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1999-12-11 03:00:00
2025-07-19 00:40:46
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A380512
Expansion of e.g.f. exp(x*G(x)^3) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.
[ "1", "1", "7", "91", "1753", "45001", "1447471", "56041987", "2539200721", "131859347473", "7723214721271", "503787793244011", "36223369111466857", "2846582772323685721", "242741539845295265503", "22325483241906758894611", "2202979676409063904473121", "232158319570869255177386017", "26024052774273208806612761191" ]
[ "nonn" ]
23
0
3
[ "A000262", "A001764", "A251568", "A251569", "A380511", "A380512", "A380516", "A382033" ]
null
Seiichi Manyama, Jan 26 2025
2025-03-15T09:43:31
oeisdata/seq/A380/A380512.seq
3316f5c8ef99a2bc8a4498adaefb8d57
A380513
Expansion of e.g.f. exp(x*G(x)) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
[ "1", "1", "3", "31", "649", "20241", "831691", "42281023", "2558247441", "179401012129", "14301145772371", "1276863732880671", "126200478678828313", "13677209933635675441", "1612657716714084149019", "205505541279096688937791", "28144314031348292162103841", "4122178445898981809990411073", "642961375302043479923591655331" ]
[ "nonn" ]
11
0
3
[ "A000262", "A002293", "A080893", "A251569", "A380513", "A380514", "A380515", "A380516" ]
null
Seiichi Manyama, Jan 26 2025
2025-01-26T09:06:49
oeisdata/seq/A380/A380513.seq
5cf555a7a3ee5456468a05a429b42e65
A380514
Expansion of e.g.f. exp(x*G(x)^2) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
[ "1", "1", "5", "67", "1537", "50021", "2107021", "108885295", "6665443457", "471522589417", "37843890892021", "3397250515809371", "337267132243022785", "36687625652474612557", "4339368321317331858557", "554467482301151809302151", "76112537023512618262963201", "11170667360636927554290623825", "1745500813880455301486766050917" ]
[ "nonn" ]
10
0
3
[ "A002293", "A069271", "A380513", "A380514", "A380515", "A380516" ]
null
Seiichi Manyama, Jan 26 2025
2025-01-26T09:06:37
oeisdata/seq/A380/A380514.seq
aaf732b294f419245a0008ce49165827
A380515
Expansion of e.g.f. exp(x*G(x)^3) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
[ "1", "1", "7", "109", "2689", "91261", "3950191", "208064137", "12917499169", "923765042809", "74780847503191", "6760168138392901", "675023676995501857", "73787463232202560309", "8763902701210982610559", "1123850728979698205132641", "154757223522414820829369281", "22775744033825102490806751217" ]
[ "nonn" ]
19
0
3
[ "A002293", "A006632", "A080893", "A091695", "A250917", "A370057", "A380511", "A380512", "A380513", "A380514", "A380515", "A380516", "A382059" ]
null
Seiichi Manyama, Jan 26 2025
2025-03-15T09:43:35
oeisdata/seq/A380/A380515.seq
1eb762ad2bbf9326219cd56771f43731
A380516
Expansion of e.g.f. exp(x*G(x)^4) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
[ "1", "1", "9", "157", "4129", "146001", "6502681", "349790029", "22069858497", "1598577634369", "130757736096361", "11922399644742621", "1199121973234651489", "131887738425602277457", "15748194681225620534649", "2028885239529647188594381", "280525944581514367875035521", "41434950383158772951280658689" ]
[ "nonn" ]
26
0
3
[ "A000262", "A002293", "A251568", "A380512", "A380513", "A380514", "A380515", "A380516", "A382034" ]
null
Seiichi Manyama, Jan 26 2025
2025-03-15T09:43:39
oeisdata/seq/A380/A380516.seq
9a9f7a9c3ac767a5abdba339d56377d1
A380517
Absolute value of the minimum coefficient of (1 - x)^3 * (1 - x^2)^3 * (1 - x^3)^3 * ... * (1 - x^n)^3.
[ "1", "3", "6", "15", "24", "50", "81", "186", "305", "561", "972", "1761", "3129", "5789", "10470", "19023", "33549", "62388", "113418", "205653", "366198", "674085", "1226181", "2211462", "3953679", "7287672", "13261764", "24005627", "42998125", "79033269", "143513301", "260061408", "465444889", "855436899", "1553736558", "2813222766", "5052061560", "9250734231" ]
[ "nonn" ]
8
0
2
[ "A010816", "A086394", "A369709", "A369711", "A369983", "A380499", "A380517" ]
null
Ilya Gutkovskiy, Jan 26 2025
2025-01-28T15:56:19
oeisdata/seq/A380/A380517.seq
6106994bcb4d8f3971961e1ea5e2371d
A380518
Irregular triangle read by rows: T(n,k) is the number of non-isomorphic formulas in conjunctive normal form (CNF) with n variables and k distinct clauses up to permutations of the variables and clauses, 0 <= k <= 3^n.
[ "1", "1", "1", "3", "3", "1", "1", "6", "21", "47", "69", "69", "47", "21", "6", "1", "1", "10", "82", "573", "3176", "14066", "50646", "150508", "374266", "787691", "1415279", "2184842", "2911290", "3358258", "3358258", "2911290", "2184842", "1415279", "787691", "374266", "150508", "50646", "14066", "3176", "573", "82", "10", "1" ]
[ "nonn", "tabf" ]
93
0
4
[ "A000217", "A034472", "A052265", "A380518", "A380610", "A380630" ]
null
Frank Schwidom, Jan 26 2025
2025-02-26T06:31:50
oeisdata/seq/A380/A380518.seq
2c8e418653094f822ef0a60e57b65b46
A380519
Decimal expansion of least x>1 so that Re(x^rho) has a local maximum, with rho as the first zeta zero.
