", "1", "1", "2", "1", "6" ]
[ "nonn", "tabf" ]
11
1
3
[ "A000005", "A001221", "A001222", "A001223", "A001414", "A003963", "A028334", "A055874", "A056239", "A060680", "A060683", "A066205", "A073491", "A073492", "A073493", "A073495", "A112798", "A132747", "A132881", "A137921", "A193829", "A286470", "A287170", "A328166", "A356069", "A356224", "A356225", "A356226", "A356227", "A356228", "A356229", "A356230", "A356231", "A356232" ]
null
Gus Wiseman, Aug 10 2022
2022-08-13T22:24:56
oeisdata/seq/A356/A356226.seq
8951110129e9f8821c329b13935ac2af
A356227
Smallest size of a maximal gapless submultiset of the prime indices of n.
[ "0", "1", "1", "2", "1", "2", "1", "3", "2", "1", "1", "3", "1", "1", "2", "4", "1", "3", "1", "1", "1", "1", "1", "4", "2", "1", "3", "1", "1", "3", "1", "5", "1", "1", "2", "4", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "5", "2", "1", "1", "1", "1", "4", "1", "1", "1", "1", "1", "4", "1", "1", "1", "6", "1", "1", "1", "1", "1", "1", "1", "5", "1", "1", "3", "1", "2", "1", "1", "1", "4", "1", "1", "1", "1", "1", "1" ]
[ "nonn" ]
8
1
4
[ "A000005", "A000079", "A001221", "A001222", "A001223", "A001414", "A003963", "A028334", "A055874", "A056239", "A060680", "A060683", "A066205", "A073491", "A073492", "A073495", "A112798", "A132747", "A132881", "A137921", "A193829", "A286470", "A287170", "A356224", "A356225", "A356226", "A356227", "A356228", "A356229", "A356232" ]
null
Gus Wiseman, Aug 13 2022
2022-08-13T22:24:52
oeisdata/seq/A356/A356227.seq
ef45352727ed1f53ff2926221a7b304c
A356228
Greatest size of a gapless submultiset of the prime indices of n.
[ "0", "1", "1", "2", "1", "2", "1", "3", "2", "1", "1", "3", "1", "1", "2", "4", "1", "3", "1", "2", "1", "1", "1", "4", "2", "1", "3", "2", "1", "3", "1", "5", "1", "1", "2", "4", "1", "1", "1", "3", "1", "2", "1", "2", "3", "1", "1", "5", "2", "2", "1", "2", "1", "4", "1", "3", "1", "1", "1", "4", "1", "1", "2", "6", "1", "2", "1", "2", "1", "2", "1", "5", "1", "1", "3", "2", "2", "2", "1", "4", "4", "1", "1", "3", "1", "1", "1" ]
[ "nonn" ]
6
1
4
[ "A000005", "A000079", "A001221", "A001222", "A001223", "A001414", "A003963", "A028334", "A055874", "A056239", "A060680", "A060683", "A066205", "A073491", "A073492", "A073495", "A112798", "A132747", "A132881", "A137921", "A193829", "A286470", "A287170", "A328162", "A328457", "A356069", "A356224", "A356225", "A356226", "A356227", "A356228", "A356229", "A356232" ]
null
Gus Wiseman, Aug 13 2022
2022-08-14T10:20:28
oeisdata/seq/A356/A356228.seq
f80e46b044e2565a2506447c43116471
A356229
Number of maximal gapless submultisets of the prime indices of 2n.
[ "1", "1", "1", "1", "2", "1", "2", "1", "1", "2", "2", "1", "2", "2", "1", "1", "2", "1", "2", "2", "2", "2", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "2", "2", "1", "2", "2", "2", "2", "2", "2", "2", "2", "1", "2", "2", "1", "2", "2", "2", "2", "2", "1", "3", "2", "2", "2", "2", "1", "2", "2", "2", "1", "3", "2", "2", "2", "2", "2", "2", "1", "2", "2", "1", "2", "2", "2", "2", "2", "1", "2", "2", "2", "3", "2", "2", "2", "2", "1", "3", "2", "2", "2", "3", "1", "2", "2", "2", "2", "2", "2", "2", "2", "1" ]
[ "nonn" ]
12
1
5
[ "A000005", "A001221", "A001222", "A001414", "A003963", "A056239", "A060680", "A060681", "A066205", "A073093", "A073491", "A073492", "A073495", "A112798", "A132747", "A132881", "A286470", "A287170", "A289509", "A356226", "A356227", "A356228", "A356229", "A356230", "A356231", "A356232" ]
null
Gus Wiseman, Aug 16 2022
2025-01-19T09:26:33
oeisdata/seq/A356/A356229.seq
cc44b9461b60a2da43bf64af49c19eab
A356230
The a(n)-th composition in standard order is the sequence of lengths of maximal gapless submultisets of the prime indices of n.
[ "0", "1", "1", "2", "1", "2", "1", "4", "2", "3", "1", "4", "1", "3", "2", "8", "1", "4", "1", "5", "3", "3", "1", "8", "2", "3", "4", "5", "1", "4", "1", "16", "3", "3", "2", "8", "1", "3", "3", "9", "1", "5", "1", "5", "4", "3", "1", "16", "2", "6", "3", "5", "1", "8", "3", "9", "3", "3", "1", "8", "1", "3", "5", "32", "3", "5", "1", "5", "3", "6", "1", "16", "1", "3", "4", "5", "2", "5", "1", "17", "8", "3", "1", "9", "3" ]
[ "nonn" ]
7
1
4
[ "A000120", "A001221", "A001222", "A001414", "A003963", "A056239", "A060680", "A060683", "A066099", "A066205", "A073491", "A073495", "A112798", "A132747", "A132881", "A286470", "A287170", "A328166", "A333627", "A356069", "A356224", "A356225", "A356226", "A356227", "A356228", "A356229", "A356230", "A356231", "A356232", "A356603" ]
null
Gus Wiseman, Aug 16 2022
2022-08-20T23:20:32
oeisdata/seq/A356/A356230.seq
df401a8aff9aff4a647f8c86ad19b80a
A356231
Heinz number of the sequence (A356226) of lengths of maximal gapless submultisets of the prime indices of n.
[ "1", "2", "2", "3", "2", "3", "2", "5", "3", "4", "2", "5", "2", "4", "3", "7", "2", "5", "2", "6", "4", "4", "2", "7", "3", "4", "5", "6", "2", "5", "2", "11", "4", "4", "3", "7", "2", "4", "4", "10", "2", "6", "2", "6", "5", "4", "2", "11", "3", "6", "4", "6", "2", "7", "4", "10", "4", "4", "2", "7", "2", "4", "6", "13", "4", "6", "2", "6", "4", "6", "2", "11", "2", "4", "5", "6", "3", "6", "2", "14", "7", "4", "2", "10" ]
[ "nonn" ]
7
1
2
[ "A000005", "A001221", "A001222", "A001414", "A003963", "A055932", "A056239", "A060680", "A060683", "A066205", "A073491", "A073492", "A073493", "A073495", "A112798", "A132747", "A132881", "A193829", "A286470", "A287170", "A328166", "A356069", "A356224", "A356225", "A356226", "A356227", "A356228", "A356229", "A356230", "A356231", "A356232", "A356233", "A356237", "A356603" ]
null
Gus Wiseman, Aug 18 2022
2022-08-21T14:13:31
oeisdata/seq/A356/A356231.seq
8e9fcf3f1ee648164c67c1645e598b28
A356232
Numbers whose prime indices are all odd and cover an initial interval of odd positive integers.
[ "1", "2", "4", "8", "10", "16", "20", "32", "40", "50", "64", "80", "100", "110", "128", "160", "200", "220", "250", "256", "320", "400", "440", "500", "512", "550", "640", "800", "880", "1000", "1024", "1100", "1210", "1250", "1280", "1600", "1760", "1870", "2000", "2048", "2200", "2420", "2500", "2560", "2750", "3200", "3520", "3740", "4000", "4096", "4400" ]
[ "nonn" ]
8
1
2
[ "A000005", "A001221", "A001222", "A001223", "A001414", "A003963", "A028334", "A053251", "A055932", "A056239", "A061395", "A066205", "A066208", "A073491", "A073492", "A073493", "A112798", "A132747", "A137921", "A193829", "A286470", "A287170", "A356224", "A356226", "A356227", "A356228", "A356229", "A356230", "A356231", "A356232", "A356237", "A356603" ]
null
Gus Wiseman, Aug 20 2022
2022-08-27T21:30:27
oeisdata/seq/A356/A356232.seq
9f0d1755baccc9825ca65aee18e02e2b
A356233
Number of integer factorizations of n into gapless numbers (A066311).
