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int64
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666,262,453B
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1999-12-11 03:00:00
2025-07-19 00:40:46
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A354501
The inverse Rijndael S-box used in the Advanced Encryption Standard (AES); inverse permutation of A354500.
[ "82", "9", "106", "213", "48", "54", "165", "56", "191", "64", "163", "158", "129", "243", "215", "251", "124", "227", "57", "130", "155", "47", "255", "135", "52", "142", "67", "68", "196", "222", "233", "203", "84", "123", "148", "50", "166", "194", "35", "61", "238", "76", "149", "11", "66", "250", "195", "78", "8", "46", "161", "102", "40", "217", "36", "178", "118", "91", "162", "73", "109" ]
[ "nonn", "easy", "fini", "full" ]
14
0
1
[ "A354500", "A354501", "A355891" ]
null
Jianing Song, Aug 15 2022
2022-08-15T23:32:47
oeisdata/seq/A354/A354501.seq
609422e8f4b8cdd2c74f97b9be08cfa6
A354502
Squarefree semiprimes p*q such that (p*q+1+p-q)/2 and (p*q+1+q-p)/2 are prime.
[ "35", "65", "77", "133", "143", "161", "209", "215", "221", "235", "265", "335", "377", "391", "403", "413", "451", "517", "527", "551", "553", "565", "583", "623", "635", "667", "685", "707", "721", "731", "763", "779", "793", "817", "835", "851", "871", "893", "917", "923", "965", "1007", "1057", "1067", "1133", "1147", "1157", "1207", "1243", "1247", "1271", "1273", "1313", "1333", "1337", "1363", "1385" ]
[ "nonn", "less" ]
20
1
1
[ "A006881", "A354502" ]
null
J. M. Bergot and Robert Israel, Aug 15 2022
2024-03-01T17:12:30
oeisdata/seq/A354/A354502.seq
5134f4d1eb4c938d90f913e5cbb6ccfd
A354503
Expansion of e.g.f. ( Product_{k>0} (1 + x^k)^(1/k) )^exp(x).
[ "1", "1", "3", "14", "67", "424", "3093", "26060", "233917", "2427224", "27565317", "339002146", "4450167269", "63343680802", "964189902141", "15769859929260", "270255218753593", "4913097747513800", "94513145955643993", "1904990351069631390", "40153307898034641361", "893402292594225679438" ]
[ "nonn" ]
16
0
3
[ "A347915", "A354503", "A354504", "A354506", "A356392" ]
null
Seiichi Manyama, Aug 15 2022
2022-08-16T10:21:24
oeisdata/seq/A354/A354503.seq
377df913e964f15dc56be9649a32adbe
A354504
Expansion of e.g.f. ( Product_{k>0} (1 + x^k)^k )^exp(x).
[ "1", "1", "6", "48", "402", "4375", "54595", "777189", "12284188", "215999025", "4132338673", "85640640877", "1910121348674", "45571124446445", "1157169377895739", "31150000798832647", "885481496002286200", "26498034473000080321", "832407848080194500301", "27378188500890922864153" ]
[ "nonn" ]
15
0
3
[ "A347915", "A354503", "A354504", "A354508", "A356394" ]
null
Seiichi Manyama, Aug 15 2022
2022-08-16T10:19:49
oeisdata/seq/A354/A354504.seq
93092db2ff263e662d65e8bb52faba22
A354505
Expansion of e.g.f. ( Product_{k>0} (1 + x^k)^(1/k!) )^exp(x).
[ "1", "1", "3", "13", "54", "291", "1778", "12167", "82869", "655100", "5658257", "51691806", "454932679", "4527660281", "48270581011", "553646849053", "5561424579562", "72988254250439", "1010390962699396", "12295679951427509", "67360732923382327", "1515500302797716376", "45199587363022824107", "1001538050395504921200", "-699211952404047871075" ]
[ "sign" ]
14
0
3
[ "A354505", "A354509", "A356402" ]
null
Seiichi Manyama, Aug 15 2022
2022-08-16T10:20:03
oeisdata/seq/A354/A354505.seq
52ea6a978e0aec0e037e84cfaf360ba7
A354506
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) )/(k * (n-k)!).
[ "1", "2", "7", "14", "63", "284", "2385", "3940", "87717", "940126", "12743267", "30055618", "562302323", "9005878920", "423435780989", "2080544097000", "24457758561001", "444510436079706", "17533073308723423", "46973556239255702", "7501223613055891783", "178483805340054632084", "4396051786608296882889", "-31788150263554644516724" ]
[ "sign" ]
13
1
2
[ "A048272", "A354506", "A354507", "A354508", "A356389" ]
null
Seiichi Manyama, Aug 15 2022
2022-08-16T10:20:43
oeisdata/seq/A354/A354506.seq
e3f34836e06b23e6de4a54b2af952c89
A354507
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) * d )/(k * (n-k)!).
[ "1", "3", "14", "48", "269", "1615", "12662", "73528", "836817", "8476243", "99348534", "948849176", "13193115597", "177346261391", "3684976294222", "45021819481808", "734808219625345", "13524660020400771", "290452222949307070", "4639956700466396256", "128621330002689008237", "2735863084773695212719" ]
[ "nonn" ]
14
1
2
[ "A000593", "A354506", "A354507", "A354508", "A356390" ]
null
Seiichi Manyama, Aug 15 2022
2022-08-16T10:20:54
oeisdata/seq/A354/A354507.seq
ce0da620af6cf44c541e784c0a491545
A354508
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) * d^2 )/(k * (n-k)!).
[ "1", "5", "32", "168", "1189", "8785", "77384", "646296", "7306737", "79997893", "1005481784", "12518370128", "184109233125", "2671256865121", "47934480000112", "754158322407248", "13813898274148737", "262680987222463269", "5518034466415262320", "107988236156057411096", "2605128008760639636677" ]
[ "nonn" ]
14
1
2
[ "A078306", "A354506", "A354507", "A354508", "A356391" ]
null
Seiichi Manyama, Aug 15 2022
2022-08-16T10:21:03
oeisdata/seq/A354/A354508.seq
76e544fb33c942d5a44c2df31a4475f4
A354509
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(d+1)/(d * (k/d)!) )/(n-k)!.
[ "1", "2", "6", "5", "5", "-8", "560", "-5997", "-14765", "176826", "5206410", "-42491623", "-427057527", "-412183484", "147180377804", "-569782989113", "-8367671807033", "-119681999820906", "4440973420854454", "-121033449284728099", "49772248126885197", "36615485147317407728", "1696495197400394891912" ]
[ "sign" ]
15
1
2
[ "A352013", "A354505", "A354509", "A356401" ]
null
Seiichi Manyama, Aug 15 2022
2022-08-16T10:21:13
oeisdata/seq/A354/A354509.seq
825bf33bde308a46a49be6eea6bb9722
A354510
Primes of the form p+q^2+r where p,q,r are three consecutive members of A007528.
[ "13007", "28211", "36857", "39227", "86441", "272507", "345731", "459671", "467867", "553529", "599087", "746507", "777911", "788561", "910127", "1354901", "1425653", "1512923", "1587587", "1710869", "2039171", "2509061", "2624411", "3196913", "3617597", "3896657", "4161611", "4260077", "4359749", "4460549", "4536893", "4639757", "5171093", "5280791", "5673911", "5963351" ]
[ "nonn" ]
15
1
1
[ "A007528", "A354510" ]
null
J. M. Bergot and Robert Israel, Aug 16 2022
2022-08-18T11:45:01
oeisdata/seq/A354/A354510.seq
c60fa84a122027b9d247f00b71ef6520
A354511
Number of SAWs crossing a square domain of the hexagonal lattice.
[ "2", "14", "264", "21512", "5663596", "6478476233", "23432328776346", "365121393771314359", "18039965927005597824652", "3847346539490622663060402802", "2604549807872636495439504536518768", "7613280873970130888072912524910312775000", "70659728324509466176595292882340210105184200002" ]
[ "nonn" ]
10
1
1
[ "A001006", "A002026", "A007764", "A116485", "A354511" ]
null
Vaclav Kotesovec, Aug 16 2022
2022-08-16T05:14:37
oeisdata/seq/A354/A354511.seq
c2143247e33d030351f1895be88d2c76
A354512
Number of solutions m >= 2 to m - gpf(m) = n, gpf = A006530.
[ "0", "1", "1", "0", "1", "2", "1", "0", "1", "1", "1", "0", "1", "2", "2", "0", "1", "0", "1", "1", "2", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "2", "1", "2", "0", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "0", "1", "0", "2", "1", "1", "0", "2", "1", "1", "1", "1", "0", "1", "2", "1", "0", "1", "1", "1", "1", "2", "1", "1", "0", "1", "1", "1", "1", "2", "2", "1", "0", "0", "1", "1", "0", "2", "1", "1", "1", "1", "0", "2" ]
[ "nonn", "easy" ]
25
1
6
[ "A001221", "A006530", "A076563", "A354512", "A354514", "A354515", "A354516", "A354525", "A354526", "A354527" ]
null
Jianing Song, Aug 16 2022
2022-08-17T05:07:13
oeisdata/seq/A354/A354512.seq
32ef3a7a71838361309dc20e0779ef11
A354513
The numbers whose square's position in the Wythoff array is immediately followed by another square in the next column.
[ "11", "386", "2441", "25748423", "637519684", "2799936925", "3934324789543", "127501370029150", "21274660147684109", "644571595359295797", "15845190736671957299", "995980378496501932493", "47375682236837399943653", "213688560255016550712685", "28372206851301867342910959", "3120729065082950391169492805" ]
[ "nonn" ]
64
1
1
[ "A001622", "A026274", "A035513", "A225204", "A225205", "A352538", "A354513", "A354549" ]
null
Chittaranjan Pardeshi, Aug 16 2022
2024-10-06T12:25:33
oeisdata/seq/A354/A354513.seq
e4186bd2065f742e036f318e0ad36c15
A354514
Numbers k such that m - gpf(m) = k has solutions m >= 2, gpf = A006530.