[ "1", "0", "0", "2", "5", "0", "4", "7", "1", "0", "5", "5", "1", "4", "0", "7", "1", "3", "1", "3", "9", "6", "8", "5", "3", "7", "8", "2", "8", "0", "2", "2", "2", "4", "7", "5", "9", "1", "9", "1", "2", "2", "7", "9", "4", "8", "6", "1", "5", "6", "5", "1", "7", "8", "1", "0", "0", "4", "2", "1", "3", "5", "7", "5", "0", "8", "5", "1", "5", "1", "9", "3", "5", "1", "1", "9", "9", "4", "6", "4", "8", "3", "0", "7", "7", "2" ]
[ "nonn", "cons" ]
6
1
4
[ "A058303", "A199499", "A380519" ]
null
Friedjof Tellkamp, Jan 26 2025
2025-02-08T15:26:26
oeisdata/seq/A380/A380519.seq
c2b331175b0a278f0929a792f91aed4d
A380520
Numbers m such that the sum of squares of nondivisors of m is prime.
[ "5", "6", "26", "38", "66", "166", "206", "238", "266", "318", "321", "333", "341", "369", "405", "406", "445", "458", "481", "553", "606", "658", "706", "784", "873", "893", "933", "946", "1125", "1166", "1173", "1273", "1286", "1293", "1353", "1546", "1578", "1606", "1666", "1678", "1705", "1726", "1745", "1773", "1781", "1786", "1858", "1906", "1918", "1941" ]
[ "nonn" ]
19
1
1
[ "A024816", "A200981", "A380520", "A380569" ]
null
Michel Lagneau, Jan 26 2025
2025-02-27T07:58:11
oeisdata/seq/A380/A380520.seq
90bf708cf5c409d1313fa8d5b1cd5ff4
A380521
Primes p such that between p and the next prime there exist 2 distinct integers which are a square and a cube, respectively.
[ "7", "23", "113", "32749", "79493", "97327" ]
[ "nonn", "hard", "more" ]
13
1
1
[ "A053706", "A380521", "A380522", "A380523" ]
null
Zhining Yang, Jan 26 2025
2025-01-26T20:45:12
oeisdata/seq/A380/A380521.seq
d84d7f1f5c01b77c59de34517d14011e
A380522
Primes p such that between p and the previous prime there exist 2 distinct integers which are a square and a cube, respectively.
[ "11", "29", "127", "32771", "79531", "97367" ]
[ "nonn", "hard", "more" ]
14
1
1
[ "A053706", "A380521", "A380522", "A380523" ]
null
Zhining Yang, Jan 26 2025
2025-01-26T20:44:00
oeisdata/seq/A380/A380522.seq
099575141858553aac3b4a7d10ec5c5f
A380523
Positive cubes k such that there are no primes between k and the nearest square that is not k.
[ "8", "27", "125", "32768", "79507", "97336" ]
[ "nonn", "hard", "more" ]
16
1
1
[ "A053706", "A380405", "A380521", "A380522", "A380523" ]
null
Zhining Yang, Jan 26 2025
2025-01-31T11:56:24
oeisdata/seq/A380/A380523.seq
c32e2fb2bb86025222a1c6222a5c1fe6
A380524
a(n) = 1 if n is a squarefree and for all factorizations of n as x*y, the sum (x * y') + (x' * y) is carryfree when the addition is done in the primorial base, otherwise 0. Here u' stands for A003415(u), the arithmetic derivative of u.
[ "1", "1", "1", "0", "1", "1", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0" ]
[ "nonn" ]
9
1
null
[ "A003415", "A008966", "A010051", "A358672", "A380467", "A380524", "A380525" ]
null
Antti Karttunen, Feb 04 2025
2025-02-09T18:10:07
oeisdata/seq/A380/A380524.seq
126137949175c4894290ba81cb167b08
A380525
Squarefree numbers k such that for all factorizations of k as x*y, the sum (x * y') + (x' * y) is carryless when the addition is done in the primorial base, A049345. Here n' stands for A003415(n), the arithmetic derivative of n.
[ "1", "2", "3", "5", "6", "7", "11", "13", "14", "17", "19", "23", "26", "29", "31", "37", "38", "41", "43", "47", "53", "59", "61", "62", "67", "70", "71", "73", "74", "79", "83", "86", "89", "97", "101", "103", "107", "109", "113", "122", "127", "131", "134", "137", "139", "146", "149", "151", "154", "157", "158", "163", "167", "173", "179", "181", "186", "190", "191", "193", "194", "195", "197", "199", "206", "211", "218", "223", "227", "229", "233" ]
[ "nonn" ]
13
1
2
[ "A003415", "A005117", "A049345", "A358673", "A380468", "A380524", "A380525", "A380526" ]
null
Antti Karttunen, Feb 04 2025
2025-02-09T18:10:17
oeisdata/seq/A380/A380525.seq
8ef126dae44599463d2488b5729fffd0
A380526
Terms of A380525 with at least 5 prime factors.
[ "36465", "452670", "485970", "1627782", "3153345", "3257170", "3848370", "4324470", "4891470", "4905762", "5406270", "5413902", "6448794", "7664595", "7669545", "7834290", "8884869", "8951370", "15031527", "16408770", "32288577", "34805967", "36841470", "39912522", "42356814", "43724265", "43978398", "48547670", "54287682", "55924170", "61226790", "61406295", "62976246", "64326426" ]
[ "nonn" ]
8
1
1
[ "A001221", "A001222", "A380524", "A380525", "A380526" ]
null
Antti Karttunen, Feb 09 2025
2025-02-09T14:23:10
oeisdata/seq/A380/A380526.seq
ae14b39c575fc57d5f14c6e84c60ff37
A380527
Numbers k such that k is a multiple of A327860(k), where A327860 is the arithmetic derivative of the primorial base exp-function.