[ "1", "1", "1", "2", "1", "2", "1", "3", "2", "1", "1", "4", "1", "1", "2", "5", "1", "4", "1", "2", "1", "1", "1", "7", "2", "1", "3", "2", "1", "4", "1", "7", "1", "1", "2", "9", "1", "1", "1", "3", "1", "2", "1", "2", "4", "1", "1", "12", "2", "2", "1", "2", "1", "7", "1", "3", "1", "1", "1", "8", "1", "1", "2", "11", "1", "2", "1", "2", "1", "2", "1", "16", "1", "1", "4", "2", "2", "2", "1", "5", "5", "1", "1", "4", "1", "1" ]
[ "nonn" ]
6
1
4
[ "A000005", "A001055", "A001221", "A001222", "A001414", "A003963", "A060680", "A060683", "A073491", "A073495", "A132747", "A132881", "A193829", "A287170", "A328195", "A328335", "A328458", "A356069", "A356224", "A356225", "A356226", "A356227", "A356228", "A356229", "A356230", "A356231", "A356232", "A356233", "A356234" ]
null
Gus Wiseman, Aug 28 2022
2022-08-30T09:41:27
oeisdata/seq/A356/A356233.seq
ed721989fce812fdd20220cc07d20681
A356234
Irregular triangle read by rows where row n is the ordered factorization of n into maximal gapless divisors.
[ "2", "3", "4", "5", "6", "7", "8", "9", "2", "5", "11", "12", "13", "2", "7", "15", "16", "17", "18", "19", "4", "5", "3", "7", "2", "11", "23", "24", "25", "2", "13", "27", "4", "7", "29", "30", "31", "32", "3", "11", "2", "17", "35", "36", "37", "2", "19", "3", "13", "8", "5", "41", "6", "7", "43", "4", "11", "45", "2", "23", "47", "48", "49", "2", "25", "3", "17", "4", "13", "53", "54", "5", "11", "8" ]
[ "nonn", "tabf" ]
5
1
1
[ "A000005", "A001055", "A001221", "A001222", "A001414", "A003963", "A056239", "A060680", "A060683", "A066205", "A073491", "A073495", "A112798", "A132747", "A132881", "A193829", "A287170", "A330103", "A356069", "A356224", "A356225", "A356226", "A356227", "A356229", "A356232", "A356233", "A356234", "A356237" ]
null
Gus Wiseman, Aug 28 2022
2022-08-30T09:41:31
oeisdata/seq/A356/A356234.seq
2e7a81919dfe7b09da3ebe0b3124e310
A356235
Number of integer partitions of n with a neighborless singleton.
[ "0", "1", "1", "1", "2", "3", "5", "8", "12", "16", "25", "33", "45", "62", "84", "109", "148", "192", "251", "325", "421", "536", "690", "870", "1100", "1385", "1739", "2161", "2697", "3334", "4121", "5071", "6228", "7609", "9303", "11308", "13732", "16629", "20101", "24206", "29140", "34957", "41882", "50060", "59745", "71124", "84598", "100365" ]
[ "nonn" ]
7
0
5
[ "A000009", "A000041", "A000837", "A007690", "A066205", "A183558", "A289509", "A325160", "A328171", "A328172", "A328187", "A328221", "A355393", "A355394", "A356233", "A356235", "A356236", "A356237", "A356606", "A356607" ]
null
Gus Wiseman, Aug 23 2022
2022-08-25T08:33:36
oeisdata/seq/A356/A356235.seq
bd2624b2c516f16fd9441138bd4a8c27
A356236
Number of integer partitions of n with a neighborless part.
[ "0", "1", "2", "2", "4", "4", "8", "9", "16", "20", "31", "40", "59", "76", "105", "138", "184", "238", "311", "400", "515", "656", "831", "1052", "1322", "1659", "2064", "2572", "3182", "3934", "4837", "5942", "7264", "8872", "10789", "13109", "15865", "19174", "23105", "27796", "33361", "39956", "47766", "56985", "67871", "80675", "95750", "113416" ]
[ "nonn" ]
11
0
3
[ "A000009", "A000041", "A000837", "A007690", "A066205", "A112798", "A183558", "A289509", "A319630", "A325160", "A328171", "A328172", "A328187", "A328221", "A355393", "A355394", "A356235", "A356236", "A356237", "A356606", "A356607", "A356736" ]
null
Gus Wiseman, Aug 24 2022
2024-02-17T14:08:09
oeisdata/seq/A356/A356236.seq
1b64a3a17f892a9cddd4717c5f1ff9af
A356237
Heinz numbers of integer partitions with a neighborless singleton.
[ "2", "3", "5", "7", "10", "11", "13", "14", "17", "19", "20", "21", "22", "23", "26", "28", "29", "31", "33", "34", "37", "38", "39", "40", "41", "42", "43", "44", "46", "47", "50", "51", "52", "53", "55", "56", "57", "58", "59", "61", "62", "63", "65", "66", "67", "68", "69", "70", "71", "73", "74", "76", "78", "79", "80", "82", "83", "84", "85", "86", "87", "88", "89", "91", "92", "93" ]
[ "nonn" ]
11
1
1
[ "A001221", "A001222", "A001414", "A003963", "A007690", "A056239", "A073491", "A073492", "A112798", "A132747", "A132881", "A183558", "A286470", "A289508", "A325160", "A328166", "A328335", "A355393", "A355394", "A356069", "A356224", "A356225", "A356231", "A356233", "A356234", "A356235", "A356236", "A356237", "A356606", "A356607", "A356734" ]
null
Gus Wiseman, Aug 24 2022
2022-08-26T23:40:50
oeisdata/seq/A356/A356237.seq
e9a1e115cde983c3d1cd04f0d6ffe248
A356238
a(n) = Sum_{k=1..n} (k * floor(n/k))^n.
[ "1", "8", "62", "849", "8541", "206345", "2581403", "76623522", "1617299079", "49463993875", "952905453423", "59000021366675", "1198427462876421", "54128102218676115", "2321105129608323165", "117387839988330848902", "3205342976298888473968", "268263812478494295219717" ]
[ "nonn" ]
18
1
2
[ "A007778", "A350109", "A350125", "A356238", "A356239", "A356240" ]
null
Seiichi Manyama, Jul 30 2022
2022-08-02T10:37:59
oeisdata/seq/A356/A356238.seq
67e044243ed7e8170f704b4644e69367
A356239
a(n) = Sum_{k=1..n} k^n * sigma_0(k).
[ "1", "9", "71", "963", "9873", "231749", "2976863", "86348423", "1824883450", "55584932826", "1104642697680", "64932555347084", "1366828157222090", "61273696016238014", "2581786206601959958", "129797968403021602450", "3678372903755436314440", "295835829367866540495396" ]
[ "nonn" ]
25
1
2
[ "A000005", "A319194", "A356129", "A356239", "A356243" ]
null
Seiichi Manyama, Jul 30 2022
2024-01-21T18:10:13
oeisdata/seq/A356/A356239.seq
1982620fc7be89189c4908fd3742780c
A356240
a(n) = Sum_{k=1..n} (k-1)^n * Sum_{j=1..floor(n/k)} j^n.
[ "0", "1", "9", "114", "1332", "25404", "395460", "9724901", "207584371", "6120938951", "151737244257", "5932533980409", "168400694345669", "7145593797561899", "260681076993636793", "12410128414690753548", "473029927456547840472", "27572016889372245275679" ]
[ "nonn" ]
17
1
3
[ "A356131", "A356238", "A356239", "A356240", "A356244" ]
null
Seiichi Manyama, Jul 30 2022
2022-07-30T14:14:16
oeisdata/seq/A356/A356240.seq
ad8aa4b9bf07150ee6196b0617954136
A356241
a(n) is the number of distinct Fermat numbers dividing n.