[ "0", "2", "3", "5", "6", "7", "9", "10", "11", "13", "14", "15", "17", "19", "20", "21", "22", "23", "24", "25", "26", "28", "29", "30", "31", "33", "34", "35", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "49", "51", "52", "53", "55", "56", "57", "58", "59", "61", "62", "63", "65", "66", "67", "68", "69", "70", "71", "73", "74", "75", "76", "77", "78", "79", "82", "83", "85", "86", "87", "88" ]
[ "nonn", "easy" ]
17
1
2
[ "A006530", "A076563", "A151800", "A354512", "A354514", "A354515" ]
null
Jianing Song, Aug 16 2022
2022-08-17T05:07:33
oeisdata/seq/A354/A354514.seq
a127d47386aaad181398988051b6ea16
A354515
Numbers k such that m - gpf(m) = k has no solution m >= 2, gpf = A006530.
[ "1", "4", "8", "12", "16", "18", "27", "32", "36", "48", "50", "54", "60", "64", "72", "80", "81", "84", "90", "96", "100", "108", "112", "125", "128", "132", "135", "144", "147", "150", "160", "162", "176", "180", "192", "196", "198", "200", "208", "210", "216", "224", "225", "234", "242", "243", "250", "252", "256", "270", "275", "280", "288", "294", "300", "306", "320", "324" ]
[ "nonn", "easy" ]
18
1
2
[ "A006530", "A076563", "A354512", "A354514", "A354515" ]
null
Jianing Song, Aug 16 2022
2022-08-17T05:07:05
oeisdata/seq/A354/A354515.seq
00334212cf5bd6d388807171b55ae352
A354516
Smallest k such that m - gpf(m) = k has exactly n solutions m >= 2, gpf = A006530; or -1 if no such k exists.
[ "1", "2", "6", "483", "1660577" ]
[ "nonn", "hard", "more" ]
14
0
2
[ "A006530", "A076563", "A354512", "A354516", "A354525" ]
null
Jianing Song, Aug 16 2022
2022-08-17T00:00:19
oeisdata/seq/A354/A354516.seq
5d2d897a991253484c3fce7098d0a0cb
A354517
Expansion of e.g.f. cos(x)^exp(x).
[ "1", "0", "-1", "-3", "-5", "10", "134", "742", "2325", "-2820", "-118756", "-1138368", "-7132025", "-20945990", "196411214", "4438271692", "50498101545", "400644382200", "1571151012344", "-16415635331328", "-500300343321365", "-7486919544207050", "-81415563206142166", "-563533196469890228" ]
[ "sign" ]
16
0
4
[ "A000248", "A009189", "A215515", "A354517", "A354518", "A354519" ]
null
Seiichi Manyama, Aug 16 2022
2022-08-17T03:51:04
oeisdata/seq/A354/A354517.seq
d8ce1f166ae8ba19a0153970d7de99c3
A354518
Expansion of e.g.f. cosh(x)^exp(x).
[ "1", "0", "1", "3", "7", "30", "166", "798", "4117", "27660", "196756", "1328448", "9866407", "86205210", "759842266", "6460661028", "60841732777", "651349676280", "6795873687496", "67981177154688", "770224145659627", "9854500496860470", "116983085896035646", "1301594922821009028", "17440543467561038557" ]
[ "sign" ]
22
0
4
[ "A000248", "A003727", "A215518", "A354517", "A354518", "A354520" ]
null
Seiichi Manyama, Aug 16 2022
2022-08-17T10:27:13
oeisdata/seq/A354/A354518.seq
e144691d8e53861770626b0805c4daba
A354519
Expansion of e.g.f. exp(x) * log(sec(x)).
[ "0", "1", "3", "8", "20", "61", "203", "888", "4080", "24001", "140283", "1028048", "7248020", "63374221", "522164243", "5299033488", "49924707840", "576514338721", "6110861416083", "79100066353208", "931434877343540", "13355627237749501", "172948115797623803", "2720827878727067208", "38424408320191299120" ]
[ "nonn" ]
25
1
3
[ "A000182", "A354517", "A354519", "A354520" ]
null
Seiichi Manyama, Aug 16 2022
2023-04-15T15:25:11
oeisdata/seq/A354/A354519.seq
1e13fc7cc4877cc17a1066a386099b82
A354520
Expansion of e.g.f. exp(x) * log(cosh(x)).
[ "0", "1", "3", "4", "0", "1", "63", "64", "-1320", "-1319", "49203", "49204", "-2653560", "-2653559", "196707423", "196707424", "-19194804720", "-19194804719", "2385684870723", "2385684870724", "-367985503366800", "-367985503366799", "68980888889771103", "68980888889771104", "-15445553274667315800" ]
[ "sign" ]
28
1
3
[ "A000182", "A354518", "A354519", "A354520" ]
null
Seiichi Manyama, Aug 16 2022
2023-04-15T15:53:56
oeisdata/seq/A354/A354520.seq
14ead06d0e8a2397f7cb989de5b2e8dd
A354521
a(n) is the position of the first letter in the US English name of n that can also be found in the English name of n+1.
[ "2", "1", "1", "3", "1", "2", "1", "2", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn", "easy", "word" ]
47
0
1
null
null
Ray G. Opao, Aug 16 2022
2022-10-01T19:44:40
oeisdata/seq/A354/A354521.seq
a5e81a608ab27b4fec51609f07723ee8
A354522
Square array A(n, k), n, k >= 0, read by antidiagonals; A(n, k) = g(f(n) + f(k)) where f denotes A001057 and g denotes its inverse.
[ "0", "1", "1", "2", "3", "2", "3", "0", "0", "3", "4", "5", "4", "5", "4", "5", "2", "1", "1", "2", "5", "6", "7", "6", "7", "6", "7", "6", "7", "4", "3", "0", "0", "3", "4", "7", "8", "9", "8", "9", "8", "9", "8", "9", "8", "9", "6", "5", "2", "1", "1", "2", "5", "6", "9", "10", "11", "10", "11", "10", "11", "10", "11", "10", "11", "10", "11", "8", "7", "4", "3", "0", "0", "3", "4", "7", "8", "11", "12", "13", "12", "13", "12", "13", "12", "13", "12", "13", "12", "13", "12" ]
[ "nonn", "tabl" ]
34
0
4
[ "A001057", "A014601", "A014681", "A047264", "A047521", "A354522", "A355278", "A357144" ]
null
Rémy Sigrist, Sep 14 2022
2022-09-18T12:37:54
oeisdata/seq/A354/A354522.seq
5d3963a277b01caf806e47cb80f544b2
A354523
Number of distinct letters in the English word for n that can also be found in the English word for n+1.
[ "2", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "3", "2", "4", "4", "4", "4", "3", "4", "3", "5", "6", "5", "6", "6", "6", "6", "5", "6", "3", "5", "6", "5", "5", "6", "5", "6", "6", "6", "3", "5", "5", "5", "5", "5", "6", "6", "6", "7", "4", "4", "5", "4", "5", "4", "4", "5", "5", "5", "3", "5", "6", "5", "6", "6", "5", "5", "6", "6", "5", "6", "7", "6", "7", "7", "7", "6", "6", "7", "4", "6", "7", "6", "7", "7", "6", "7", "6", "6", "5", "5", "6", "5", "6", "6", "5", "6", "5", "5", "2", "7" ]
[ "nonn", "easy", "word" ]
24
0
1
null
null
Ray G. Opao, Aug 16 2022
2022-10-01T19:45:30
oeisdata/seq/A354/A354523.seq
c3149df1cfeee3d9a744b0c9888e0705
A354524
Primes p such that p+1 is the concatenation of a power of 3 and a power of 2.
[ "11", "13", "17", "31", "37", "97", "131", "163", "271", "277", "331", "811", "1511", "2437", "2731", "3511", "7297", "9127", "9511", "18191", "21871", "27127", "65617", "72931", "196831", "196837", "278191", "332767", "729511", "812047", "1262143", "1524287", "1968331", "2187511", "5314411", "5314417", "5904931", "6561127", "7298191", "15943237", "47829697", "53144131" ]
[ "nonn", "base" ]
15
1
1
[ "A068715", "A068801", "A354524" ]
null
J. M. Bergot and Robert Israel, Aug 16 2022
2022-08-18T11:45:16
oeisdata/seq/A354/A354524.seq
d83c2ecc91048e3e517407c3c04a2fe7
A354525
Numbers k such that A354512(k) = A001221(k).
[ "1", "2", "3", "5", "6", "7", "9", "11", "13", "14", "15", "17", "19", "21", "23", "25", "29", "31", "33", "35", "37", "41", "43", "45", "47", "49", "51", "53", "55", "59", "61", "62", "67", "69", "71", "73", "77", "79", "83", "85", "89", "91", "93", "95", "97", "101", "103", "107", "109", "113", "115", "119", "121", "127", "131", "133", "137", "139", "141", "143", "145", "149", "151", "155", "157" ]
[ "nonn", "easy" ]
22
1
2
[ "A001221", "A006530", "A354512", "A354525", "A354526", "A354527", "A354531", "A354532", "A354533", "A354534" ]
null
Jianing Song, Aug 16 2022
2023-06-16T03:17:04
oeisdata/seq/A354/A354525.seq
f220556827dfa05c18f7e4f6e1168a8a
A354526
Numbers k such that A354512(k) < omega(k); complement of A354525.
[ "4", "8", "10", "12", "16", "18", "20", "22", "24", "26", "27", "28", "30", "32", "34", "36", "38", "39", "40", "42", "44", "46", "48", "50", "52", "54", "56", "57", "58", "60", "63", "64", "65", "66", "68", "70", "72", "74", "75", "76", "78", "80", "81", "82", "84", "86", "87", "88", "90", "92", "94", "96", "98", "99", "100", "102", "104", "105", "106", "108", "110", "111", "112", "114", "116", "117" ]
[ "nonn", "easy" ]
16
1
1
[ "A001221", "A006530", "A354512", "A354526", "A354527" ]
null
Jianing Song, Aug 16 2022
2022-08-17T05:07:26
oeisdata/seq/A354/A354526.seq
8a0bd733b77d1adf9ccdd7e50e94d9d9
A354527
a(n) = A001221(n) - A354512(n).