[ "1", "2", "6", "7", "8", "30", "36", "210", "2310", "2340", "2520", "2556", "30030", "30240", "32340", "510510", "510720", "540540", "9699690", "9699720", "9702000", "9729720", "10210200", "223092870", "223092900", "223093080", "223095180", "232792560", "6469693230", "6469693236", "6469693440", "6469695540", "6692786100" ]
[ "nonn", "more" ]
23
1
2
[ "A002110", "A003415", "A053669", "A143293", "A177711", "A276086", "A276156", "A327860", "A328110", "A351087", "A380527", "A381035", "A381037" ]
null
Antti Karttunen, Feb 11 2025
2025-02-17T14:28:22
oeisdata/seq/A380/A380527.seq
0a717c326bada11979afedf17b6499c6
A380528
Smallest prime p such that p^p is a divisor of A380459(n), or 1 if no such factor exists, where A380459(n) = Product_{d|n} A276086(n/d)^A349394(d).
[ "1", "1", "1", "2", "1", "1", "1", "2", "2", "3", "1", "2", "1", "1", "2", "2", "1", "3", "1", "2", "2", "3", "1", "2", "2", "1", "2", "2", "1", "3", "1", "2", "2", "3", "2", "2", "1", "1", "2", "2", "1", "5", "1", "2", "2", "3", "1", "2", "2", "3", "2", "2", "1", "3", "2", "2", "2", "3", "1", "2", "1", "1", "2", "2", "2", "3", "1", "2", "2", "3", "1", "2", "1", "1", "2", "2", "2", "5", "1", "2", "2", "3", "1", "2", "2", "1", "2", "2", "1", "3", "2", "2", "2", "3", "2", "2", "1", "3", "2", "2", "1", "3", "1", "2", "2" ]
[ "nonn" ]
14
1
4
[ "A005117", "A129252", "A276086", "A349394", "A380459", "A380468", "A380528", "A380529", "A380530" ]
null
Antti Karttunen, Feb 09 2025
2025-02-10T04:37:01
oeisdata/seq/A380/A380528.seq
136e66b283672c5956e4d559cdb0325f
A380529
Smallest prime p such that p^p is a divisor of A380459(A005117(n)), or 1 if no such factor exists, where A380459(n) = Product_{d|n} A276086(n/d)^A349394(d) and A005117 lists the squarefree numbers.
[ "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "2", "1", "1", "2", "3", "1", "1", "1", "3", "1", "2", "3", "2", "1", "1", "2", "1", "5", "1", "3", "1", "2", "1", "2", "2", "3", "1", "1", "1", "2", "3", "1", "2", "3", "1", "1", "1", "2", "5", "1", "3", "1", "2", "1", "2", "1", "2", "2", "3", "2", "1", "1", "3", "1", "2", "3", "1", "1", "3", "2", "1", "5", "2", "3", "2", "1", "2", "1", "2", "3", "1", "2", "1", "1", "3", "1", "2", "3", "2", "2", "1", "1", "1", "3", "2", "1", "1", "2", "2", "1", "2", "3", "1", "3", "1" ]
[ "nonn" ]
6
1
7
[ "A005117", "A129252", "A276086", "A349394", "A380459", "A380468", "A380470", "A380528", "A380529" ]
null
Antti Karttunen, Feb 09 2025
2025-02-09T10:23:39
oeisdata/seq/A380/A380529.seq
6b2a643ce99e1146e166e06bb1e105f6
A380530
Positions of records in A380528.
[ "1", "4", "10", "42", "366", "3246", "37266", "631266", "11563926", "271591926" ]
[ "nonn", "hard", "more" ]
30
1
2
[ "A008578", "A046387", "A380459", "A380468", "A380470", "A380475", "A380476", "A380528", "A380530" ]
null
Antti Karttunen, Feb 09 2025
2025-05-09T16:19:28
oeisdata/seq/A380/A380530.seq
f728dd685c19355eec891b9a3c25faae
A380531
a(n) is the multiplicative order of -4 modulo prime(n); a(1) = 0 for completion.
[ "0", "2", "1", "6", "10", "3", "4", "18", "22", "7", "10", "9", "5", "14", "46", "13", "58", "15", "66", "70", "18", "78", "82", "22", "24", "25", "102", "106", "9", "7", "14", "130", "17", "138", "37", "30", "13", "162", "166", "43", "178", "45", "190", "48", "49", "198", "210", "74", "226", "19", "58", "238", "12", "50", "8", "262", "67", "270", "23", "70" ]
[ "nonn", "easy", "changed" ]
28
1
2
[ "A002371", "A014664", "A062117", "A082654", "A105876", "A211241", "A211242", "A211243", "A211244", "A211245", "A337878", "A380482", "A380531", "A380532", "A380533", "A380540", "A380541", "A380542", "A385222" ]
null
Jianing Song, Jun 27 2025
2025-07-07T10:43:45
oeisdata/seq/A380/A380531.seq
d049a412349ef2a7c19ba32feeccd41d
A380532
a(n) is the multiplicative order of -5 modulo prime(n); a(3) = 0 for completion.
[ "1", "1", "0", "3", "10", "4", "16", "18", "11", "7", "6", "36", "20", "21", "23", "52", "58", "15", "11", "10", "72", "78", "41", "44", "96", "50", "51", "53", "54", "112", "21", "130", "136", "138", "74", "150", "156", "27", "83", "172", "178", "30", "38", "192", "196", "66", "70", "111", "113", "57", "232", "238", "40", "50", "256", "131", "134", "54", "276", "140" ]
[ "nonn", "easy", "changed" ]
31
1
4
[ "A002371", "A014664", "A062117", "A082654", "A105877", "A211241", "A211242", "A211243", "A211244", "A211245", "A337878", "A380482", "A380531", "A380532", "A380533", "A380540", "A380541", "A380542", "A385222" ]
null
Jianing Song, Jun 27 2025
2025-07-07T10:43:48
oeisdata/seq/A380/A380532.seq
526015ae3c70f306c1a5e50b075a1e1d
A380533
a(n) is the multiplicative order of -6 modulo prime(n); a(1) = a(2) = 0 for completion.