[ "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "1", "0", "0", "2", "0", "1", "1", "0", "1", "1", "0", "0", "1", "1", "0", "1", "0", "0", "2", "0", "0", "1", "1", "1", "1", "0", "0", "1", "1", "0", "1", "0", "0", "2", "0", "0", "1", "0", "1", "2", "0", "0", "1", "1", "0", "1", "0", "0", "2", "0", "0", "1", "0", "1", "1", "0", "1", "1", "1", "0", "1", "0", "0", "2", "0", "0", "1", "0", "1", "1", "0", "0", "1", "2", "0", "1" ]
[ "nonn" ]
12
1
15
[ "A000215", "A007404", "A051158", "A051179", "A080307", "A080308", "A356241", "A356242" ]
null
Amiram Eldar, Jul 30 2022
2025-02-16T08:34:03
oeisdata/seq/A356/A356241.seq
6fb849aa59f7fdf72b8f64e358355541
A356242
a(n) is the number of Fermat numbers dividing n, counted with multiplicity.
[ "0", "0", "1", "0", "1", "1", "0", "0", "2", "1", "0", "1", "0", "0", "2", "0", "1", "2", "0", "1", "1", "0", "0", "1", "2", "0", "3", "0", "0", "2", "0", "0", "1", "1", "1", "2", "0", "0", "1", "1", "0", "1", "0", "0", "3", "0", "0", "1", "0", "2", "2", "0", "0", "3", "1", "0", "1", "0", "0", "2", "0", "0", "2", "0", "1", "1", "0", "1", "1", "1", "0", "2", "0", "0", "3", "0", "0", "1", "0", "1", "4", "0", "0", "1", "2", "0", "1" ]
[ "nonn" ]
11
1
9
[ "A000215", "A000244", "A007404", "A051158", "A051179", "A080307", "A080308", "A169594", "A356241", "A356242" ]
null
Amiram Eldar, Jul 30 2022
2025-02-16T08:34:03
oeisdata/seq/A356/A356242.seq
e7efa025f180ef313437aeb480ab8efe
A356243
a(n) = Sum_{k=1..n} k^2 * sigma_{n-2}(k).
[ "1", "9", "49", "447", "4607", "71009", "1210855", "24980627", "575624572", "14958422046", "427890493960", "13431874937840", "457651929853662", "16844143705998554", "665499756005678382", "28102799297908820326", "1262909308355648335240", "60183118566605371095996" ]
[ "nonn" ]
16
1
2
[ "A000330", "A319194", "A356129", "A356239", "A356243" ]
null
Seiichi Manyama, Jul 30 2022
2023-10-21T19:38:55
oeisdata/seq/A356/A356243.seq
811b7750a4709fec6f9e7a67e79f281b
A356244
a(n) = Sum_{k=1..n} (k-1)^n * Sum_{j=1..floor(n/k)} j^2.
[ "0", "1", "9", "102", "1304", "20784", "377286", "7934693", "186969913", "4918785791", "142381832107", "4506907611825", "154723950495961", "5729421493899419", "227586600129484543", "9654927881195999544", "435660032125475809618", "20836109197604840372979", "1052865018045922422499409" ]
[ "nonn" ]
15
1
3
[ "A000330", "A350125", "A356131", "A356243", "A356244" ]
null
Seiichi Manyama, Jul 30 2022
2022-07-30T14:14:09
oeisdata/seq/A356/A356244.seq
4e5be031a1eeea84aa13d73d27836c30
A356245
A family of squares A(m), m >= 0, read by squares and then by rows; A(0) is [1, 1; 1, 1]; for m >= 0, square A(m+1) is obtained by replacing each subsquare [t, u; v, w] by [t, t+u, t+u, u; t+v, t+u+v, t+u+w, u+w; t+v, t+v+w, u+v+w, u+w; v, v+w, v+w, w] in A(m).
[ "1", "1", "1", "1", "1", "2", "2", "1", "2", "3", "3", "2", "2", "3", "3", "2", "1", "2", "2", "1", "1", "3", "3", "2", "4", "4", "2", "3", "3", "1", "3", "5", "6", "5", "7", "7", "5", "6", "5", "3", "3", "6", "7", "5", "8", "8", "5", "7", "6", "3", "2", "5", "5", "3", "6", "6", "3", "5", "5", "2", "4", "7", "8", "6", "9", "9", "6", "8", "7", "4", "4", "7", "8", "6", "9", "9", "6", "8", "7", "4", "2", "5", "5", "3", "6", "6", "3", "5", "5", "2" ]
[ "nonn", "tabf" ]
12
0
6
[ "A355855", "A356002", "A356096", "A356097", "A356098", "A356245" ]
null
Rémy Sigrist, Jul 30 2022
2023-01-18T03:29:04
oeisdata/seq/A356/A356245.seq
94dc7395d28e6d0c286cec5de580efe1
A356246
Primes whose reversal is a multiple of 14.
[ "41", "89", "211", "223", "281", "293", "463", "487", "499", "691", "827", "839", "2129", "2213", "2237", "2333", "2357", "2441", "2477", "2503", "2539", "2647", "2659", "2693", "2731", "2767", "2851", "2887", "2971", "4021", "4057", "4091", "4153", "4177", "4261", "4273", "4297", "4409", "4517", "4637", "4649", "4721", "4733", "4877", "4889", "4903", "4973" ]
[ "nonn", "base" ]
10
1
1
[ "A045711", "A074895", "A087762", "A087764", "A087765", "A087766", "A087767", "A355430", "A355983", "A355984", "A355985", "A356246" ]
null
Bernard Schott, Jul 30 2022
2022-07-31T07:48:46
oeisdata/seq/A356/A356246.seq
2930776a1c652c623c57416b550df10a
A356247
Denominator of the continued fraction 1/(2 - 3/(3 - 4/(4 - 5/(...(n-1) - n/(-1))))).
[ "1", "5", "11", "19", "29", "41", "11", "71", "89", "109", "131", "31", "181", "19", "239", "271", "61", "31", "379", "419", "461", "101", "29", "599", "59", "701", "151", "811", "79", "929", "991", "211", "59", "41", "1259", "1", "281", "1481", "1559", "149", "1721", "1", "61", "1979", "2069", "2161", "1", "2351", "79", "2549", "241", "1", "2861", "2969", "3079", "3191" ]
[ "nonn", "easy", "frac" ]
114
2
2
[ "A002327", "A028387", "A051403", "A165900", "A356247", "A356684" ]
null
Mohammed Bouras, Jul 30 2022
2024-05-31T14:05:42
oeisdata/seq/A356/A356247.seq
f1320d4c2c727a05b8a93b6368d790c3
A356248
Image of 1 under repeated application of the map k -> (2k-1,2k,2k-1).
[ "1", "2", "1", "3", "4", "3", "1", "2", "1", "5", "6", "5", "7", "8", "7", "5", "6", "5", "1", "2", "1", "3", "4", "3", "1", "2", "1", "9", "10", "9", "11", "12", "11", "9", "10", "9", "13", "14", "13", "15", "16", "15", "13", "14", "13", "9", "10", "9", "11", "12", "11", "9", "10", "9", "1", "2", "1", "3", "4", "3", "1", "2", "1", "5", "6", "5", "7", "8", "7", "5", "6", "5", "1", "2", "1", "3", "4", "3", "1", "2", "1" ]
[ "nonn" ]
20
0
2
[ "A289813", "A356248" ]
null
Arie Bos, Jul 31 2022
2022-08-01T16:40:31
oeisdata/seq/A356/A356248.seq
3504172ab79de293818391437e14bd26
A356249
a(n) = Sum_{k=1..n} (k * floor(n/k))^3.
[ "1", "16", "62", "219", "405", "1053", "1523", "2948", "4407", "7041", "8703", "15283", "17949", "24657", "32685", "44806", "50536", "70687", "78573", "105411", "125879", "149879", "163565", "222425", "247476", "286134", "327634", "396258", "423084", "532236", "564818", "664763", "738095", "821693", "904937", "1107618", "1162268", "1277588", "1395760" ]
[ "nonn" ]
28
1
2
[ "A000537", "A024916", "A064603", "A318742", "A319086", "A350123", "A356125", "A356249", "A356250" ]
null
Seiichi Manyama, Jul 31 2022
2023-10-21T18:00:33
oeisdata/seq/A356/A356249.seq
41056a73f550f1c6036c865dc55db5f2
A356250
Square array T(n,k), n >= 1, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=1..n} (j * floor(n/j))^k.