[ "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "2", "0", "0", "0", "1", "0", "2", "0", "1", "0", "1", "0", "1", "0", "1", "1", "1", "0", "2", "0", "1", "0", "1", "0", "2", "0", "1", "1", "1", "0", "2", "0", "1", "0", "1", "0", "2", "0", "2", "0", "1", "0", "2", "0", "1", "1", "1", "0", "3", "0", "0", "1", "1", "1", "2", "0", "1", "0", "2", "0", "2", "0", "1", "1", "1", "0", "1", "0", "2", "1", "1", "0", "3", "0", "1", "1", "1", "0", "3", "0" ]
[ "nonn", "easy" ]
18
1
12
[ "A001221", "A006530", "A354512", "A354525", "A354526", "A354527" ]
null
Jianing Song, Aug 16 2022
2022-08-17T05:07:40
oeisdata/seq/A354/A354527.seq
c6b76dbcfd9b2d2c820b2fb0730d2033
A354528
Square array T(m,n) read by antidiagonals - see Comments for definition.
[ "0", "1", "1", "3", "5", "3", "7", "12", "12", "7", "11", "21", "23", "21", "11", "17", "32", "39", "32", "17", "23", "45", "55", "61", "55", "45", "23", "31", "60", "77", "87", "77", "60", "31", "39", "77", "99", "117", "119", "117", "99", "77", "39", "49", "96", "127", "151", "161", "151", "127", "96", "49", "59", "117", "155", "189", "203", "213" ]
[ "nonn", "tabl" ]
26
1
4
[ "A028347", "A047838", "A179094", "A354528", "A354529" ]
null
Sela Fried, Aug 16 2022
2022-09-23T03:46:56
oeisdata/seq/A354/A354528.seq
efcc34eaa51bfe131d4fa095b2d40906
A354529
a(1) = 3, a(2) = 12 and a(n) = (3n^2+8n-2)/2 if n is even or = (3n^2+8n-5)/2, if n is odd, for n >= 3.
[ "3", "12", "23", "39", "55", "77", "99", "127", "155", "189", "223", "263", "303", "349", "395", "447", "499", "557", "615", "679", "743", "813", "883", "959", "1035", "1117", "1199", "1287", "1375", "1469", "1563", "1663", "1763", "1869", "1975", "2087", "2199", "2317", "2435", "2559", "2683", "2813", "2943", "3079", "3215", "3357", "3499", "3647", "3795", "3949", "4103", "4263", "4423" ]
[ "nonn", "easy" ]
33
1
1
[ "A028347", "A047838", "A179094", "A354528", "A354529" ]
null
Sela Fried, Aug 16 2022
2022-09-11T10:30:54
oeisdata/seq/A354/A354529.seq
ae20eda7c06e911f9e725d7007353f47
A354530
Numbers k such that k^2 is a minimal number; numbers k whose square is in A007416.
[ "1", "2", "4", "6", "8", "12", "24", "30", "32", "36", "60", "64", "72", "96", "120", "180", "192", "210", "216", "256", "288", "360", "420", "480", "512", "576", "768", "840", "864", "900", "960", "1080", "1260", "1440", "1536", "1680", "1728", "1800", "2048", "2304", "2520", "2880", "3360", "3840", "4320", "4608", "4620", "5400", "6144", "6300", "6720", "6912", "7200", "7560" ]
[ "nonn", "easy" ]
28
1
2
[ "A000005", "A007416", "A016017", "A025487", "A071571", "A166721", "A166722", "A354530" ]
null
Jianing Song, Aug 16 2022
2022-09-04T12:35:29
oeisdata/seq/A354/A354530.seq
f8e15ceffb5e8f125856d6a1c7da8c2c
A354531
Numbers k such that 2*(2^k-1) is in A354525.
[ "1", "2", "3", "5", "7", "9", "13", "17", "19", "31", "61", "67", "89", "107", "127", "137", "521", "607", "727" ]
[ "nonn", "hard", "more" ]
25
1
2
[ "A000043", "A354525", "A354531", "A354532", "A354533", "A354536" ]
null
Jianing Song, Aug 16 2022
2025-01-21T09:01:49
oeisdata/seq/A354/A354531.seq
9afc0d9bed2903cdb0098b9ce4be7ee6
A354532
Numbers k that are not Mersenne exponents (A000043) such that 2*(2^k-1) is in A354525.
[ "1", "9", "67", "137", "727" ]
[ "nonn", "hard", "more" ]
24
1
2
[ "A000043", "A354525", "A354531", "A354532", "A354534", "A354537" ]
null
Jianing Song, Aug 16 2022
2025-01-21T09:01:45
oeisdata/seq/A354/A354532.seq
1fd73d52a2c92f6fd89bd3405b9b4fc3
A354533
Even terms in A354525.
[ "2", "6", "14", "62", "254", "1022", "16382", "262142", "1048574", "4294967294", "4611686018427387902", "295147905179352825854", "1237940039285380274899124222", "324518553658426726783156020576254", "340282366920938463463374607431768211454", "348449143727040986586495598010130648530942" ]
[ "nonn", "hard" ]
17
1
1
[ "A006530", "A354525", "A354531", "A354532", "A354533", "A354534", "A354536" ]
null
Jianing Song, Aug 16 2022
2022-08-17T10:15:18
oeisdata/seq/A354/A354533.seq
7da75374a64592d46e2b361d117456a8
A354534
Even terms in A354525 that are not twice the Mersenne primes (A000668).
[ "2", "1022", "295147905179352825854", "348449143727040986586495598010130648530942" ]
[ "nonn", "hard" ]
21
1
1
[ "A006530", "A354525", "A354532", "A354533", "A354534", "A354537" ]
null
Jianing Song, Aug 16 2022
2025-01-21T09:05:00
oeisdata/seq/A354/A354534.seq
0c7ae5773d067f6c9d82cf6eb768c96a
A354535
a(n) is the number of different tile sizes after n iterations of the "Square Multiscale" substitution.
[ "1", "2", "3", "4", "5", "5", "6", "6", "7", "7", "8", "8", "8", "9", "9", "9", "10", "10", "10", "11", "11", "11", "11", "12", "12", "12", "12", "13", "13", "13", "13", "14", "14", "14", "14", "14", "15", "15", "15", "15", "15", "16", "16", "16", "16", "16", "17", "17", "17", "17", "17", "17", "18", "18", "18", "18", "18", "18", "19", "19", "19", "19", "19", "19", "20", "20", "20", "20", "20" ]
[ "nonn" ]
16
0
2
[ "A329919", "A329927", "A354535" ]
null
Rémy Sigrist, Aug 17 2022
2022-08-21T06:12:34
oeisdata/seq/A354/A354535.seq
2b177213c56e3e6bb075c8a95871ff06
A354536
Numbers k such that 2*k is in A354525.
[ "1", "3", "7", "31", "127", "511", "8191", "131071", "524287", "2147483647", "2305843009213693951", "147573952589676412927", "618970019642690137449562111", "162259276829213363391578010288127", "170141183460469231731687303715884105727", "174224571863520493293247799005065324265471" ]
[ "nonn", "hard" ]
20
1
2
[ "A006530", "A354525", "A354531", "A354532", "A354533", "A354536", "A354537" ]
null
Jianing Song, Aug 17 2022
2025-01-21T13:31:29
oeisdata/seq/A354/A354536.seq
8de33d4dda903878e6d78cac043af194
A354537
Numbers k that are not Mersenne primes (A000668) such that 2*k is in A354525.
[ "1", "511", "147573952589676412927", "174224571863520493293247799005065324265471" ]
[ "nonn", "hard" ]
22
1
2
[ "A000668", "A354525", "A354532", "A354534", "A354536", "A354537" ]
null
Jianing Song, Aug 17 2022
2025-01-21T13:32:41
oeisdata/seq/A354/A354537.seq
fb0e9539010c17fa61980a3a9f84b66e
A354538
a(n) is the least k such that A322523(k) = n.
[ "1", "3", "8", "17", "44", "125", "368", "1097", "3284", "9845", "29528", "88577", "265724", "797165", "2391488", "7174457", "21523364", "64570085", "193710248", "581130737", "1743392204", "5230176605", "15690529808", "47071589417", "141214768244", "423644304725", "1270932914168", "3812798742497", "11438396227484" ]
[ "nonn", "easy" ]
42
0
2
[ "A322523", "A354538" ]
null
Hugh Williamson, Aug 17 2022
2024-06-10T13:31:38
oeisdata/seq/A354/A354538.seq
4dc178600cd547bbb60b526cf0ea5f9f
A354539
Number of decorated Dyck paths of length n without peaks at level 1 ending at arbitrary levels.
[ "1", "1", "1", "2", "5", "8", "18", "31", "71", "126", "290", "527", "1218", "2253", "5223", "9796", "22763", "43170", "100502", "192347", "448476", "864887", "2019121", "3919162", "9159252", "17877619", "41819003", "82021628", "192015633" ]
[ "nonn" ]
11
0
4
[ "A128723", "A354539" ]
null
R. J. Mathar, Aug 17 2022
2023-03-02T08:33:20
oeisdata/seq/A354/A354539.seq
0f55dc78cbb802006a9c39ab7025632a
A354540
Number of decorated Dyck paths of length n ending at arbitrary levels.
[ "1", "1", "2", "3", "7", "11", "26", "43", "102", "175", "416", "733", "1745", "3137", "7476", "13651", "32559", "60199", "143672", "268369", "640823", "1207277", "2884008", "5472821", "13078414", "24973213", "59696622", "114609547", "274037261", "528622499", "1264251474", "2449053107" ]
[ "nonn" ]
10
0
3
null
null
R. J. Mathar, Aug 17 2022
2022-08-17T11:49:55
oeisdata/seq/A354/A354540.seq
8ac1984bbf4ba9dc884b0fa66e7a1869
A354541
Number of ways to tile a double-hexagon strip of n hexagons, using single and double hexagons.
[ "1", "1", "2", "4", "8", "12", "24", "48", "72", "144", "288", "432", "864", "1728", "2592", "5184", "10368", "15552", "31104", "62208", "93312", "186624", "373248", "559872", "1119744", "2239488", "3359232", "6718464", "13436928", "20155392", "40310784", "80621568", "120932352", "241864704", "483729408" ]
[ "nonn", "easy" ]
23
0
3
null
null
Greg Dresden and Zeno Changze Song, Aug 17 2022
2024-05-28T18:29:09
oeisdata/seq/A354/A354541.seq
7a6093a65922e713b87905ed705cc2d3
A354542
Primes in A354543.