[ "0", "0", "2", "1", "5", "12", "16", "18", "22", "7", "3", "4", "40", "6", "46", "13", "29", "60", "66", "70", "36", "39", "41", "88", "12", "5", "51", "53", "108", "112", "63", "65", "136", "46", "74", "75", "156", "54", "166", "86", "89", "60", "38", "96", "7", "99", "210", "111", "113", "228", "232", "34", "20", "125", "256", "262", "67", "135", "276", "56" ]
[ "nonn", "easy", "changed" ]
32
1
3
[ "A002371", "A014664", "A062117", "A082654", "A105878", "A211241", "A211242", "A211243", "A211244", "A211245", "A337878", "A380482", "A380531", "A380532", "A380533", "A380540", "A380541", "A380542", "A385222" ]
null
Jianing Song, Jun 27 2025
2025-07-07T10:43:56
oeisdata/seq/A380/A380533.seq
4e4ce6b88ae80951dc1eacd6b16dae43
A380534
a(n) = 1 if the least significant nonzero digit in primorial base representation of n (A049345) is greater than 1, otherwise 0.
[ "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1" ]
[ "nonn", "base", "easy" ]
13
1
null
[ "A049345", "A053669", "A064648", "A276088", "A327860", "A329029", "A380527", "A380534", "A380535" ]
null
Antti Karttunen, Feb 11 2025
2025-02-18T19:01:56
oeisdata/seq/A380/A380534.seq
279b9650a1ecf8fe4eafbe8b8c03ddc2
A380535
Numbers such that the least significant nonzero digit in their primorial base representation (A049345) is greater than 1.
[ "4", "10", "12", "16", "18", "22", "24", "28", "34", "40", "42", "46", "48", "52", "54", "58", "60", "64", "70", "72", "76", "78", "82", "84", "88", "90", "94", "100", "102", "106", "108", "112", "114", "118", "120", "124", "130", "132", "136", "138", "142", "144", "148", "150", "154", "160", "162", "166", "168", "172", "174", "178", "180", "184", "190", "192", "196", "198", "202", "204", "208", "214", "220", "222", "226", "228", "232", "234", "238", "244", "250" ]
[ "nonn", "base", "easy" ]
14
1
1
[ "A049345", "A053669", "A064648", "A276088", "A327860", "A329029", "A342018", "A380527", "A380534", "A380535" ]
null
Antti Karttunen, Feb 11 2025
2025-02-18T11:29:53
oeisdata/seq/A380/A380535.seq
6dc354ff7b3d896909f749f540651104
A380536
a(n) = 1 if n is a multiple of A351566(n), otherwise 0, where A351566 is the radix prime of the second least significant nonzero digit in the primorial base expansion of n, or 1 if there is no such digit.
[ "1", "1", "1", "1", "0", "1", "0", "0", "1", "1", "0", "1", "0", "0", "1", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "1", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "1", "0", "0", "1", "1", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "1", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "1" ]
[ "nonn" ]
9
1
null
[ "A049345", "A351566", "A380536", "A380537", "A380538" ]
null
Antti Karttunen, Feb 12 2025
2025-02-12T14:21:16
oeisdata/seq/A380/A380536.seq
66eee89194720aa5bab294cd04b59252
A380537
Numbers k such that k is a multiple of A351566(k), where A351566 is the radix prime of the second least significant nonzero digit in the primorial base expansion of n, or 1 if there is no such digit.
[ "1", "2", "3", "4", "6", "9", "10", "12", "15", "18", "20", "21", "24", "25", "27", "30", "33", "39", "40", "42", "45", "50", "51", "55", "57", "60", "63", "69", "70", "75", "80", "81", "84", "85", "87", "90", "91", "93", "99", "100", "105", "110", "111", "115", "117", "120", "123", "126", "129", "130", "135", "140", "141", "145", "147", "150", "153", "154", "159", "160", "165", "168", "170", "171", "175", "177", "180", "182", "183", "189", "190", "195", "200" ]
[ "nonn" ]
8
1
2
[ "A053669", "A060735", "A119288", "A276086", "A351566", "A380536", "A380537", "A380538" ]
null
Antti Karttunen, Feb 12 2025
2025-02-12T14:21:20
oeisdata/seq/A380/A380537.seq
370a541cbedebe64e025a8eb47a89b8f
A380538
Numbers k such that k is not a multiple of A351566(k), where A351566 is the radix prime of the second least significant nonzero digit in the primorial base expansion of n, or 1 if there is no such digit.
[ "5", "7", "8", "11", "13", "14", "16", "17", "19", "22", "23", "26", "28", "29", "31", "32", "34", "35", "36", "37", "38", "41", "43", "44", "46", "47", "48", "49", "52", "53", "54", "56", "58", "59", "61", "62", "64", "65", "66", "67", "68", "71", "72", "73", "74", "76", "77", "78", "79", "82", "83", "86", "88", "89", "92", "94", "95", "96", "97", "98", "101", "102", "103", "104", "106", "107", "108", "109", "112", "113", "114", "116", "118", "119", "121", "122", "124", "125" ]
[ "nonn" ]
6
1
1
[ "A049345", "A351566", "A380536", "A380537", "A380538" ]
null
Antti Karttunen, Feb 12 2025
2025-02-12T14:21:25
oeisdata/seq/A380/A380538.seq
8bcde1f2f421c46d1f2df69c21cc3d9d
A380539
The second smallest prime not dividing n.
[ "3", "5", "5", "5", "3", "7", "3", "5", "5", "7", "3", "7", "3", "5", "7", "5", "3", "7", "3", "7", "5", "5", "3", "7", "3", "5", "5", "5", "3", "11", "3", "5", "5", "5", "3", "7", "3", "5", "5", "7", "3", "11", "3", "5", "7", "5", "3", "7", "3", "7", "5", "5", "3", "7", "3", "5", "5", "5", "3", "11", "3", "5", "5", "5", "3", "7", "3", "5", "5", "11", "3", "7", "3", "5", "7", "5", "3", "7", "3", "7", "5", "5", "3", "11", "3", "5", "5", "5", "3", "11", "3", "5", "5", "5", "3", "7", "3", "5", "5", "7", "3", "7", "3", "5", "11" ]
[ "nonn" ]
14
1
1
[ "A053669", "A351566", "A380539", "A381031", "A381113" ]
null
Antti Karttunen, Feb 12 2025
2025-02-15T14:29:17
oeisdata/seq/A380/A380539.seq
ac1959a0006a0dc3d679b2091800970c
A380540
a(n) is the multiplicative order of -7 modulo prime(n); a(4) = 0 for completion.