[ "1", "1", "2", "1", "4", "3", "1", "8", "8", "4", "1", "16", "22", "15", "5", "1", "32", "62", "57", "21", "6", "1", "64", "178", "219", "91", "33", "7", "1", "128", "518", "849", "405", "185", "41", "8", "1", "256", "1522", "3315", "1843", "1053", "247", "56", "9", "1", "512", "4502", "13017", "8541", "6065", "1523", "402", "69", "10", "1", "1024", "13378", "51339", "40171", "35253", "9571", "2948", "545", "87", "11" ]
[ "nonn", "tabl" ]
17
1
3
[ "A001477", "A024916", "A344725", "A350123", "A356238", "A356249", "A356250" ]
null
Seiichi Manyama, Jul 31 2022
2022-07-31T13:17:35
oeisdata/seq/A356/A356250.seq
81673f66ac7fc309e234e62c306cdf95
A356251
a(n) = n*(n+1)*(n+2)*(n+3)*(2*n+1)/12.
[ "0", "6", "50", "210", "630", "1540", "3276", "6300", "11220", "18810", "30030", "46046", "68250", "98280", "138040", "189720", "255816", "339150", "442890", "570570", "726110", "913836", "1138500", "1405300", "1719900", "2088450", "2517606", "3014550", "3587010", "4243280", "4992240", "5843376", "6806800", "7893270", "9114210" ]
[ "nonn", "easy" ]
34
0
2
[ "A033487", "A356251" ]
null
Edward Krogius, Jul 31 2022
2025-06-20T08:21:46
oeisdata/seq/A356/A356251.seq
f3d574abfdc878bcce69594e941c0956
A356252
The smallest number of straight lines that can be used to draw n non-overlapping pentagonal stars.
[ "5", "8", "9", "11", "12", "13" ]
[ "nonn", "more" ]
26
1
1
null
null
Nicolay Avilov, Jul 31 2022
2022-09-15T11:46:54
oeisdata/seq/A356/A356252.seq
00ded5695b9c4588999ae914c55b1085
A356253
a(n) is the largest coefficient of P(x) := Product_{k} (x + p_k), where (p_k) are the primes dividing n listed with multiplicity.
[ "1", "2", "3", "4", "5", "6", "7", "12", "9", "10", "11", "16", "13", "14", "15", "32", "17", "21", "19", "24", "21", "22", "23", "44", "25", "26", "27", "32", "29", "31", "31", "80", "33", "34", "35", "60", "37", "38", "39", "68", "41", "42", "43", "48", "45", "46", "47", "112", "49", "50", "51", "56", "53", "81", "55", "92", "57", "58", "59", "92", "61", "62", "63", "240", "65", "66", "67", "72" ]
[ "nonn" ]
45
1
2
[ "A002110", "A003415", "A024451", "A065048", "A070918", "A083348", "A109388", "A260613", "A356253", "A369657" ]
null
Thomas Scheuerle, Jul 31 2022
2024-02-14T14:24:00
oeisdata/seq/A356/A356253.seq
72baf39c1ddeb5e0ddf8d5e9dedc95b4
A356254
Given n balls, all of which are initially in the first of n numbered boxes, a(n) is the number of steps required to get one ball in each box when a step consists of moving to the next box every second ball from the highest-numbered box that has more than one ball.
[ "0", "1", "3", "5", "9", "13", "18", "23", "31", "39", "47", "56", "67", "78", "91", "103", "119", "135", "150", "167", "185", "203", "223", "243", "266", "289", "313", "337", "364", "391", "420", "447", "479", "511", "541", "574", "607", "640", "675", "711", "749", "787", "826", "865", "907", "949", "993", "1036", "1083", "1130", "1177", "1225", "1275", "1325", "1377" ]
[ "nonn" ]
40
1
3
[ "A000217", "A001855", "A181132", "A356254" ]
null
Mikhail Kurkov, Oct 15 2022
2024-10-20T21:13:24
oeisdata/seq/A356/A356254.seq
22eb4aee9758d5fc7a94fc536db15680
A356255
a(1) = 1; for n > 1, a(n) is the smallest magnitude number not occurring earlier such that n is divisible by s = Sum_{k = 1..n} a(k), where |s| > 1.
[ "1", "-3", "-1", "5", "3", "-2", "4", "-5", "7", "-4", "6", "-7", "9", "-6", "8", "-11", "13", "-8", "10", "-9", "11", "-10", "12", "-15", "-13", "18", "14", "-20", "22", "-14", "16", "-23", "-19", "28", "-12", "-17", "-25", "35", "15", "-18", "-36", "20", "-22", "21", "17", "-41", "93", "-31", "33", "-24", "26", "-38", "40", "-26", "-16", "-39", "25", "32", "30", "-29", "31", "-30", "-28", "29", "-27", "61", "-133", "50", "-52", "34" ]
[ "sign", "fini", "full" ]
17
1
2
[ "A019444", "A027749", "A027750", "A356255" ]
null
Scott R. Shannon, Oct 15 2022
2023-01-16T09:10:46
oeisdata/seq/A356/A356255.seq
f7ecb04b6363973d5b81fd1e37c2a725
A356256
The lesser of the 2^n-th twin prime pair (A001359).
[ "3", "5", "17", "71", "227", "821", "2087", "5021", "13757", "33149", "81197", "186647", "435401", "1002719", "2241779", "5060171", "11296421", "25121207", "55559507", "121831601", "266187827", "578653919", "1253242691", "2705496551", "5820833729", "12491149637", "26733605159", "57077657321", "121575837179", "258438193379" ]
[ "nonn" ]
27
0
1
[ "A001359", "A356256" ]
null
Robert G. Wilson v, Oct 03 2022
2022-11-19T14:00:39
oeisdata/seq/A356/A356256.seq
4daf069a98cb1491def5254216b5f9ae
A356257
Irregular triangle: row n consists of the frequencies of positive distances between permutations P and reverse(P), as P ranges through the permutations of (1, 2, ..., n); see Comments.
[ "1", "2", "4", "2", "8", "16", "24", "16", "32", "32", "16", "48", "192", "192", "288", "192", "144", "576", "576", "576", "576", "960", "576", "576", "288", "384", "2304", "4608", "7680", "9216", "6912", "9216", "1920", "1536", "9216", "9216", "16128", "18432", "29184", "26112", "36864", "32256", "41472", "23040", "39168", "32256", "18432", "18432" ]
[ "nonn", "tabf", "more" ]
17
1
2
[ "A000142", "A356257", "A357329" ]
null
Clark Kimberling, Oct 04 2022
2023-06-05T08:55:48
oeisdata/seq/A356/A356257.seq
597231e770a2cbef8e328d9e436e3207
A356258
Number of 6-dimensional cubic lattice walks that start and end at origin after 2n steps, free to pass through origin at intermediate stages.
[ "1", "12", "396", "19920", "1281420", "96807312", "8175770064", "748315668672", "72729762868620", "7402621930738320", "781429888276676496", "84955810313787521472", "9463540456205136873936", "1075903653146632508721600", "124461755084172965028753600", "14615050011682746903615601920" ]
[ "nonn", "easy", "walk" ]
43
0
2
[ "A000984", "A002894", "A002896", "A039699", "A287317", "A287318", "A356258" ]
null
Dave R.M. Langers, Oct 12 2022
2023-03-10T08:59:53
oeisdata/seq/A356/A356258.seq
f56abe27c72c7fbd567761428e143fbf
A356259
Number of labeled rooted trees on [n] that have a primary branch.
[ "0", "2", "6", "60", "500", "7290", "100842", "1978368", "38263752", "949218750", "23579476910", "709026379776", "21505924728444", "760772509715764", "27246730957031250", "1109165339867873280", "45798768824157052688", "2109518949433090534902" ]
[ "nonn" ]
8
1
2
[ "A000169", "A027415", "A356074", "A356259" ]
null
Geoffrey Critzer, Jul 31 2022
2022-08-04T15:54:52
oeisdata/seq/A356/A356259.seq
b089cc67158ee17e30d4db5a2a6400fb
A356260
Lower twin primes p such that (p^2 + (p+2)^2)/10 is prime.