[ "3533", "688277", "6694673", "40577149", "55138957", "86928683", "120233569", "353700679", "363666767", "394746449", "665910173", "697048171", "1472815853", "1526776393", "1817357573", "2179037593", "2395963249", "2548619561", "2627434567", "3047031863", "3273354481", "4524129787", "6073626073", "6586863131", "9320100589", "10836344773" ]
[ "nonn" ]
19
1
1
[ "A002476", "A007528", "A354542", "A354543" ]
null
J. M. Bergot and Robert Israel, Aug 17 2022
2022-08-18T11:46:01
oeisdata/seq/A354/A354542.seq
dacf2bd943cfc0b93236aaab94d8679a
A354543
Convolution of A007528 and A002476.
[ "35", "142", "357", "746", "1351", "2250", "3533", "5248", "7467", "10232", "13675", "17910", "22979", "28972", "35931", "44192", "53677", "64392", "76727", "90640", "106209", "123614", "142849", "164232", "187841", "213802", "242181", "273080", "306733", "343266", "382745", "425218", "470685", "519740", "572275", "628302", "688277", "752440", "820557", "892634", "969475" ]
[ "nonn" ]
12
2
1
[ "A002476", "A007528", "A354542", "A354543" ]
null
J. M. Bergot and Robert Israel, Aug 17 2022
2022-08-21T09:08:47
oeisdata/seq/A354/A354543.seq
36f555c0cbc3da8888a14bfe40845332
A354544
Table read by antidiagonals: T(n,k) (n >= 3, k >= 1) is the number of vertices formed in a regular n-gon by straight line segments when connecting the n corner vertices to the points dividing the sides into k equal parts.
[ "3", "7", "5", "21", "25", "10", "25", "81", "61", "19", "63", "157", "285", "205", "42", "67", "301", "476", "541", "358", "57", "129", "381", "1020", "1327", "1526", "681", "135", "133", "665", "1311", "2185", "2682", "2417", "1234", "171", "219", "821", "2215", "3067", "5250", "5073", "4716", "2131", "341", "223", "1109", "2666", "4921", "7246", "8937", "8623", "6861", "3169", "313" ]
[ "nonn", "tabl" ]
20
3
1
[ "A007569", "A331782", "A354544", "A355949", "A356044" ]
null
Scott R. Shannon, Aug 18 2022
2022-08-18T14:22:07
oeisdata/seq/A354/A354544.seq
e2a601e9f1ef6179b7723c83919b1c00
A354545
Expansion of e.g.f. exp(x)^( cos(x) + sin(x) ).
[ "1", "1", "3", "4", "9", "-24", "-143", "-902", "-1631", "5176", "109841", "664302", "1479841", "-16079764", "-240229975", "-1395162974", "126628545", "101950486736", "1118811398113", "4468008939542", "-46600859353919", "-1019505781080044", "-7952038289388071", "10041106628453162" ]
[ "sign" ]
15
0
3
[ "A000248", "A009189", "A009214", "A354545", "A354546" ]
null
Seiichi Manyama, Aug 18 2022
2022-08-18T10:19:33
oeisdata/seq/A354/A354545.seq
7210e85e1fe8ddf6fc59dd21b139606a
A354546
Expansion of e.g.f. exp(x)^( cos(x) - sin(x) ).
[ "1", "1", "-1", "-8", "-7", "96", "385", "-1210", "-14943", "-5912", "593361", "2409298", "-22935647", "-236575468", "590041257", "20313729886", "40488350401", "-1659176093392", "-11796304552991", "120680593857514", "1966312603184321", "-4949789957167124", "-288454178376442407", "-849587090710029098" ]
[ "sign" ]
16
0
4
[ "A000248", "A009189", "A009214", "A354545", "A354546" ]
null
Seiichi Manyama, Aug 18 2022
2022-08-18T10:19:51
oeisdata/seq/A354/A354546.seq
7b931cb78d1915459de6dddf33d56b3d
A354547
Least number k <= n such that sopfr(k) = sopfr(n).
[ "1", "2", "3", "4", "5", "5", "7", "8", "8", "7", "11", "7", "13", "14", "15", "15", "17", "15", "19", "14", "21", "13", "23", "14", "21", "26", "14", "11", "29", "21", "31", "21", "33", "19", "35", "21", "37", "38", "39", "11", "41", "35", "43", "26", "11", "46", "47", "11", "33", "35", "51", "17", "53", "11", "39", "13", "57", "31", "59", "35", "61", "62", "13", "35", "65", "39", "67", "38" ]
[ "nonn" ]
41
1
2
[ "A001414", "A056240", "A064364", "A354547" ]
null
Jean-Marc Rebert, Aug 15 2022
2022-08-28T21:12:51
oeisdata/seq/A354/A354547.seq
8e0d2efd1d921d74cacfe46c737101fe
A354548
Number of edges in the graph of continuous discrete sections for a trivial bundle in a total space of the fiber bundle of size n.
[ "1", "8", "56", "296", "1380", "5952" ]
[ "nonn", "more" ]
26
1
2
[ "A000079", "A016777", "A081113", "A126360", "A188861", "A354548" ]
null
Sinuhe Perea, Aug 18 2022
2023-04-16T06:35:00
oeisdata/seq/A354/A354548.seq
f4874d4d837a18289f78b93a03b02a7a
A354549
Numbers k such that floor(k^2*phi) is a square, where phi = A001622 is the golden ratio.
[ "0", "1", "4", "125", "84277", "1435150", "9061191", "249858189", "2799936925", "146234239784", "1139643680683264", "7471434609455791", "21274660147684109", "2911209509190673141", "15845190736671957299", "995980378496501932493", "213688560255016550712685", "28372206851301867342910959" ]
[ "nonn" ]
24
1
3
[ "A000201", "A001622", "A003622", "A035513", "A225204", "A225205", "A354549" ]
null
Jianing Song, Aug 18 2022
2022-08-28T08:28:44
oeisdata/seq/A354/A354549.seq
67a9e4df33b7a3cdb181cc9643e3f357
A354550
Expansion of e.g.f. exp( x * exp(x^2/2) ).
[ "1", "1", "1", "4", "13", "46", "241", "1156", "6889", "44668", "300241", "2328976", "18390901", "159273544", "1461200833", "13995753136", "144068872081", "1531949061136", "17259159775969", "202543867724608", "2474236899786781", "31633380519660256", "417760492214548561", "5751414293905728064" ]
[ "nonn" ]
22
0
4
[ "A000248", "A216688", "A354550", "A354551", "A354552" ]
null
Seiichi Manyama, Aug 18 2022
2024-03-03T16:49:40
oeisdata/seq/A354/A354550.seq
14e03efa98b2c6ae65b9c6b87d3f68cd
A354551
Expansion of e.g.f. exp( x * exp(x^3/6) ).
[ "1", "1", "1", "1", "5", "21", "61", "211", "1401", "8065", "37241", "240021", "1997821", "13856701", "94418325", "874328911", "8304303281", "69158458881", "658339599601", "7454839614985", "78224066633781", "805961931388741", "9828080719704941", "124199805022959051", "1466207770078872745" ]
[ "nonn" ]
21
0
5
[ "A000248", "A354550", "A354551", "A354552" ]
null
Seiichi Manyama, Aug 18 2022
2025-03-03T13:08:37
oeisdata/seq/A354/A354551.seq
9f87880f6358a97b90f1264ab9346ad7
A354552
Expansion of e.g.f. exp( x * exp(x^4/24) ).
[ "1", "1", "1", "1", "1", "6", "31", "106", "281", "946", "7561", "54286", "281161", "1207636", "7997991", "81996916", "701522641", "4580581916", "29742355441", "306369616636", "3632198902321", "34710574441096", "276645112305871", "2652825718776696", "35647605796451881", "458142859493786776" ]
[ "nonn" ]
17
0
6
[ "A000248", "A354550", "A354551", "A354552" ]
null
Seiichi Manyama, Aug 18 2022
2022-08-19T02:25:17
oeisdata/seq/A354/A354552.seq
d250e17cee71b15088ced8f5ec39718a
A354553
Expansion of e.g.f. exp( x * exp(x^3) ).
[ "1", "1", "1", "1", "25", "121", "361", "3361", "42001", "275185", "1819441", "30777121", "371238121", "3057311401", "44263763545", "801096528961", "9710981323681", "125367419194081", "2643123767954401", "45840730383002305", "646414025466298681", "13258301279836276441" ]
[ "nonn" ]
18
0
5
[ "A000248", "A216688", "A354553", "A354554" ]
null
Seiichi Manyama, Aug 18 2022
2022-08-19T02:25:25
oeisdata/seq/A354/A354553.seq
1ddc2fe9de87e76772e0acb630486421
A354554
Expansion of e.g.f. exp( x * exp(x^4) ).
[ "1", "1", "1", "1", "1", "121", "721", "2521", "6721", "196561", "3659041", "29993041", "159762241", "1686639241", "60298558321", "987112886761", "9315623640961", "76611297104161", "2454331471018561", "69805324167893281", "1086439146068753281", "11530308934656915481" ]
[ "nonn" ]
17
0
6
[ "A000248", "A216688", "A354553", "A354554" ]
null
Seiichi Manyama, Aug 18 2022
2022-08-19T02:25:33
oeisdata/seq/A354/A354554.seq
33f465beb76d135c77a5ceda0ee7a029
A354555
Rectangular array read by antidiagonals. T(m,n) is the number of degree n monic polynomials in GF_2[x] such that each irreducible factor in the prime factorization has multiplicity no greater than m, m>=1, n>=0.
[ "1", "1", "2", "1", "2", "2", "1", "2", "4", "4", "1", "2", "4", "6", "8", "1", "2", "4", "8", "12", "16", "1", "2", "4", "8", "14", "24", "32", "1", "2", "4", "8", "16", "28", "48", "64", "1", "2", "4", "8", "16", "30", "56", "96", "128", "1", "2", "4", "8", "16", "32", "60", "112", "192", "256", "1", "2", "4", "8", "16", "32", "62", "120", "224", "384", "512", "1", "2", "4", "8", "16", "32", "64", "124", "240", "448", "768", "1024" ]
[ "nonn", "tabl" ]
19
0
3
[ "A001037", "A354555", "A356583" ]
null
Geoffrey Critzer, Aug 18 2022
2024-08-06T05:42:54
oeisdata/seq/A354/A354555.seq
1d5045013231bad79d323e5b8217ad6a
A354556
Numerators of a sequence related to the Secretary Problem with Multiple Stoppings.