[ "1", "2", "4", "0", "5", "12", "16", "6", "11", "14", "30", "18", "40", "3", "46", "13", "58", "60", "33", "35", "24", "39", "82", "88", "96", "100", "102", "53", "54", "7", "63", "130", "68", "138", "37", "75", "52", "81", "166", "172", "89", "12", "5", "24", "49", "198", "105", "74", "226", "228", "116", "119", "240", "250", "256", "131", "268", "270", "69", "20" ]
[ "nonn", "easy", "changed" ]
27
1
2
[ "A002371", "A014664", "A062117", "A082654", "A105879", "A211241", "A211242", "A211243", "A211244", "A211245", "A337878", "A380482", "A380531", "A380532", "A380533", "A380540", "A380541", "A380542", "A385222" ]
null
Jianing Song, Jun 27 2025
2025-07-07T10:43:52
oeisdata/seq/A380/A380540.seq
78270f9e46d7c5932542ed3b856ec5a0
A380541
a(n) is the multiplicative order of -8 modulo prime(n); a(1) = 0 for completion.
[ "0", "1", "4", "2", "5", "4", "8", "3", "22", "28", "10", "12", "20", "7", "46", "52", "29", "20", "11", "70", "6", "26", "41", "22", "16", "100", "34", "53", "12", "28", "14", "65", "68", "23", "148", "10", "52", "27", "166", "172", "89", "60", "190", "32", "196", "66", "35", "74", "113", "76", "58", "238", "8", "25", "16", "262", "268", "90", "92", "35" ]
[ "nonn", "easy", "changed" ]
27
1
3
[ "A002371", "A014664", "A062117", "A082654", "A105880", "A211241", "A211242", "A211243", "A211244", "A211245", "A337878", "A380482", "A380531", "A380532", "A380533", "A380540", "A380541", "A380542", "A385222" ]
null
Jianing Song, Jun 27 2025
2025-07-07T10:43:59
oeisdata/seq/A380/A380541.seq
3e1079b383bb6d2e1430a5b939853c3f
A380542
a(n) is the multiplicative order of -9 modulo prime(n); a(2) = 0 for completion.
[ "1", "0", "1", "6", "10", "6", "8", "18", "22", "7", "30", "18", "4", "42", "46", "13", "58", "10", "22", "70", "3", "78", "82", "44", "24", "25", "34", "106", "54", "56", "126", "130", "68", "138", "37", "50", "78", "162", "166", "43", "178", "90", "190", "8", "49", "198", "210", "222", "226", "114", "116", "238", "60", "250", "128", "262", "67", "30", "138", "140" ]
[ "nonn", "easy", "changed" ]
30
1
4
[ "A002371", "A014664", "A062117", "A082654", "A105881", "A211241", "A211242", "A211243", "A211244", "A211245", "A337878", "A380482", "A380531", "A380532", "A380533", "A380540", "A380541", "A380542", "A385222" ]
null
Jianing Song, Jun 27 2025
2025-07-07T10:44:03
oeisdata/seq/A380/A380542.seq
0d2d5ea4a33f6bcaa394a647d11c9852
A380544
Numbers of the form A073138(k) XOR A038573(k).
[ "0", "3", "5", "9", "15", "17", "27", "33", "51", "63", "65", "99", "119", "129", "195", "231", "255", "257", "387", "455", "495", "513", "771", "903", "975", "1023", "1025", "1539", "1799", "1935", "2015", "2049", "3075", "3591", "3855", "3999", "4095", "4097", "6147", "7175", "7695", "7967", "8127", "8193", "12291", "14343", "15375", "15903", "16191", "16383", "16385" ]
[ "base", "easy", "nonn", "look" ]
23
1
2
[ "A000267", "A006995", "A038573", "A073138", "A082375", "A380544" ]
null
Frederik P.J. Vandecasteele, Jun 23 2025
2025-07-03T17:39:03
oeisdata/seq/A380/A380544.seq
ee42e6864759810417fa4a534859d499
A380545
Cumulative sum of the smallest prime in the minimal Goldbach partition for 2*n, n>=2.
[ "2", "5", "8", "11", "16", "19", "22", "27", "30", "33", "38", "41", "46", "53", "56", "59", "64", "71", "74", "79", "82", "85", "90", "93", "98", "105", "108", "113", "120", "123", "126", "131", "138", "141", "146", "149", "152", "157", "164", "167", "172", "175", "180", "187", "190", "195", "202", "221", "224", "229", "232", "235", "240", "243", "246", "251", "254", "259" ]
[ "nonn" ]
38
2
1
[ "A020481", "A380545" ]
null
Michel Eduardo Beleza Yamagishi, Jun 23 2025
2025-06-24T15:14:30
oeisdata/seq/A380/A380545.seq
caae349f61439523fa1efb6ea210a179
A380546
Cumulative sum of the greatest prime in the minimal Goldbach partition for 2*n, n>=2.
[ "2", "5", "10", "17", "24", "35", "48", "61", "78", "97", "116", "139", "162", "185", "214", "245", "276", "307", "344", "381", "422", "465", "508", "555", "602", "649", "702", "755", "808", "867", "928", "989", "1050", "1117", "1184", "1255", "1328", "1401", "1474", "1553", "1632", "1715", "1798", "1881", "1970", "2059", "2148", "2227", "2324", "2421", "2522" ]
[ "nonn" ]
30
2
1
[ "A020482", "A380546" ]
null
Michel Eduardo Beleza Yamagishi, Jun 23 2025
2025-06-24T15:13:10
oeisdata/seq/A380/A380546.seq
d83ea1aca12ed00536574eab19063276
A380547
Decimal expansion of the absolute value of the sum of the Dirichlet L-series A000035 at s=1/2.