[ "11", "41", "101", "107", "197", "311", "461", "521", "827", "1061", "1277", "1451", "1487", "1871", "2027", "2141", "2801", "3251", "3671", "4091", "4547", "5651", "5657", "6197", "6791", "6827", "7307", "7457", "8837", "9011", "9041", "9437", "9857", "10007", "10301", "10457", "11777", "12041", "12251", "12611", "13691", "13721", "13997", "14321", "14387", "15287", "15641", "17027", "17747" ]
[ "nonn" ]
10
1
1
[ "A001359", "A356260" ]
null
J. M. Bergot and Robert Israel, Jul 31 2022
2022-08-03T12:40:09
oeisdata/seq/A356/A356260.seq
dbca01c3be1a8d7ec9d3c66ec8ce97f2
A356261
Partition triangle read by rows, counting irreducible permutations with weakly decreasing Lehmer code, refining triangle A119308.
[ "1", "1", "0", "1", "0", "2", "1", "0", "2", "1", "5", "1", "0", "2", "2", "7", "7", "9", "1", "0", "2", "2", "1", "9", "18", "3", "16", "24", "14", "1", "0", "2", "2", "2", "11", "22", "11", "11", "25", "75", "25", "30", "60", "20", "1", "0", "2", "2", "2", "1", "13", "26", "26", "13", "13", "36", "108", "54", "108", "9", "55", "220", "110", "50", "125", "27", "1" ]
[ "nonn", "tabf" ]
9
0
6
[ "A071724", "A119308", "A356261", "A356264" ]
null
Peter Luschny, Aug 16 2022
2022-08-21T14:09:53
oeisdata/seq/A356/A356261.seq
200de2f70eaf49fe346217c629b4e837
A356262
Partition triangle read by rows counting the irreducible permutations sorted by the partition type of their Lehmer code.
[ "1", "1", "0", "1", "0", "2", "1", "0", "2", "1", "9", "1", "0", "2", "3", "24", "17", "24", "1", "0", "2", "3", "3", "98", "29", "23", "156", "91", "55", "1", "0", "2", "8", "4", "181", "43", "157", "113", "1085", "243", "418", "714", "360", "118", "1", "0", "2", "7", "11", "4", "300", "61", "317", "461", "398", "2985", "536", "1822", "4366", "417", "7684", "1522", "3904", "2788", "1262", "245", "1" ]
[ "nonn", "tabf" ]
13
0
6
[ "A003319", "A355777", "A356262", "A356263" ]
null
Peter Luschny, Aug 01 2022
2022-08-23T06:03:25
oeisdata/seq/A356/A356262.seq
6608354797aec995e461e4e85b54ab78
A356263
Triangle read by rows. The reduced triangle of the partition triangle of irreducible permutations (A356262). T(n, k) for n >= 1 and 0 <= k < n.
[ "1", "0", "1", "0", "2", "1", "0", "3", "9", "1", "0", "5", "41", "24", "1", "0", "8", "150", "247", "55", "1", "0", "14", "494", "1746", "1074", "118", "1", "0", "24", "1537", "10126", "13110", "4050", "245", "1", "0", "43", "4642", "52129", "122521", "79396", "14111", "500", "1", "0", "77", "13745", "248494", "967644", "1126049", "425471", "46833", "1011", "1" ]
[ "nonn", "tabl" ]
15
1
5
[ "A003319", "A007059", "A008292", "A356114", "A356116", "A356262", "A356263" ]
null
Peter Luschny, Aug 01 2022
2022-08-04T14:57:47
oeisdata/seq/A356/A356263.seq
37b2c6d3571292d24a972bbafe1cc573
A356264
Partition triangle read by rows, counting reducible permutations, refining triangle A356265.
[ "0", "0", "1", "0", "1", "2", "0", "1", "5", "3", "2", "0", "1", "9", "12", "15", "10", "2", "0", "1", "14", "23", "12", "47", "94", "11", "31", "24", "2", "0", "1", "20", "38", "48", "113", "293", "154", "137", "183", "409", "78", "63", "54", "2", "0", "1", "27", "60", "87", "49", "227", "738", "883", "451", "457", "670", "2157", "1007", "1580", "79", "605", "1520", "384", "127", "116", "2", "0" ]
[ "nonn", "tabf" ]
11
0
6
[ "A356262", "A356263", "A356264", "A356265", "A356291" ]
null
Peter Luschny, Aug 05 2022
2022-08-23T05:34:56
oeisdata/seq/A356/A356264.seq
b46d30781666e565f9ee404997b119b3
A356265
Triangle read by rows. The reduced triangle of the partition triangle of reducible permutations (A356264). T(n, k) for n >= 1 and 0 <= k < n.
[ "0", "1", "0", "1", "2", "0", "1", "8", "2", "0", "1", "21", "25", "2", "0", "1", "49", "152", "55", "2", "0", "1", "106", "697", "670", "117", "2", "0", "1", "223", "2756", "5493", "2509", "243", "2", "0", "1", "459", "9966", "36105", "33669", "8838", "497", "2", "0", "1", "936", "34095", "206698", "342710", "184305", "29721", "1007", "2", "0" ]
[ "nonn", "tabl" ]
11
1
5
[ "A356264", "A356265", "A356291" ]
null
Peter Luschny, Aug 16 2022
2022-09-11T01:53:16
oeisdata/seq/A356/A356265.seq
bbae5cdd07b5eb7557aa1216e8f9d148
A356266
Partition triangle read by rows, counting reducible permutations with weakly decreasing Lehmer code, refining triangle A356115.
[ "1", "1", "0", "1", "0", "1", "1", "0", "1", "2", "1", "1", "0", "1", "3", "3", "3", "3", "1", "0", "1", "4", "4", "2", "6", "12", "2", "4", "6", "1", "0", "1", "5", "5", "5", "10", "20", "10", "10", "10", "30", "10", "5", "10", "1", "0", "1", "6", "6", "6", "3", "15", "30", "30", "15", "15", "20", "60", "30", "60", "5", "15", "60", "30", "6", "15", "1" ]
[ "nonn", "tabf" ]
10
0
10
[ "A120588", "A356115", "A356264", "A356266" ]
null
Peter Luschny, Aug 16 2022
2022-08-21T14:10:10
oeisdata/seq/A356/A356266.seq
30a95d42816eca524c1e5d04d821a0c6
A356267
a(n) = Sum_{k=0..n} binomial(2*n, k) * p(k), where p(k) is the partition function A000041.
[ "1", "3", "17", "97", "583", "3275", "18988", "104821", "584441", "3180889", "17295626", "92225785", "492811733", "2590911097", "13591889993", "70605682273", "365601169939", "1876312271003", "9605682510676", "48809295651049", "247315330613099", "1245888505795725", "6256686417801919", "31260996876796579" ]
[ "nonn" ]
7
0
2
[ "A000041", "A032443", "A218481", "A286955", "A356267", "A356268" ]
null
Vaclav Kotesovec, Aug 01 2022
2022-08-01T14:24:43
oeisdata/seq/A356/A356267.seq
2de37539d0b088ca6da494d8aa8fe419
A356268
a(n) = Sum_{k=0..n} binomial(2*n, k) * q(k), where q(k) is the number of partitions into distinct parts (A000009).
[ "1", "3", "11", "62", "289", "1472", "7581", "38014", "184453", "918512", "4548393", "22077762", "107423503", "516720332", "2483445404", "11959145079", "57022343425", "270173627092", "1282971321633", "6047971597490", "28446033085527", "133714464665108", "625893086713686", "2919093380089383", "13596052503945537" ]
[ "nonn" ]
7
0
2
[ "A000009", "A032443", "A266232", "A307496", "A356267", "A356268" ]
null
Vaclav Kotesovec, Aug 01 2022
2022-08-01T14:24:48
oeisdata/seq/A356/A356268.seq
dc72c9c8002454a30d6c6fd3e94ec599
A356269
a(n) = Sum_{k=0..n} binomial(2*k, k) * p(k), where p(k) is the partition function A000041.
[ "1", "3", "15", "75", "425", "2189", "12353", "63833", "346973", "1805573", "9565325", "49069517", "257289529", "1307750129", "6723491129", "34024174649", "172873744739", "865954792079", "4359881882579", "21679061144579", "108108834714719", "534409071271199", "2642716232918639", "12975671796056639", "63765647596939139" ]
[ "nonn" ]
7
0
2
[ "A000041", "A006134", "A032443", "A218481", "A286955", "A356267", "A356269", "A356270" ]
null
Vaclav Kotesovec, Aug 01 2022
2022-08-01T14:24:25
oeisdata/seq/A356/A356269.seq
684f67b8af824b5337d9dd0bd00f5a8f
A356270
a(n) = Sum_{k=0..n} binomial(2*k, k) * q(k), where q(k) is the number of partitions into distinct parts (A000009).