[ "1", "3", "47", "2761", "4162637", "380537052235603", "705040594914523588948186792543", "302500210177484374840641189918370275991590974715547528765249", "49554292678269029432299170288905873298367846539726510384850403192729912522937262239403638817695466470734534217406992001" ]
[ "nonn", "frac" ]
22
1
2
[ "A354556", "A354557" ]
null
José María Grau Ribas, May 28 2022
2022-08-01T08:11:18
oeisdata/seq/A354/A354556.seq
eb51fdfdf222d9738d35112172f2b54a
A354557
Denominators of a sequence related to the Secretary Problem with Multiple Stoppings.
[ "1", "2", "24", "1152", "1474560", "117413668454400", "193003573558876719588311040000", "74500758812993473612938854416966977838930799571763200000000", "11100726127423649454784549321327362347631758176882955145554591521918123315624957195621435513013513748480000000000000000" ]
[ "nonn", "frac" ]
17
1
2
[ "A354556", "A354557" ]
null
José María Grau Ribas, May 28 2022
2022-08-01T08:11:11
oeisdata/seq/A354/A354557.seq
237d3d5ea87c2ff1f8a00e0a997d4f9a
A354558
Numbers k such that k and k+1 are both divisible by the square of their largest prime factor.
[ "8", "49", "242", "288", "675", "1444", "1681", "2400", "2645", "6727", "6859", "9408", "9800", "10647", "12167", "13689", "18490", "23762", "24299", "26010", "36517", "47915", "48734", "57121", "58080", "59535", "75809", "85697", "101250", "103246", "113568", "118579", "131043", "142884", "158949", "182182", "201019", "212194", "235224" ]
[ "nonn" ]
24
1
1
[ "A006530", "A060355", "A070003", "A071178", "A354558", "A354559", "A354560", "A354562", "A354563", "A354564", "A354565", "A354566" ]
null
Amiram Eldar, May 30 2022
2022-06-05T11:47:20
oeisdata/seq/A354/A354558.seq
f23ee6398033751a9ae2ef2949c68f68
A354559
The number of terms of A354558 that are <= 10^n.
[ "1", "2", "5", "13", "28", "79", "204", "549", "1509", "4231", "12072", "36426", "112589" ]
[ "nonn", "more" ]
19
1
2
[ "A354558", "A354559" ]
null
Amiram Eldar, May 30 2022
2022-06-05T08:28:48
oeisdata/seq/A354/A354559.seq
645a6aa9625dce755ba94c8ab89ebc69
A354560
Numbers k such that k, k+1 and k+2 are all divisible by the square of their largest prime factor.
[ "1294298", "9841094", "158385500", "1947793550", "5833093013", "11587121710", "20944167840", "22979821310", "24604784814", "267631935500", "290672026412", "956544588350", "987988937343", "2399283556900", "2816075601855", "4174608151758", "4322550249043", "6789218799999", "10617595679778", "16036630184409" ]
[ "nonn" ]
10
1
1
[ "A006530", "A070003", "A071178", "A354558", "A354560" ]
null
Amiram Eldar, May 30 2022
2022-06-01T05:11:04
oeisdata/seq/A354/A354560.seq
cc7d4c36d909cc3adee1c409adbc8600
A354561
Numbers divisible by the cube of their largest prime factor.
[ "8", "16", "27", "32", "54", "64", "81", "108", "125", "128", "162", "216", "243", "250", "256", "324", "343", "375", "432", "486", "500", "512", "625", "648", "686", "729", "750", "864", "972", "1000", "1024", "1029", "1125", "1250", "1296", "1331", "1372", "1458", "1500", "1715", "1728", "1875", "1944", "2000", "2048", "2058", "2187", "2197", "2250", "2401", "2500" ]
[ "nonn" ]
16
1
1
[ "A006530", "A036966", "A070003", "A071178", "A349306", "A354561", "A354562" ]
null
Amiram Eldar, May 30 2022
2022-06-01T05:11:54
oeisdata/seq/A354/A354561.seq
239480016264153432920983a5fb3bb9
A354562
Numbers k such that k and k+1 are both divisible by the cube of their largest prime factor.
[ "6859", "11859210", "18253460", "38331320423", "41807225999", "49335445119", "50788425848", "67479324240", "203534609200", "245934780371", "250355343420", "581146348824", "779369813871", "1378677994836", "2152196307260", "2730426690524", "3616995855087", "5473549133744", "6213312123347", "6371699408179", "8817143116903" ]
[ "nonn" ]
23
1
1
[ "A006530", "A070003", "A071178", "A354558", "A354561", "A354562", "A354563", "A354564" ]
null
Amiram Eldar, May 30 2022
2022-05-31T02:17:24
oeisdata/seq/A354/A354562.seq
2f009762430f21092d2e1fed9ed6bc5e
A354563
Numbers k such that P(k)^2 | k and P(k+1)^3 | (k+1), where P(k) = A006530(k) is the largest prime dividing k.
[ "242", "2400", "6859", "10647", "47915", "57121", "344604", "499999", "830465", "1012499", "1431125", "2098853", "2825760", "2829123", "3930399", "5560691", "11859210", "12323584", "13137830", "18253460", "18279039", "21093749", "30664296", "32279841", "33999932", "37218852", "38640401", "38740085", "41485688", "45222737" ]
[ "nonn" ]
14
1
1
[ "A006530", "A070003", "A071178", "A354558", "A354562", "A354563", "A354564" ]
null
Amiram Eldar, May 30 2022
2022-06-04T02:01:56
oeisdata/seq/A354/A354563.seq
452fe663d7321d51f3645d67ef38d944
A354564
Numbers k such that P(k)^3 | k and P(k+1)^2 | (k+1), where P(k) = A006530(k) is the largest prime dividing k.
[ "8", "6859", "12167", "101250", "328509", "453962", "482447", "536238", "598950", "5619712", "7170366", "11449008", "11667159", "11859210", "13428095", "15054335", "16541965", "18085704", "18253460", "19450850", "22173969", "23049600", "24039994", "29911714", "30959144", "32580250", "33229625", "44126385", "44321375" ]
[ "nonn" ]
13
1
1
[ "A006530", "A070003", "A071178", "A354558", "A354562", "A354563", "A354564" ]
null
Amiram Eldar, May 30 2022
2022-06-04T02:01:49
oeisdata/seq/A354/A354564.seq
90ee5dd86ec8d94bde1a0273955e23bd
A354565
Numbers k such that P(k)^2 | k and P(k+1)^4 | (k+1), where P(k) = A006530(k) is the largest prime dividing k.
[ "242", "2400", "57121", "499999", "1012499", "2825760", "2829123", "11859210", "18279039", "21093749", "37218852", "38740085", "70799772", "96393374", "413428949", "642837222", "656356767", "675975026", "1065352364", "1333564323", "1418528255", "2654744949", "5547008142", "8576868299", "9515377949", "10022519999" ]
[ "nonn" ]
12
1
1
[ "A006530", "A070003", "A071178", "A354558", "A354563", "A354565", "A354566" ]
null
Amiram Eldar, May 30 2022
2022-06-04T02:47:21
oeisdata/seq/A354/A354565.seq
517e9bbf61fb44842b9e75db973cee82
A354566
Numbers k such that P(k)^4 | k and P(k+1)^2 | (k+1), where P(k) = A006530(k) is the largest prime dividing k.
[ "101250", "11859210", "23049600", "32580250", "131545575", "162364824", "969697050", "1176565754", "1271688417", "1612089680", "1862719859", "2409451520", "2441023914", "3182903731", "3697778084", "4010283270", "4329214629", "6666661950", "6932744126", "7739389944", "9188994752", "11717364285", "17306002674" ]
[ "nonn" ]
13
1
1
[ "A006530", "A070003", "A071178", "A354558", "A354564", "A354565", "A354566" ]
null
Amiram Eldar, May 30 2022
2022-06-04T02:47:34
oeisdata/seq/A354/A354566.seq
1e4dadf4c958df77d2e40144aacb88d1
A354567
a(n) is the least number k such that P(k)^n | k and P(k+1)^n | (k+1), where P(k) = A006530(k) is the largest prime dividing k, or -1 if no such k exists.
[ "1", "8", "6859", "11859210" ]
[ "nonn", "more", "bref" ]
8
1
2
[ "A006530", "A071178", "A354558", "A354562", "A354567" ]
null
Amiram Eldar, May 30 2022
2022-05-30T16:31:54
oeisdata/seq/A354/A354567.seq
007c5a00be66c607a70ba9b943d57728
A354568
Irregular triangle read by rows: T(n,k) is the number of Hamiltonian cycles in the Kneser graph K(n,k), 1 <= k < n/2.
[ "1", "3", "12", "0", "60", "155328" ]
[ "nonn", "tabf", "more" ]
18
3
2
[ "A001710", "A301560", "A354568" ]
null
Pontus von Brömssen, Aug 18 2022
2024-08-03T12:36:12
oeisdata/seq/A354/A354568.seq
b58f8a22e4c73f886bdf98830ac2bea8
A354569
Ordered even leg lengths k (listed with multiplicity) of primitive Pythagorean triangles such that all odd prime factors of k are congruent to 1 (mod 4) and at least one prime factor is congruent to 1 (mod 4).
[ "20", "20", "40", "40", "52", "52", "68", "68", "80", "80", "100", "100", "104", "104", "116", "116", "136", "136", "148", "148", "160", "160", "164", "164", "200", "200", "208", "208", "212", "212", "232", "232", "244", "244", "260", "260", "260", "260", "272", "272", "292", "292", "296", "296", "320", "320", "328", "328", "340", "340", "340", "340", "356", "356" ]
[ "nonn" ]
48
1
1
[ "A020882", "A354569" ]
null
Lothar Selle, Jun 05 2022
2022-06-22T02:29:27
oeisdata/seq/A354/A354569.seq
f996ad0416e93f05b74f13841fe24ce5
A354570
Ordered odd leg lengths k (listed with multiplicity) of primitive Pythagorean triangles such that all prime factors of k are congruent to 3 (mod 4).