[ "4", "2", "7", "7", "2", "7", "9", "3", "2", "6", "9", "3", "9", "7", "8", "2", "2", "1", "3", "2", "1", "1", "1", "6", "6", "1", "9", "1", "3", "9", "6", "7", "1", "2", "5", "6", "3", "5", "3", "7", "3", "3", "3", "9", "2", "9", "4", "1", "1", "6", "7", "0", "5", "5", "0", "8", "2", "1", "6", "9", "7", "1", "9", "8", "7", "1", "6", "7", "1", "6", "3", "7", "9", "8", "9", "7", "2", "0", "1", "3", "3", "9", "7", "4", "5", "0", "7", "7", "0" ]
[ "nonn", "cons" ]
17
0
1
[ "A000035", "A010503", "A059750", "A111003", "A113024", "A233091", "A268682", "A300707", "A380547" ]
null
R. J. Mathar, Jan 26 2025
2025-01-26T20:30:36
oeisdata/seq/A380/A380547.seq
219a06208320e44e3b6d10432bd89a97
A380548
Main diagonal of A125585.
[ "1", "3", "6", "10", "14", "18", "25", "30", "35", "40", "51", "57", "63", "69", "75", "91", "98", "105", "112", "119", "126", "148", "156", "164", "172", "180", "188", "196", "225", "234", "243", "252", "261", "270", "279", "288", "325", "335", "345", "355", "365", "375", "385", "395", "405", "451", "462", "473", "484", "495", "506", "517", "528", "539", "550", "606" ]
[ "nonn", "easy" ]
10
1
2
[ "A125585", "A380548" ]
null
Alois P. Heinz, Jan 26 2025
2025-02-07T17:08:15
oeisdata/seq/A380/A380548.seq
c38802c7f40129f10e9ffc64c081702a
A380549
List of numbers of the form i + 3*j + 4*i*j for i, j >= 1.
[ "8", "13", "15", "18", "22", "23", "24", "28", "29", "33", "35", "36", "38", "42", "43", "46", "48", "50", "51", "53", "57", "58", "60", "61", "63", "64", "68", "69", "71", "73", "74", "78", "79", "80", "83", "85", "87", "88", "90", "92", "93", "96", "97", "98", "99", "100", "101", "103", "105", "106", "108", "112", "113", "114", "118", "120", "123", "126", "127", "128", "131", "132", "133", "134", "137", "138", "139", "141", "143", "145", "148", "150" ]
[ "nonn", "easy" ]
18
1
1
[ "A047845", "A072668", "A380509", "A380549", "A380550" ]
null
Peter Bala, Jan 26 2025
2025-03-21T02:23:56
oeisdata/seq/A380/A380549.seq
09c131aeeedf2da74024886acfdc6fb7
A380550
List of numbers not of the form i + 3*j + 4*i*j for i, j >= 1.
[ "1", "2", "3", "4", "5", "6", "7", "9", "10", "11", "12", "14", "16", "17", "19", "20", "21", "25", "26", "27", "30", "31", "32", "34", "37", "39", "40", "41", "44", "45", "47", "49", "52", "54", "55", "56", "59", "62", "65", "66", "67", "70", "72", "75", "76", "77", "81", "82", "84", "86", "89", "91", "94", "95", "102", "104", "107", "109", "110", "111", "115", "116", "117", "119", "121", "122", "124", "125", "129", "130", "135", "136", "140", "142", "144", "146", "147", "149" ]
[ "nonn", "easy" ]
14
1
2
[ "A005097", "A006093", "A380549", "A380550", "A380572" ]
null
Peter Bala, Jan 26 2025
2025-01-31T04:23:23
oeisdata/seq/A380/A380550.seq
d235f40072571f09177c8a86fe2e559a
A380551
G.f. A(x) satisfies x = Sum_{n>=1} A( x^n*(1-x)^(2*n) ).
[ "1", "1", "6", "28", "142", "720", "3875", "21288", "120168", "690546", "4032014", "23840724", "142498691", "859512043", "5225263875", "31983651216", "196947587822", "1219199232294", "7583142491924", "47365473951152", "296983176365613", "1868545308601424", "11793499763070479", "74650344221104632", "473770694965305205", "3014124873709172435" ]
[ "nonn" ]
16
1
3
[ "A001764", "A006013", "A008683", "A034742", "A346925", "A380551", "A380552", "A380553" ]
null
Paul D. Hanna, Feb 16 2025
2025-02-17T17:38:07
oeisdata/seq/A380/A380551.seq
7e4fa66f44028346a93149e8a27ff82a
A380552
G.f. A(x) satisfies x = Sum_{n>=1} A( x^n*(1-x)^(3*n) ).
[ "1", "2", "14", "88", "611", "4372", "32889", "254384", "2017341", "16300550", "133767542", "1111727456", "9338434699", "79155402978", "676196048434", "5815796615520", "50318860986107", "437662918037250", "3824609516638443", "33563127916092808", "295655735395364616", "2613391671434553220", "23173063762591336049", "206066197523415007168" ]
[ "nonn" ]
13
1
2
[ "A002293", "A006632", "A008683", "A034742", "A346935", "A380551", "A380552", "A380553" ]
null
Paul D. Hanna, Feb 16 2025
2025-02-17T17:38:23
oeisdata/seq/A380/A380552.seq
b5348f232ca54ce44b8695e455dbde9f
A380553
G.f. A(x) satisfies x = Sum_{n>=1} A( x^n*(1-x)^(4*n) ).