[ "1", "3", "9", "49", "189", "945", "4641", "21801", "99021", "487981", "2335541", "10800725", "51363065", "238573865", "1121139065", "5309312105", "24543884585", "113220920945", "530677144745", "2439321389945", "11261499234425", "52169097691865", "239433905462945", "1095710701133345", "5029918350471545" ]
[ "nonn" ]
6
0
2
[ "A000009", "A006134", "A032443", "A266232", "A307496", "A356268", "A356269", "A356270" ]
null
Vaclav Kotesovec, Aug 01 2022
2022-08-01T14:24:20
oeisdata/seq/A356/A356270.seq
0ff6abebf2a2e682a80c239d7e9b88d9
A356271
Prime numbers in the sublists defined in A348168 that contain a single prime.
[ "2", "3", "5", "7", "23", "53", "89", "157", "173", "211", "293", "353", "359", "409", "449", "683", "691", "839", "919", "977", "983", "1039", "1069", "1103", "1109", "1201", "1223", "1237", "1283", "1327", "1381", "1439", "1459", "1511", "1613", "1627", "1637", "1709", "2039", "2099", "2179", "2213", "2221", "2243", "2251", "2273", "2447", "2633", "2917" ]
[ "nonn" ]
20
1
1
[ "A348168", "A356271" ]
null
Ya-Ping Lu, Aug 01 2022
2024-04-25T13:53:31
oeisdata/seq/A356/A356271.seq
adf226ad3ffa14b11d853d9e055bfa47
A356272
a(n) is the least k such that exactly n consecutive integers starting from k belong to A124665.
[ "20", "134", "1934", "9773", "19042", "138902", "104024", "512255", "1400180", "1558490", "1441174", "9363253", "20454244", "98854550", "57515874", "201139683", "49085531", "213492618", "475478220", "1152519092" ]
[ "nonn", "base", "more" ]
17
1
1
[ "A124665", "A356272" ]
null
Michel Marcus, Aug 01 2022
2022-08-03T02:38:30
oeisdata/seq/A356/A356272.seq
3c7debe15e313042ed2bd45bbc47150b
A356273
a(n) is the position of the least prime in the ordered set of numbers obtained by inserting/placing any digit anywhere in the digits of n (except a zero before 1st digit), or 0 if there is no prime in that set.
[ "2", "5", "1", "5", "8", "7", "1", "11", "1", "2", "1", "10", "1", "14", "7", "10", "1", "10", "1", "0", "4", "7", "4", "7", "8", "11", "1", "11", "4", "10", "1", "0", "2", "14", "11", "16", "1", "14", "1", "5", "2", "7", "8", "11", "16", "11", "3", "19", "1", "8", "1", "8", "3", "10", "17", "14", "1", "20", "3", "7", "4", "0", "1", "11", "14", "13", "1", "17", "2", "8", "2", "16", "1", "14", "13", "14", "2", "22", "1", "17" ]
[ "nonn", "base" ]
18
1
1
[ "A068166", "A068167", "A068169", "A068170", "A068171", "A068172", "A068173", "A068174", "A124665", "A356273" ]
null
Michel Marcus, Aug 01 2022
2022-08-02T09:20:05
oeisdata/seq/A356/A356273.seq
4f0a26045b91479eb4661c04242cab50
A356274
a(n) is the number whose base-(n+1) expansion equals the binary expansion of n.
[ "1", "3", "5", "25", "37", "56", "73", "729", "1001", "1342", "1741", "2366", "2941", "3615", "4369", "83521", "104977", "130340", "160021", "194922", "234741", "280393", "332377", "406250", "474553", "551151", "636637", "732511", "837901", "954304", "1082401", "39135393", "45435425", "52521910", "60466213", "69345326", "79236613" ]
[ "nonn", "base" ]
72
1
2
[ "A000523", "A007814", "A104257", "A104258", "A128889", "A136516", "A356274" ]
null
Thomas Scheuerle, Aug 02 2022
2022-08-23T09:42:38
oeisdata/seq/A356/A356274.seq
e1617ad5071a0ca4c99d91d919a22497
A356275
a(n) is the number of tuples (t_1,t_2,m) of integers 2 <= t_1 <= t_2 and 0 < m < n such that (3 + 1/t_1)^m * (3 + 1/t_2)^(n-m) is an integer.
[ "3", "2", "4", "2", "5", "3", "5", "5", "5", "4" ]
[ "more", "nonn" ]
21
2
1
[ "A355626", "A356275", "A356276", "A356277", "A356278", "A356279" ]
null
Markus Sigg, Aug 03 2022
2025-01-12T09:31:16
oeisdata/seq/A356/A356275.seq
0603d94b779cbb01101a3d351ad68fde
A356276
a(n) is the number of integers that can be written as (3 + 1/t_1)^m * (3 + 1/t_2)^(n-m) with integers t_1,t_2 >= 2 and 0 < m < n.
[ "2", "2", "3", "2", "4", "3", "4", "5", "4", "4" ]
[ "nonn", "more" ]
10
2
1
[ "A355626", "A356275", "A356276", "A356277", "A356278", "A356279" ]
null
Markus Sigg, Aug 03 2022
2022-08-04T10:20:20
oeisdata/seq/A356/A356276.seq
2a88d4d17209bd726a95c518d6f2afed
A356277
a(n) is the smallest integer that can be written as (3 + 1/t_1)^m * (3 + 1/t_2)^(n-m) with integers t_1,t_2 >= 2 and 0 < m < n.
[ "10", "32", "100", "320", "1000", "3125", "10000", "31250", "100000", "312500" ]
[ "nonn", "more" ]
10
2
1
[ "A355626", "A356275", "A356276", "A356277", "A356278", "A356279" ]
null
Markus Sigg, Aug 03 2022
2022-08-04T10:20:23
oeisdata/seq/A356/A356277.seq
df6f6fb60f6079d1e28d4b62bc58f618
A356278
a(n) is the largest integer that can be written as (3 + 1/t_1)^m * (3 + 1/t_2)^(n-m) with integers t_1,t_2 >= 2 and 0 < m < n.
[ "11", "37", "121", "325", "1369", "3250", "14641", "50653", "161051", "327680" ]
[ "nonn", "more" ]
10
2
1
[ "A355626", "A356275", "A356276", "A356277", "A356278", "A356279" ]
null
Markus Sigg, Aug 03 2022
2022-08-04T10:20:27
oeisdata/seq/A356/A356278.seq
719ea19fd3ead1d35cb844970df159f2
A356279
Integers that can be written as (3 + 1/t_1)^m * (3 + 1/t_2)^k with integers t_1,t_2 >= 2 and m,k > 0.
[ "10", "11", "32", "37", "100", "103", "121", "320", "325", "1000", "1024", "1331", "1369", "3125", "3200", "3250", "10000", "10240", "10609", "14641", "31250", "32000", "32500", "32768", "50653", "100000", "102400", "105625", "161051", "312500", "320000", "325000", "327680" ]
[ "nonn", "more" ]
15
1
1
[ "A355626", "A356275", "A356276", "A356277", "A356278", "A356279" ]
null
Markus Sigg, Aug 03 2022
2022-08-04T10:20:36
oeisdata/seq/A356/A356279.seq
93049fbe28fcb95dafd57dcd61a8bda6
A356280
a(n) = Sum_{k=0..n} binomial(2*n, n-k) * p(k), where p(k) is the partition function A000041.
[ "1", "3", "12", "50", "211", "894", "3791", "16068", "68032", "287675", "1214761", "5122428", "21571028", "90718913", "381050570", "1598645263", "6699355413", "28044720813", "117281866330", "489999068614", "2045341248508", "8530263939665", "35547083083270", "148015639243691", "615870619714675", "2560734764460360" ]
[ "nonn" ]
10
0
2
[ "A000041", "A032443", "A218481", "A286955", "A356267", "A356280", "A356281" ]
null
Vaclav Kotesovec, Aug 01 2022
2022-08-02T07:52:21
oeisdata/seq/A356/A356280.seq
6202f281c435e0d1a748b2e93a3e6557
A356281
a(n) = Sum_{k=0..n} binomial(2*n, n-k) * q(k), where q(k) is the number of partitions into distinct parts (A000009).