[ "3", "7", "9", "11", "19", "21", "21", "23", "27", "31", "33", "33", "43", "47", "49", "57", "57", "59", "63", "63", "67", "69", "69", "71", "77", "77", "79", "81", "83", "93", "93", "99", "99", "103", "107", "121", "127", "129", "129", "131", "133", "133", "139", "141", "141", "147", "147", "151", "161", "161", "163", "167", "171", "171", "177", "177", "179", "189", "189", "191" ]
[ "nonn" ]
54
1
1
[ "A004614", "A120890", "A354570", "A354571" ]
null
Lothar Selle, Jun 03 2022
2022-08-28T08:41:46
oeisdata/seq/A354/A354570.seq
8af49c285b95a88ded76524108ca5519
A354571
Ordered even leg lengths k (listed with multiplicity) of primitive Pythagorean triangles such that all odd prime factors of k are congruent to 3 (mod 4) and at least one prime factor is odd.
[ "12", "12", "24", "24", "28", "28", "36", "36", "44", "44", "48", "48", "56", "56", "72", "72", "76", "76", "84", "84", "84", "84", "88", "88", "92", "92", "96", "96", "108", "108", "112", "112", "124", "124", "132", "132", "132", "132", "144", "144", "152", "152", "168", "168", "168", "168", "172", "172", "176", "176", "184", "184", "188", "188", "192", "192", "196", "196" ]
[ "nonn" ]
41
1
1
[ "A354570", "A354571" ]
null
Lothar Selle, Jun 04 2022
2022-08-30T13:34:22
oeisdata/seq/A354/A354571.seq
842e2db90d36319d8fdea762ed7bbea7
A354572
Prime partial sums of the primes == 1 (mod 6).
[ "7", "107", "211", "739", "1657", "2953", "4091", "20479", "23459", "33713", "35671", "46133", "60527", "63127", "77237", "80209", "86399", "106277", "127997", "139871", "178757", "183361", "197569", "238853", "255239", "272171", "353611", "367019", "394759", "416089", "460189", "475421", "625199", "652499", "808111", "860393", "903871", "925979", "959603", "1005217" ]
[ "nonn" ]
17
1
1
[ "A038349", "A354572", "A354573" ]
null
J. M. Bergot and Robert Israel, Aug 18 2022
2022-09-05T09:10:47
oeisdata/seq/A354/A354572.seq
53dfd5c162cb9b0d4541b0c9f9eda5db
A354573
Prime partial sums of the primes == 5 (mod 6).
[ "5", "173", "439", "1117", "1433", "2633", "3643", "6173", "11489", "22727", "25867", "36523", "51341", "71707", "80347", "89413", "98947", "102203", "119869", "135209", "155653", "173087", "182233", "196387", "226063", "298031", "353921", "367219", "460127", "483179", "498859", "547387", "555683", "572581", "826201", "932801", "988453", "1057741", "1203421", "1253999" ]
[ "nonn" ]
14
1
1
[ "A038361", "A354572", "A354573" ]
null
J. M. Bergot and Robert Israel, Aug 18 2022
2022-08-23T17:49:03
oeisdata/seq/A354/A354573.seq
bdf46cac8e31521f3e0e25da83d37647
A354574
E.g.f. A(x) satisfies A(x) = 1 + x * A(1 - exp(-x)).
[ "1", "1", "2", "3", "-8", "-65", "366", "4284", "-71392", "-377919", "28218760", "-249587877", "-14356069056", "587285561746", "153563287892", "-954498079774950", "39921820513516256", "533333406684245239", "-158979463609003391970", "8008135971419079188618", "190727236066813163686860" ]
[ "sign" ]
12
0
3
[ "A048801", "A353177", "A354574", "A354729", "A354730" ]
null
Seiichi Manyama, Jun 04 2022
2022-06-05T00:44:01
oeisdata/seq/A354/A354574.seq
c34b86d82a360acaed42ffc7dcc0a898
A354575
a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared that is coprime to a(n-1) and the difference a(n) - a(n-1) is distinct from all previous differences.
[ "1", "2", "5", "3", "7", "4", "9", "8", "15", "11", "6", "17", "10", "19", "13", "21", "23", "12", "25", "16", "31", "14", "33", "20", "37", "18", "41", "26", "47", "22", "49", "27", "43", "29", "35", "53", "24", "55", "28", "57", "34", "59", "38", "71", "30", "67", "32", "73", "36", "79", "39", "61", "45", "77", "46", "81", "91", "40", "87", "44", "83", "50", "99", "52", "97", "42", "95", "51", "65", "89", "63", "101", "48", "103", "54", "113" ]
[ "nonn", "look" ]
17
1
2
[ "A354575", "A354679", "A354687", "A354688", "A354727", "A354739" ]
null
Scott R. Shannon, Jun 05 2022
2022-10-25T13:48:32
oeisdata/seq/A354/A354575.seq
40ceee9b4e2a118888ffab65770918eb
A354576
Variant of A253028 using only odd numbers: a mirror symmetric array of odd numbers where the n-th term is equal to the number of terms in the n-th row of the array.
[ "1", "3", "1", "5", "7", "9", "3", "1", "5", "11", "13", "7", "3", "1", "5", "9", "15", "17", "11", "7", "3", "1", "5", "9", "13", "19", "21", "15", "23", "25", "27", "17", "11", "19", "29", "31", "21", "13", "7", "3", "1", "5", "9", "15", "23", "33", "35", "25", "17", "11", "7", "3", "1", "5", "9", "13", "19", "27", "37", "39", "29", "21", "15", "23", "31", "41" ]
[ "nonn", "tabf" ]
14
1
2
[ "A253028", "A354576", "A354577" ]
null
Felix Fröhlich, May 30 2022
2023-11-11T08:50:26
oeisdata/seq/A354/A354576.seq
0c7f30add148e746b45e4d94a6d1b471
A354577
Variant of A253028 using only even numbers: a mirror symmetric array of even numbers where the n-th term is equal to the number of terms in the n-th row of the array.
[ "2", "4", "6", "2", "4", "8", "10", "6", "2", "4", "8", "12", "14", "16", "18", "10", "12", "20", "22", "14", "6", "2", "4", "8", "16", "24", "26", "18", "10", "6", "2", "4", "8", "12", "20", "28", "30", "22", "14", "16", "24", "32", "34", "36", "38", "26", "28", "40", "42", "30", "18", "10", "12", "20", "32", "44", "46", "34", "22", "14", "6", "2", "4", "8", "16", "24", "36", "48", "50", "38", "26" ]
[ "nonn", "tabf" ]
8
1
1
[ "A253028", "A354576", "A354577" ]
null
Felix Fröhlich, May 30 2022
2022-06-22T21:04:11
oeisdata/seq/A354/A354577.seq
79c7d38f0c130e07dd6e3317c5f25b2d
A354578
Number of ways to choose a divisor of each part of the n-th composition in standard order such that no adjacent divisors are equal.
[ "1", "1", "2", "0", "2", "1", "1", "0", "3", "1", "2", "0", "1", "1", "0", "0", "2", "2", "3", "0", "3", "1", "1", "0", "2", "1", "1", "0", "0", "0", "0", "0", "4", "1", "4", "0", "2", "2", "1", "0", "4", "2", "2", "0", "1", "1", "0", "0", "1", "2", "2", "0", "2", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "3", "3", "0", "5", "2", "2", "0", "5", "1", "3", "0", "1", "1", "0", "0", "3", "3", "5", "0", "3", "1", "1" ]
[ "nonn", "tabf" ]
9
0
3
[ "A000005", "A003242", "A005811", "A011782", "A029837", "A066099", "A124767", "A175413", "A238279", "A275870", "A300273", "A333381", "A333489", "A333755", "A353832", "A353837", "A353838", "A353840", "A353846", "A353847", "A353848", "A353849", "A353850", "A353851", "A353852", "A353853", "A353859", "A353860", "A353863", "A354578", "A354584", "A354904", "A354905" ]
null
Gus Wiseman, Jun 11 2022
2022-06-12T22:52:29
oeisdata/seq/A354/A354578.seq
1d66dfef60d30f2a21c988cd20e51c1e
A354579
Number of distinct lengths of runs in the n-th composition in standard order.
[ "0", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "2", "1", "1", "2", "2", "2", "2", "2", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "2", "1", "2", "1", "2", "2", "2", "1", "2", "2", "2", "2", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "2", "2", "1", "1", "2", "2", "1", "1", "1", "2", "2", "2", "2" ]
[ "nonn" ]
9
0
12
[ "A003242", "A005811", "A029837", "A066099", "A071625", "A124767", "A181819", "A238279", "A329738", "A329739", "A333381", "A333489", "A333627", "A333755", "A351014", "A351015", "A351596", "A353744", "A353835", "A353839", "A353847", "A353848", "A353849", "A353850", "A353851", "A353852", "A353860", "A353861", "A354579", "A354906" ]
null
Gus Wiseman, Jun 11 2022
2022-06-12T22:52:33
oeisdata/seq/A354/A354579.seq
e0bbcbcc300d24977addaf17209311c4
A354580
Number of rucksack compositions of n: every distinct partial run has a different sum.