[ "1", "3", "25", "200", "1770", "16351", "158223", "1577328", "16112031", "167708890", "1772645419", "18974340640", "205263418940", "2240623110285", "24648785800540", "272994642782048", "3041495503591364", "34064252952038769", "383302465665133013", "4331178750570145160", "49126274119206904221", "559128033687856289017" ]
[ "nonn" ]
12
1
2
[ "A002294", "A008683", "A034742", "A118971", "A346936", "A380551", "A380552", "A380553" ]
null
Paul D. Hanna, Feb 16 2025
2025-02-17T17:38:36
oeisdata/seq/A380/A380553.seq
65f278b4dbc3c2a510a2e4bba72cbb04
A380554
G.f. A(x) satisfies A(x)^4 = A( A(x)^3 * x/(1-x) ).
[ "1", "1", "1", "1", "2", "6", "16", "36", "75", "163", "391", "991", "2498", "6150", "15016", "37116", "93482", "238154", "608074", "1551370", "3964200", "10176384", "26261500", "68034484", "176661828", "459534596", "1197777556", "3129475636", "8195867902", "21508247446", "56540427826", "148863643466", "392539322259", "1036662269875", "2741706892035" ]
[ "nonn" ]
7
1
5
[ "A075864", "A374565", "A380554" ]
null
Paul D. Hanna, Jan 26 2025
2025-01-29T12:46:08
oeisdata/seq/A380/A380554.seq
2a99a5e50ca58ad176a71f0e9317182f
A380555
E.g.f. A(x) satisfies A(x) = log( 1 + x * cos(2*A(x)) ).
[ "1", "-1", "-10", "90", "364", "-17760", "85280", "5447120", "-116082720", "-1709304480", "123520217600", "-637137072000", "-136024779843200", "3988924415257600", "131963952741504000", "-11250603940363008000", "19125068757338752000", "28119635304260378112000", "-943657308179458552576000", "-59184868918118854443520000" ]
[ "sign" ]
11
1
3
[ "A380055", "A380555", "A380556" ]
null
Paul D. Hanna, Jan 28 2025
2025-01-29T12:46:16
oeisdata/seq/A380/A380555.seq
48bcb5622c89afece97017dccd6aeed6
A380556
E.g.f. A(x) satisfies A(x) = real( 1 + x*A(x)^(2*i) ), where i^2 = -1.
[ "1", "1", "0", "-12", "48", "820", "-14160", "-69160", "5900160", "-44796960", "-3089865600", "88646729600", "1412786918400", "-135956951062400", "1023512450688000", "203887248898944000", "-7307555382586368000", "-252816835499795840000", "26110132266648748032000", "-95216226972043640320000", "-80962066973581160140800000" ]
[ "sign" ]
10
0
4
[ "A380057", "A380555", "A380556" ]
null
Paul D. Hanna, Jan 28 2025
2025-01-29T12:46:29
oeisdata/seq/A380/A380556.seq
385572f3ab43f46c83b91601f4b54326
A380557
G.f. satisfies A(x) such that: -1 = Sum_{n=-oo..+oo} (-1)^n * x^(2*n+1) * (1 + x^n)^(n+1) * A(x)^n.
[ "1", "1", "2", "10", "35", "146", "589", "2521", "10880", "48130", "215490", "978131", "4483493", "20740309", "96667511", "453596099", "2140879339", "10157274086", "48414142443", "231726319442", "1113290775079", "5366873616498", "25952658569610", "125856499026093", "611930422986515", "2982444057333882", "14568259180879990", "71307949455547118" ]
[ "nonn" ]
8
0
3
[ "A356783", "A380557" ]
null
Paul D. Hanna, Feb 03 2025
2025-02-03T13:51:21
oeisdata/seq/A380/A380557.seq
f23276716f163de6078a430dacdba94c
A380558
G.f. A(x) satisfies A(x - A(x)) = x^2/(1 - x^2).
[ "1", "2", "10", "62", "469", "4028", "37984", "385202", "4144798", "46882400", "553733875", "6795347708", "86314711993", "1131422763410", "15268625617174", "211726229534738", "3012057754693912", "43903115899714844", "654923002676505376", "9989373316478767304", "155663132037403882606", "2476418549848925209424", "40195761790035415573939" ]
[ "nonn" ]
12
2
2
[ "A004760", "A276370", "A380558", "A380678" ]
null
Paul D. Hanna, Feb 13 2025
2025-02-15T11:16:44
oeisdata/seq/A380/A380558.seq
9d8db726cc6bb07735844175dbcf327b
A380559
With p(n) = A002144(n) = n-th Pythagorean prime, a(n) is the least k such p(n) + k is a Pythagorean prime and 2 p(n) + k - 1 is a Pythagorean prime; set a(n) = 0 if there is no such k.
[ "8", "4", "20", "32", "16", "20", "8", "28", "28", "20", "4", "56", "40", "44", "20", "92", "24", "8", "12", "4", "116", "4", "44", "28", "56", "80", "4", "32", "56", "36", "20", "36", "4", "56", "16", "20", "4", "8", "12", "12", "16", "152", "64", "140", "32", "20", "16", "104", "44", "40", "8", "12", "4", "44", "20", "56", "40", "28", "56", "8", "64", "24", "40", "92", "60", "56", "140" ]
[ "nonn" ]
8
1
1
[ "A000041", "A002144", "A002145", "A378184", "A378186", "A378187", "A380559" ]
null
Clark Kimberling, Jan 26 2025
2025-01-29T12:57:25
oeisdata/seq/A380/A380559.seq
e7b600ed85a08877b1c1aaca96821b70
A380560
Rectangular array R, read by descending antidiagonals: (row 1) = (R(1,k)) = (A006337(k)), k >= 1; (row n+1) = inverse runlength sequence of row n; and R(n,1) = 1 for n >=1, See Comments.