[ "1", "3", "11", "43", "172", "695", "2823", "11501", "46940", "191791", "784148", "3207196", "13119733", "53670793", "219545353", "897957702", "3672093558", "15013596535", "61370565546", "250803861369", "1024716136043", "4185683293934", "17093143284723", "69786349712519", "284847779542644", "1162385753008079" ]
[ "nonn" ]
6
0
2
[ "A000009", "A032443", "A266232", "A307496", "A356268", "A356280", "A356281" ]
null
Vaclav Kotesovec, Aug 01 2022
2022-08-02T04:13:06
oeisdata/seq/A356/A356281.seq
c5a095bce657249d596de8d1d4b7a07a
A356282
a(n) = Sum_{k=0..n} binomial(3*n, n-k) * p(k), where p(k) is the partition function A000041.
[ "1", "4", "23", "141", "888", "5675", "36602", "237563", "1548995", "10135554", "66504699", "437359454", "2881641263", "19016505326", "125664684700", "831400186740", "5506287269802", "36501297800013", "242167539749593", "1607851773270316", "10682384379036741", "71016046921543562", "472376627798814453" ]
[ "nonn" ]
9
0
2
[ "A000041", "A188675", "A356280", "A356282", "A356283" ]
null
Vaclav Kotesovec, Aug 01 2022
2022-08-02T05:51:06
oeisdata/seq/A356/A356282.seq
a50708c91b1f6e2e1e34dbbcb4d82b1d
A356283
a(n) = Sum_{k=0..n} binomial(3*n, n-k) * q(k), where q(k) is the number of partitions into distinct parts (A000009).
[ "1", "4", "22", "131", "807", "5066", "32188", "206242", "1329733", "8614685", "56024538", "365491218", "2390613557", "15671221522", "102925324569", "677110860689", "4460956827127", "29427611146335", "194348311824025", "1284856925961827", "8502252246841668", "56309476194587377", "373220349572126265" ]
[ "nonn" ]
5
0
2
[ "A000009", "A188675", "A356281", "A356282", "A356283" ]
null
Vaclav Kotesovec, Aug 01 2022
2022-08-02T05:51:12
oeisdata/seq/A356/A356283.seq
73a5a4dec28a61ec331e38471147e9eb
A356284
a(n) = Sum_{k=0..n} binomial(3*n, k) * p(k), where p(k) is the partition function A000041.
[ "1", "4", "37", "334", "3280", "29437", "282253", "2517904", "23209785", "206685325", "1858085653", "16266231810", "144339750406", "1250038867329", "10882952174845", "93546973843450", "804847296088574", "6843680884286307", "58300294406199829", "491683063753997014", "4148296662116385627", "34746182976196757434" ]
[ "nonn" ]
8
0
2
[ "A000041", "A188675", "A356267", "A356284", "A356285" ]
null
Vaclav Kotesovec, Aug 01 2022
2022-08-02T05:51:19
oeisdata/seq/A356/A356284.seq
617f0a9fd619d3ce445468373c2eaa82
A356285
a(n) = Sum_{k=0..n} binomial(3*n, k) * q(k), where q(k) is the number of partitions into distinct parts (A000009).
[ "1", "4", "22", "214", "1509", "12770", "107884", "874365", "6834843", "56722759", "463069914", "3666488610", "29512199193", "233492075573", "1858649112464", "14890457067926", "117154630898329", "917101099859767", "7257072314543086", "56653800922475280", "442687465112658972", "3467083846726752495" ]
[ "nonn" ]
5
0
2
[ "A000009", "A188675", "A356268", "A356284", "A356285" ]
null
Vaclav Kotesovec, Aug 01 2022
2022-08-02T05:51:25
oeisdata/seq/A356/A356285.seq
b7b08a1f73dd8355e71b65ba9f64929d
A356286
a(n) = Sum_{k=0..n} binomial(3*k, k) * p(k), where p(k) is the partition function A000041.
[ "1", "4", "34", "286", "2761", "23782", "227986", "1972186", "18152548", "158757298", "1420647928", "12258704248", "108637887148", "929002856992", "8065133782792", "68761800685576", "589631899738033", "4976639418495358", "42293283621258283", "354415428588891283", "2982701933728936648", "24857294772400460368" ]
[ "nonn" ]
8
0
2
[ "A000041", "A188675", "A356269", "A356286", "A356287" ]
null
Vaclav Kotesovec, Aug 01 2022
2022-08-02T05:51:32
oeisdata/seq/A356/A356286.seq
4c1cfe583a63549a57ae5182bba3b8c1
A356287
a(n) = Sum_{k=0..n} binomial(3*k, k) * q(k), where q(k) is the number of partitions into distinct parts (A000009).
[ "1", "4", "19", "187", "1177", "10186", "84442", "665842", "5078668", "42573268", "343023418", "2665464058", "21440629558", "167644287550", "1330569327310", "10641989818078", "82797155054782", "644097780350332", "5102709814966162", "39499844158337962", "307777892529889642", "2406854983109480302" ]
[ "nonn" ]
5
0
2
[ "A000009", "A188675", "A356270", "A356286", "A356287" ]
null
Vaclav Kotesovec, Aug 01 2022
2022-08-02T05:51:37
oeisdata/seq/A356/A356287.seq
72ec768b71c6e67d6e33a8b523f935af
A356288
Sum of numbers in n-th upward diagonal of triangle the sum of {1; 2,3; 4,5,6; 7,8,9,10; ...} and {1; 2,3; 3,4,5; 4,5,6,7; ...}.
[ "2", "4", "13", "20", "40", "55", "90", "116", "170", "210", "287", "344", "448", "525", "660", "760", "930", "1056", "1265", "1420", "1672", "1859", "2158", "2380", "2730", "2990", "3395", "3696", "4160", "4505", "5032", "5424", "6018", "6460", "7125", "7620", "8360", "8911", "9730", "10340", "11242", "11914", "12903", "13640", "14720", "15525", "16700" ]
[ "nonn", "easy" ]
31
1
1
[ "A079824", "A093005", "A356288" ]
null
Torlach Rush, Aug 02 2022
2022-10-05T04:55:02
oeisdata/seq/A356/A356288.seq
8f6092fce30e0a6bcf52a847e4243b33
A356289
a(n) = Sum_{k=0..n} binomial(2*n, n-k) * v(k), where v(k) is the number of overpartitions of n (A015128).
[ "1", "4", "18", "82", "372", "1676", "7500", "33358", "147570", "649722", "2848524", "12441434", "54155774", "235008672", "1016971480", "4389589484", "18902538548", "81222609020", "348308661820", "1490884718484", "6370468593732", "27176620756392", "115760526170340", "492386739902574", "2091554077819948", "8873225318953248" ]
[ "nonn" ]
5
0
2
[ "A015128", "A266497", "A356280", "A356281", "A356282", "A356283", "A356289", "A356290" ]
null
Vaclav Kotesovec, Aug 02 2022
2022-08-02T06:40:22
oeisdata/seq/A356/A356289.seq
feb9973532d361b3c95e4bd923b85784
A356290
a(n) = Sum_{k=0..n} binomial(3*n, n-k) * v(k), where v(k) is the number of overpartitions of n (A015128).
[ "1", "5", "31", "200", "1309", "8627", "57082", "378648", "2516111", "16740913", "111494801", "743137984", "4956359312", "33074272702", "220810039566", "1474764797488", "9853307017341", "65853733243281", "440255398634199", "2944041287677060", "19691951641479427", "131744163990056479", "881586559906575688" ]
[ "nonn" ]
4
0
2
[ "A015128", "A266497", "A356280", "A356281", "A356282", "A356283", "A356289", "A356290" ]
null
Vaclav Kotesovec, Aug 02 2022
2022-08-02T06:40:19
oeisdata/seq/A356/A356290.seq
24f97adebe23fd8306b09afc5a5eca58
A356291
Number of reducible permutations.