[ "1", "1", "2", "4", "6", "12", "22", "39", "68", "125", "227", "402", "710", "1280", "2281", "4040", "7196", "12780", "22623", "40136", "71121", "125863", "222616", "393305", "695059", "1227990", "2167059", "3823029", "6743268", "11889431", "20955548", "36920415", "65030404", "114519168", "201612634", "354849227" ]
[ "nonn" ]
24
0
3
[ "A003242", "A011782", "A108917", "A143823", "A169942", "A238279", "A242882", "A275870", "A275972", "A299702", "A300273", "A325545", "A325676", "A325680", "A325682", "A325685", "A325687", "A329739", "A333223", "A333489", "A333755", "A351017", "A353836", "A353837", "A353838", "A353839", "A353847", "A353848", "A353849", "A353850", "A353851", "A353852", "A353853", "A353859", "A353860", "A353864", "A353865", "A353866", "A353867", "A354580", "A354581", "A354908" ]
null
Gus Wiseman, Jun 13 2022
2023-09-11T15:53:18
oeisdata/seq/A354/A354580.seq
ce84b45fd40cf7d8cd3d04bc5b8a9f38
A354581
Numbers k such that the k-th composition in standard order is rucksack, meaning every distinct partial run has a different sum.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "13", "15", "16", "17", "18", "19", "20", "21", "22", "24", "25", "26", "28", "31", "32", "33", "34", "35", "36", "37", "38", "40", "41", "42", "44", "45", "48", "49", "50", "51", "52", "53", "54", "56", "57", "63", "64", "65", "66", "67", "68", "69", "70", "71", "72", "73", "74", "76", "77", "80", "81", "82", "84", "85", "86", "88" ]
[ "nonn" ]
8
0
3
[ "A000120", "A000225", "A005811", "A029837", "A063787", "A066099", "A124767", "A124771", "A175413", "A181819", "A238279", "A330036", "A333381", "A333489", "A333755", "A334299", "A351014", "A351015", "A353832", "A353835", "A353837", "A353838", "A353847", "A353848", "A353849", "A353850", "A353851", "A353852", "A353853", "A353859", "A353860", "A353861", "A353864", "A353866", "A353932", "A354580", "A354581", "A354583", "A354907" ]
null
Gus Wiseman, Jun 15 2022
2022-06-17T08:35:06
oeisdata/seq/A354/A354581.seq
4a725715294f7c6fed432b64cf076502
A354582
Number of distinct contiguous constant subsequences (or partial runs) in the k-th composition in standard order.
[ "0", "1", "1", "2", "1", "2", "2", "3", "1", "2", "2", "3", "2", "2", "3", "4", "1", "2", "2", "3", "2", "3", "2", "4", "2", "2", "3", "3", "3", "3", "4", "5", "1", "2", "2", "3", "2", "3", "3", "4", "2", "3", "3", "4", "3", "2", "3", "5", "2", "2", "3", "3", "3", "3", "2", "4", "3", "3", "4", "3", "4", "4", "5", "6", "1", "2", "2", "3", "2", "3", "3", "4", "2", "3", "3", "4", "2", "3", "4", "5", "2", "3", "2", "4", "3", "4", "3" ]
[ "nonn", "tabf" ]
6
0
4
[ "A000120", "A001221", "A001222", "A003242", "A005811", "A029837", "A063787", "A066099", "A124767", "A124771", "A126646", "A175413", "A238279", "A274174", "A330036", "A333381", "A333489", "A333755", "A334299", "A351014", "A351015", "A353832", "A353835", "A353847", "A353849", "A353850", "A353852", "A353853", "A353859", "A353860", "A353861", "A353864", "A353932", "A354582", "A354907" ]
null
Gus Wiseman, Jun 13 2022
2022-06-17T08:35:11
oeisdata/seq/A354/A354582.seq
6ae14553e1be687d6a05059365ed7012
A354583
Heinz numbers of non-rucksack partitions: not every prime-power divisor has a different sum of prime indices.
[ "12", "24", "36", "40", "48", "60", "63", "72", "80", "84", "96", "108", "112", "120", "126", "132", "144", "156", "160", "168", "180", "189", "192", "200", "204", "216", "224", "228", "240", "252", "264", "276", "280", "288", "300", "312", "315", "320", "324", "325", "336", "348", "351", "352", "360", "372", "378", "384", "396", "400", "408", "420", "432", "440" ]
[ "nonn" ]
10
1
1
[ "A001221", "A001222", "A005811", "A056239", "A073093", "A108917", "A112798", "A118914", "A124010", "A175413", "A181819", "A182857", "A275870", "A296150", "A299702", "A299729", "A300273", "A304442", "A316413", "A325676", "A325862", "A333223", "A353832", "A353833", "A353834", "A353835", "A353836", "A353837", "A353838", "A353839", "A353850", "A353852", "A353861", "A353864", "A353865", "A353866", "A353867", "A353931", "A354580", "A354583", "A354584" ]
null
Gus Wiseman, Jun 15 2022
2022-06-17T22:12:44
oeisdata/seq/A354/A354583.seq
10f1897d765ae90e8e68a36eb23c232b
A354584
Irregular triangle read by rows where row k lists the run-sums of the multiset (weakly increasing sequence) of prime indices of n.
[ "1", "2", "2", "3", "1", "2", "4", "3", "4", "1", "3", "5", "2", "2", "6", "1", "4", "2", "3", "4", "7", "1", "4", "8", "2", "3", "2", "4", "1", "5", "9", "3", "2", "6", "1", "6", "6", "2", "4", "10", "1", "2", "3", "11", "5", "2", "5", "1", "7", "3", "4", "2", "4", "12", "1", "8", "2", "6", "3", "3", "13", "1", "2", "4", "14", "2", "5", "4", "3", "1", "9", "15", "4", "2", "8", "1", "6", "2", "7", "2", "6", "16" ]
[ "nonn", "tabf" ]
10
1
2
[ "A000040", "A000961", "A001221", "A001222", "A002110", "A027748", "A056239", "A071625", "A073093", "A112798", "A118914", "A124010", "A181819", "A238279", "A275870", "A296150", "A300273", "A304117", "A304442", "A308495", "A333755", "A353832", "A353833", "A353834", "A353835", "A353837", "A353838", "A353839", "A353840", "A353846", "A353847", "A353850", "A353852", "A353861", "A353862", "A353864", "A353866", "A353867", "A353931", "A353932", "A354584" ]
null
Gus Wiseman, Jun 17 2022
2022-06-17T22:12:49
oeisdata/seq/A354/A354584.seq
d1550853846d7c90410ff2dd23b9378f
A354585
Least prime p such that 2^x - 2 + p produces primes for x=1..n and a composite for x=n+1.
[ "2", "3", "11", "5", "227", "17", "65837", "1607", "19427", "2397347207", "153535525937", "157542769194527", "29503289812427", "32467505340816977", "1109038455070356527", "143924005810811657", "305948728878647722727" ]
[ "nonn", "hard", "more" ]
32
1
1
[ "A164926", "A354585" ]
null
Robert C. Lyons, Aug 18 2022
2022-12-17T08:22:00
oeisdata/seq/A354/A354585.seq
ca5ae4cd55e239e25cc66eacb74b9db6
A354586
Table of Sprague-Grundy values for n X m 2D Toppling Dominoes L's read by antidiagonals.
[ "1", "2", "2", "3", "3", "3", "4", "4", "4", "4", "5", "5", "1", "5", "5", "6", "6", "6", "6", "6", "6", "7", "7", "7", "7", "7", "7", "7", "8", "8", "8", "8", "8", "8", "8", "8", "9", "9", "5", "9", "1", "9", "5", "9", "9", "10", "10", "10", "10", "2", "2", "10", "10", "10", "10", "11", "11", "11", "11", "3", "3", "3", "11", "11", "11", "11", "12", "12", "12", "12", "12", "12", "12", "12", "12", "12", "12", "12" ]
[ "easy", "nonn", "tabl" ]
22
1
2
null
null
Ian C Haile, Aug 18 2022
2022-10-01T19:39:52
oeisdata/seq/A354/A354586.seq
21b4246496f50c099e0d70c58cadad61
A354587
Diagonal of Sprague-Grundy values for n X m 2D Toppling Dominoes L's.
[ "1", "3", "1", "7", "1", "3", "1", "15", "1", "3", "1", "7", "1", "3", "1", "31", "1", "3", "1", "7", "1", "3", "1", "15", "1", "3", "1", "49", "1", "3", "1", "63", "1", "3", "1", "7", "1", "3", "1", "15", "1", "3", "1", "7", "1", "3", "1", "31", "1", "3", "1", "8", "1", "9", "1", "11", "1", "5", "1", "5", "1", "111", "1", "127", "1", "3", "1", "7", "1", "3", "1", "15", "1", "3", "1", "21", "1", "3", "1", "31", "1", "3" ]
[ "easy", "nonn" ]
20
1
2
[ "A354586", "A354587" ]
null
Ian C Haile, Aug 18 2022
2022-10-01T19:41:03
oeisdata/seq/A354/A354587.seq
3418b5787aed61b1a73dc23ff3a046eb
A354588
Number of marked chord diagrams (linear words in which each letter appears twice) with n chords, whose intersection graph is connected and distance-hereditary.
[ "1", "4", "27", "226", "2116", "21218", "222851", "2420134", "26954622", "306203536", "3534170486", "41326973520", "488562349730", "5829471835390", "70112478797987", "849110215237094", "10345827793291654", "126734013316914248", "1559884942820510474", "19281814963272771308", "239263099541276559360", "2979328903819471935332" ]
[ "nonn" ]
21
0
2
[ "A277862", "A277869", "A354588", "A357596" ]
null
Christopher-Lloyd Simon, May 31 2022
2022-10-08T14:16:54
oeisdata/seq/A354/A354588.seq
1c1741fa6d8345b2c07031d8bb442edc
A354589
Primes p starting a sequence of 4 consecutive primes whose final digits are 1,3,7,9 (in any order).
[ "11", "23", "47", "53", "67", "83", "89", "101", "109", "149", "167", "191", "193", "197", "199", "211", "251", "257", "263", "383", "443", "449", "461", "487", "557", "563", "587", "593", "599", "613", "647", "659", "739", "757", "761", "821", "859", "983", "991", "1061", "1063", "1069", "1117", "1217", "1223", "1283", "1301", "1303", "1367", "1433", "1439", "1447", "1481", "1553", "1567", "1571", "1579" ]
[ "nonn", "base" ]
20
1
1
[ "A007652", "A007811", "A354589", "A354590" ]
null
J. M. Bergot and Robert Israel, Aug 18 2022
2025-06-02T15:25:31
oeisdata/seq/A354/A354589.seq
39ef83ab27116bf357c6d29410820b6c
A354590
a(n) is the first prime that is the start of a sequence of exactly n consecutive primes that are in A354589.
[ "11", "47", "251", "9431", "191", "19457", "280627", "2213", "1006253", "9129563", "66945301", "184171621", "726512053", "2732087209", "10206934519", "59883612989", "25650350371" ]
[ "nonn", "more", "base" ]
20
1
1
[ "A007652", "A354589", "A354590" ]
null
J. M. Bergot and Robert Israel, Aug 18 2022
2022-08-23T10:17:54
oeisdata/seq/A354/A354590.seq
8cefa534675159045c5dc62281dd913a
A354591
Numbers k that can be written as the sum of 4 divisors of k (not necessarily distinct).
[ "4", "6", "8", "10", "12", "16", "18", "20", "24", "28", "30", "32", "36", "40", "42", "44", "48", "50", "52", "54", "56", "60", "64", "66", "68", "70", "72", "76", "78", "80", "84", "88", "90", "92", "96", "100", "102", "104", "108", "110", "112", "114", "116", "120", "124", "126", "128", "130", "132", "136", "138", "140", "144", "148", "150", "152", "156", "160", "162", "164", "168", "170", "172" ]
[ "nonn", "changed" ]
45
1
1
[ "A000027", "A080671", "A299174", "A354591", "A355200", "A355641", "A356609", "A356635", "A356657", "A356659", "A356660" ]
null
Wesley Ivan Hurt, Aug 18 2022
2025-07-17T07:36:19
oeisdata/seq/A354/A354591.seq
b6f6384328bbdc39268d4e05b34ab4fe
A354592
Decimal expansion of Sum_{k>=1} (1/k - (1 - log(k)/k)^k).
[ "1", "0", "3", "0", "5", "4", "2", "3", "5", "3", "7", "8", "4", "9", "4", "1", "2", "0", "8", "9", "9", "6", "2", "8", "0", "9", "2", "9", "8", "2", "8", "8", "7", "4", "6", "0", "7", "8", "2", "8", "1", "1", "0", "5", "5", "4", "1", "4", "5", "3", "5", "6", "7", "1", "3", "6", "3", "1", "9", "2", "1", "6", "4", "4", "6", "1", "6", "6", "7", "5", "1", "0", "9", "5", "0", "4", "0", "4", "8", "3", "2", "9", "0", "2", "5", "7", "5", "5", "5", "4", "7", "4", "0", "0", "3", "0", "3", "0", "7", "4", "9", "0", "2", "4", "3" ]
[ "nonn", "cons" ]
10
1
3
[ "A354450", "A354592", "A354593" ]
null
Vaclav Kotesovec, Jun 01 2022
2022-06-01T07:59:23
oeisdata/seq/A354/A354592.seq
286ef23fd0845853b127711e5e54688c
A354593
Decimal expansion of Sum_{k>=1} (1 - log(k)/k)^(3*k).
[ "1", "1", "0", "9", "8", "1", "2", "3", "5", "1", "6", "7", "2", "7", "4", "0", "9", "0", "2", "5", "9", "7", "7", "2", "3", "0", "0", "5", "6", "8", "6", "1", "6", "4", "7", "7", "9", "3", "8", "0", "1", "6", "3", "2", "5", "6", "1", "0", "3", "3", "4", "2", "3", "8", "6", "7", "9", "2", "0", "8", "1", "3", "4", "8", "4", "1", "9", "8", "3", "1", "0", "9", "3", "6", "0", "1", "2", "2", "5", "5", "7", "4", "1", "4", "4", "0", "2", "2", "5", "4", "5", "2", "0", "9", "9", "8", "8", "3", "9", "4", "0", "4", "5", "3", "8" ]
[ "nonn", "cons" ]
11
1
4
[ "A354450", "A354592", "A354593" ]
null
Vaclav Kotesovec, Jun 01 2022
2022-06-01T05:08:56
oeisdata/seq/A354/A354593.seq
2a02071349efc96aec16f45cfd66c911
A354594
a(n) = n^2 + 2*floor(n/2)^2.
[ "0", "1", "6", "11", "24", "33", "54", "67", "96", "113", "150", "171", "216", "241", "294", "323", "384", "417", "486", "523", "600", "641", "726", "771", "864", "913", "1014", "1067", "1176", "1233", "1350", "1411", "1536", "1601", "1734", "1803", "1944", "2017", "2166", "2243", "2400", "2481", "2646", "2731", "2904" ]
[ "nonn", "easy" ]
19
0
3
[ "A000290", "A008794", "A033581", "A080859", "A213037", "A247375", "A322744", "A354594", "A354595", "A354596" ]
null
David Lovler, Jun 01 2022
2022-07-08T08:23:46
oeisdata/seq/A354/A354594.seq
0d1517283acd311f913282848804d8f1
A354595
a(n) = n^2 + 4*floor(n/2)^2.
[ "0", "1", "8", "13", "32", "41", "72", "85", "128", "145", "200", "221", "288", "313", "392", "421", "512", "545", "648", "685", "800", "841", "968", "1013", "1152", "1201", "1352", "1405", "1568", "1625", "1800", "1861", "2048", "2113", "2312", "2381", "2592", "2665", "2888", "2965", "3200", "3281", "3528", "3613", "3872" ]
[ "nonn", "easy" ]
19
0
3
[ "A000290", "A008794", "A102083", "A139098", "A213037", "A247375", "A327259", "A354594", "A354595", "A354596" ]
null
David Lovler, Jun 01 2022
2022-07-08T08:23:54
oeisdata/seq/A354/A354595.seq
ac64caed4063c0bb6f9b745beaa91c53
A354596
Array T(n,k) = k^2 + (2n-4)*floor(k/2)^2, n >= 0, k >= 0, read by descending antidiagonals.
[ "0", "1", "0", "0", "1", "0", "5", "2", "1", "0", "0", "7", "4", "1", "0", "9", "8", "9", "6", "1", "0", "0", "17", "16", "11", "8", "1", "0", "13", "18", "25", "24", "13", "10", "1", "0", "0", "31", "36", "33", "32", "15", "12", "1", "0", "17", "32", "49", "54", "41", "40", "17", "14", "1", "0", "0", "49", "64", "67", "72", "49", "48", "19", "16", "1", "0", "21", "50", "81", "96", "85", "90", "57", "56", "21", "18", "1", "0" ]
[ "nonn", "tabl", "easy" ]
39
0
7
[ "A000290", "A008794", "A133728", "A213037", "A247375", "A266222", "A266439", "A319929", "A322630", "A322744", "A327259", "A327263", "A354594", "A354595", "A354596" ]
null
David Lovler, Jun 01 2022
2022-09-26T01:31:12
oeisdata/seq/A354/A354596.seq
c1968705feae12db556249433b6b1288
A354597
a(n) is the smallest number k>0 such that -n is not a quadratic residue modulo k.
[ "3", "4", "5", "3", "4", "4", "3", "5", "4", "3", "7", "5", "3", "4", "7", "3", "4", "4", "3", "11", "4", "3", "5", "9", "3", "4", "5", "3", "4", "4", "3", "5", "4", "3", "8", "7", "3", "4", "7", "3", "4", "4", "3", "7", "4", "3", "5", "5", "3", "4", "7", "3", "4", "4", "3", "11", "4", "3", "8", "7", "3", "4", "5", "3", "4", "4", "3", "5", "4", "3", "7", "5", "3", "4", "8", "3", "4", "4", "3", "11", "4", "3", "5", "9", "3", "4", "5", "3", "4", "4", "3", "5", "4", "3", "7", "9", "3", "4", "7", "3" ]
[ "nonn" ]
13
1
1
[ "A139401", "A354597" ]
null
Bruno Langlois, Jul 08 2022
2022-07-09T11:09:48
oeisdata/seq/A354/A354597.seq
63880d286d74f4350baa965f75cc8d32
A354598
Maximal GCD of eight positive integers with sum n.
[ "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "2", "1", "2", "1", "3", "1", "2", "3", "2", "1", "3", "1", "4", "3", "2", "1", "4", "1", "2", "3", "5", "1", "3", "1", "4", "5", "2", "1", "6", "1", "5", "3", "4", "1", "6", "5", "7", "3", "2", "1", "6", "1", "2", "7", "8", "5", "6", "1", "4", "3", "7", "1", "9", "1", "2", "5", "4", "7", "6", "1", "10", "9", "2", "1", "7", "5", "2", "3", "11", "1", "10", "7", "4", "3", "2", "5", "12", "1", "7", "11", "10" ]
[ "nonn" ]
19
8
9
[ "A009694", "A032742", "A162787", "A354598", "A354599", "A354601", "A355249", "A355319", "A355366", "A355368", "A355402" ]
null
Wesley Ivan Hurt, Jul 08 2022
2022-09-21T11:28:16
oeisdata/seq/A354/A354598.seq
96e25b57d2a7e923e3b76a7b111f2ff4
A354599
Maximal GCD of nine positive integers with sum n.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "3", "2", "1", "3", "1", "2", "3", "2", "1", "4", "1", "2", "3", "4", "1", "3", "1", "4", "5", "2", "1", "4", "1", "5", "3", "4", "1", "6", "5", "4", "3", "2", "1", "6", "1", "2", "7", "4", "5", "6", "1", "4", "3", "7", "1", "8", "1", "2", "5", "4", "7", "6", "1", "8", "9", "2", "1", "7", "5", "2", "3", "8", "1", "10", "7", "4", "3", "2", "5", "8", "1", "7", "11", "10" ]
[ "nonn" ]
20
9
10
[ "A009714", "A032742", "A354598", "A354599", "A354601", "A355249", "A355319", "A355366", "A355368", "A355402" ]
null
Wesley Ivan Hurt, Jul 08 2022
2022-09-21T10:39:35
oeisdata/seq/A354/A354599.seq
d9f8042db9e0b354b3ab8c2c82fbd31d
A354600
a(n) = Product_{k=0..9} floor((n+k)/10).
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "2", "4", "8", "16", "32", "64", "128", "256", "512", "1024", "1536", "2304", "3456", "5184", "7776", "11664", "17496", "26244", "39366", "59049", "78732", "104976", "139968", "186624", "248832", "331776", "442368", "589824", "786432", "1048576", "1310720", "1638400", "2048000", "2560000", "3200000", "4000000" ]
[ "nonn", "easy" ]
27
0
12
[ "A002620", "A006501", "A008233", "A008382", "A008454", "A008881", "A009641", "A009694", "A009714", "A013668", "A354600" ]
null
Wesley Ivan Hurt, Jul 08 2022
2025-03-19T08:23:48
oeisdata/seq/A354/A354600.seq
ba9cd947bf498690bfa0f38cc80948e4