[ "0", "0", "1", "3", "11", "49", "259", "1593", "11227", "89537", "799475", "7917897", "86257643", "1025959345", "13234866787", "184078090137", "2746061570587", "43736283267137", "740674930879379", "13289235961616937", "251805086618856395", "5024288943352588369", "105295629327037117123" ]
[ "nonn" ]
15
0
4
[ "A000142", "A003319", "A260503", "A356291" ]
null
Peter Luschny, Aug 02 2022
2022-08-04T02:09:00
oeisdata/seq/A356/A356291.seq
152a920686c410fa64e57c6bc202224e
A356292
Number of labeled trees on [n] that are centered.
[ "1", "1", "0", "3", "4", "65", "726", "8617", "127688", "2374353", "50692330", "1198835561", "31297606572", "901114484569", "28449258421598", "976863784939785", "36199494609008656", "1438734246518372897", "61037354387458904274", "2753490065023053584713", "131645635680595606832180" ]
[ "nonn" ]
10
0
4
[ "A000272", "A000676", "A034854", "A355671", "A356292" ]
null
Geoffrey Critzer, Aug 02 2022
2022-08-04T15:55:02
oeisdata/seq/A356/A356292.seq
676e0d485f986171bc659969a11be946
A356293
Primes p such that if q is the next prime, (p+q)/6 is a triangular number.
[ "7", "17", "29", "43", "107", "163", "197", "313", "457", "569", "757", "827", "1303", "1487", "1783", "1997", "2339", "2707", "2969", "3527", "3673", "3967", "4289", "4787", "5119", "5857", "7243", "9007", "9719", "10457", "10709", "10957", "12281", "13679", "16067", "17657", "20357", "21773", "23623", "27127", "27539", "31319", "33073", "33521", "37201", "38153", "45673", "48869", "50503" ]
[ "nonn" ]
12
1
1
[ "A000217", "A356293" ]
null
J. M. Bergot and Robert Israel, Aug 02 2022
2022-08-03T11:45:37
oeisdata/seq/A356/A356293.seq
f2409f7ecfcf395389cbdfac6f26a5ff
A356294
a(n) = A054633(n) if A030190(n) = 1, else a(n) = a(n-A054633(n)+1).
[ "1", "2", "1", "3", "4", "5", "2", "1", "6", "3", "7", "8", "9", "4", "10", "11", "12", "13", "5", "2", "1", "14", "6", "3", "15", "16", "7", "17", "8", "18", "9", "19", "20", "21", "22", "4", "10", "23", "24", "11", "25", "26", "27", "28", "12", "29", "30", "31", "32", "33", "13", "5", "2", "1", "34", "14", "6", "3", "35", "36", "15", "16", "37", "7", "38", "17", "8", "39", "40", "41", "18", "42", "9" ]
[ "nonn", "easy", "base", "look" ]
17
1
2
[ "A030190", "A054633", "A356294" ]
null
Michael De Vlieger and David James Sycamore, Aug 03 2022
2025-06-29T18:28:55
oeisdata/seq/A356/A356294.seq
b7ca03b6d56332b5053844c7b4efa1c2
A356295
Numbers that are not the sum of a nonnegative cube and a prime.
[ "1", "9", "16", "22", "26", "28", "33", "35", "36", "52", "57", "63", "65", "76", "78", "82", "85", "92", "96", "99", "112", "118", "119", "120", "122", "126", "129", "133", "141", "146", "155", "160", "169", "170", "183", "185", "188", "202", "209", "210", "216", "217", "225", "236", "244", "246", "248", "267", "273", "280", "286", "300", "302", "309", "326", "328", "330", "342" ]
[ "nonn" ]
6
1
2
[ "A014090", "A045911", "A257772", "A302354", "A356295" ]
null
Jianing Song, Aug 03 2022
2022-08-03T11:04:32
oeisdata/seq/A356/A356295.seq
9411386b4e3ef11b13bd179a63819f79
A356296
a(n) = Fibonacci(n)^2 mod n.
[ "0", "1", "1", "1", "0", "4", "1", "1", "4", "5", "1", "0", "1", "1", "10", "9", "1", "10", "1", "5", "4", "1", "1", "0", "0", "1", "22", "9", "1", "10", "1", "25", "4", "1", "25", "0", "1", "1", "4", "25", "1", "22", "1", "9", "40", "1", "1", "0", "22", "25", "4", "9", "1", "10", "25", "49", "4", "1", "1", "0", "1", "1", "22", "25", "25", "64", "1", "9", "4", "15", "1", "0", "1", "1", "25", "9", "4", "64", "1", "25", "49", "1", "1", "72", "25", "1" ]
[ "nonn", "easy" ]
25
1
6
[ "A000045", "A002708", "A023172", "A337231", "A337232", "A356296" ]
null
R. J. Mathar, Aug 03 2022
2024-03-19T19:16:47
oeisdata/seq/A356/A356296.seq
93a67e814de9c2653946675dfca30753
A356297
a(n) = n! * Sum_{k=1..n} sigma_0(k)/k.
[ "1", "4", "16", "82", "458", "3228", "24036", "212448", "2032992", "21781440", "246853440", "3201742080", "42580650240", "621037186560", "9664270963200", "161166707251200", "2781679603046400", "52204357423411200", "1004687538456268800", "20823621371578368000", "447027656835852288000" ]
[ "nonn" ]
18
1
2
[ "A000005", "A006218", "A356010", "A356297", "A356298", "A356323" ]
null
Seiichi Manyama, Aug 03 2022
2022-08-07T04:50:19
oeisdata/seq/A356/A356297.seq
2e7c844ed2f3f1b11fc0b5ecda25a771
A356298
a(n) = n! * Sum_{k=1..n} sigma_2(k)/k.
[ "1", "7", "41", "290", "2074", "18444", "165108", "1749264", "19412496", "241299360", "3097006560", "45546606720", "673536159360", "10986261431040", "187460277177600", "3445281394329600", "64637392771123200", "1325310849663897600", "27498565425087590400", "616389533324974080000" ]
[ "nonn" ]
17
1
2
[ "A001157", "A064602", "A356010", "A356297", "A356298", "A356323" ]
null
Seiichi Manyama, Aug 03 2022
2022-08-07T04:45:18
oeisdata/seq/A356/A356298.seq
867294313868685be7723b4c03d3fc6b
A356299
a(n) = gcd(A276086(n), A342001(n)), where A276086 is the primorial base exp-function, and A342001 is the arithmetic derivative without its inherited divisor.
[ "2", "1", "1", "1", "1", "5", "1", "3", "2", "1", "1", "1", "1", "3", "2", "1", "1", "1", "1", "3", "10", "1", "1", "1", "2", "15", "3", "1", "1", "1", "1", "1", "14", "1", "6", "5", "1", "21", "2", "1", "1", "1", "1", "3", "1", "25", "1", "7", "2", "3", "10", "7", "1", "1", "2", "1", "2", "1", "1", "1", "1", "3", "1", "3", "18", "1", "1", "3", "2", "1", "1", "1", "1", "3", "1", "5", "18", "1", "1", "1", "2", "1", "1", "1", "2", "15", "2", "35", "1", "1", "2", "3", "2", "49", "6", "1", "1", "1", "5", "7", "1", "7", "1", "1", "1" ]
[ "nonn" ]
11
1
1
[ "A003415", "A003557", "A046337", "A276086", "A327858", "A342001", "A356299" ]
null
Antti Karttunen, Nov 03 2022
2022-11-04T11:26:08
oeisdata/seq/A356/A356299.seq
22420f529f1449c685f161f89332a823
A356300
Square array read by antidiagonals. A(n,k) is the nearest common ancestor of n and k in the binary tree depicted in A253563.
[ "1", "1", "1", "1", "2", "1", "1", "2", "2", "1", "1", "2", "3", "2", "1", "1", "2", "2", "2", "2", "1", "1", "2", "3", "4", "3", "2", "1", "1", "2", "2", "2", "2", "2", "2", "1", "1", "2", "3", "4", "5", "4", "3", "2", "1", "1", "2", "2", "2", "2", "2", "2", "2", "2", "1", "1", "2", "3", "4", "5", "6", "5", "4", "3", "2", "1", "1", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "1", "1", "2", "3", "4", "3", "4", "7", "4", "3", "4", "3", "2", "1", "1", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "1" ]
[ "nonn", "tabl" ]
7
1
5
[ "A253553", "A253563", "A253565", "A348041", "A356300", "A356301" ]
null
Antti Karttunen, Aug 03 2022
2022-08-03T15:27:49
oeisdata/seq/A356/A356300.seq
804b338c8da200e303f273cd2158199c