[ "1", "2", "1", "1", "2", "1", "2", "2", "2", "1", "1", "1", "2", "2", "1", "1", "2", "1", "2", "2", "1", "2", "2", "1", "1", "2", "2", "1", "1", "1", "2", "1", "1", "2", "2", "1", "2", "2", "1", "2", "1", "1", "2", "2", "1", "1", "1", "1", "1", "2", "1", "1", "2", "2", "1", "1", "1", "2", "2", "1", "2", "1", "1", "2", "2", "1", "2", "2", "2", "2", "2", "1", "2", "1", "1", "2", "2", "1" ]
[ "nonn", "tabl" ]
7
1
2
[ "A000002", "A000012", "A006337", "A380560" ]
null
Clark Kimberling, Jan 27 2025
2025-02-06T12:37:32
oeisdata/seq/A380/A380560.seq
86024af1c92c39aef7032161c8d0e16f
A380561
Rectangular array R read by descending antidiagonals: (row 1) = (R(1,k)) = (A006337(k)), k >= 1; (row n+1) = inverse runlength sequence of row n; and R(n,1) = (1, 1, 2, 1, 1, 2, 1, 1, 2, ...) = (A100063(n)) for n >= 1. See Comments.
[ "1", "2", "1", "1", "2", "2", "2", "2", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "2", "2", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "2", "2", "2", "2", "2", "2", "2", "2", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "1", "2", "2", "1", "2", "2", "2", "2", "2", "2", "2", "2", "2" ]
[ "nonn", "tabl" ]
13
1
2
[ "A000002", "A006337", "A100063", "A380560", "A380561" ]
null
Clark Kimberling, Jan 27 2025
2025-06-11T03:03:07
oeisdata/seq/A380/A380561.seq
a171839731726e4db748fb9deceb424c
A380562
Rectangular array R read by descending antidiagonals: (row 1) = (R(1,k)) = (A006337(k)), k >= 1; (row n+1) = inverse runlength sequence of row n; and R(n,1) = (1, 2, 2, 1, 2, 2, 1, 2, 2, ...) = (A130196(n)) for n >= 1. See Comments.
[ "1", "2", "2", "1", "1", "2", "2", "1", "2", "1", "1", "2", "1", "1", "2", "1", "1", "2", "2", "1", "2", "2", "1", "1", "2", "2", "2", "1", "1", "2", "1", "1", "2", "1", "1", "2", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "2", "1", "2", "1", "2", "2", "2", "2", "1", "1", "2", "2", "1", "2", "1", "1", "2", "1", "1", "2", "2", "1", "2", "2", "1", "1", "2", "1", "2", "2", "1", "2" ]
[ "nonn", "tabl" ]
9
1
2
[ "A000002", "A006337", "A130196", "A380560", "A380562" ]
null
Clark Kimberling, Jan 27 2025
2025-06-11T03:04:30
oeisdata/seq/A380/A380562.seq
d6c46322c7cb56a213d3f55dc2f3a16d
A380563
Rectangular array R read by descending antidiagonals: (row 1) = (R(1,k)) = (1 + A010060(k)), k >= 1; (row n+1) = inverse runlength sequence of row n; and R(n,1) = (1, 1, 1, 1, 1,...) = (A130196(n)) for n >= 1. See Comments.
[ "1", "2", "1", "2", "2", "1", "1", "2", "2", "1", "2", "1", "2", "2", "1", "1", "1", "1", "2", "2", "1", "1", "2", "1", "1", "2", "2", "1", "2", "1", "2", "1", "1", "2", "2", "1", "2", "1", "1", "2", "1", "1", "2", "2", "1", "1", "2", "2", "1", "2", "1", "1", "2", "2", "1", "1", "1", "2", "2", "1", "2", "1", "1", "2", "2", "1", "2", "2", "1", "2", "2", "1", "2", "1", "1", "2", "2", "1" ]
[ "nonn", "tabl" ]
6
1
2
[ "A000002", "A000012", "A010060", "A380563" ]
null
Clark Kimberling, Jan 27 2025
2025-01-29T22:24:16
oeisdata/seq/A380/A380563.seq
650af06d7be14e20ca00ff5c2f32f70a
A380564
Triangle read by rows q(b1,b2) with 1<b1<b2 with q(b1,b2) being the least integer k equal to or greater than b1 such that all the digits of k read in base b2 are the beginning digits of k read in base b1; or 0 iff b2 is perfect power, m^k (A001597), and b1 is m^j, 0<j<k.
[ "9", "0", "265", "5", "117032", "2123333591", "7", "44", "291720", "10757067", "57", "449", "16879", "18042", "19032324921", "0", "332930", "0", "2180306", "174631931663663360", "51981761666123", "9", "0", "93", "839", "407917265", "50732175", "197761284636128964", "10", "10", "133302001", "124343", "155133423353" ]
[ "base", "nonn", "tabl" ]
39
1
1
[ "A181929", "A379651", "A380564", "A380599" ]
null
Dominic McCarty and Robert G. Wilson v, Feb 03 2025
2025-02-05T21:58:51
oeisdata/seq/A380/A380564.seq
27fee66acaf831e491f9f617ef641015
A380565
Numbers k such that k^2 - 2 divides 2^k - 2.
[ "1", "2", "4", "46", "256" ]
[ "nonn", "more" ]
30
1
2
[ "A000918", "A008865", "A380565" ]
null
Juri-Stepan Gerasimov, Feb 03 2025
2025-02-07T22:46:24
oeisdata/seq/A380/A380565.seq
9394dd5aae1fe264b9bfde746a111d35
A380566
a(n) = k is the largest k for which k^5 is n digits long and the sum of digits of k^5 is the maximum for any n digit 5th power (A374025).
[ "1", "2", "3", "6", "9", "15", "18", "37", "58", "93", "156", "179", "368", "579", "756", "1379", "2337", "3965", "6006", "9746", "14198", "25046", "38779", "60006", "98746", "151446", "231755", "389658", "585516", "819199", "1584779", "2452779", "3897999", "5400759", "9744998", "15517759", "23936959", "28737498", "62943519", "95635199", "156373159", "225142779", "351816939", "595519999" ]
[ "nonn", "base" ]
25
1
2
[ "A374025", "A379650", "A380052", "A380193", "A380566" ]
null
Zhining Yang, Jan 26 2025
2025-02-01T23:18:28
oeisdata/seq/A380/A380566.seq
8f23ab6839c67643180a406733a7b3ce
A380567
a(n) = k the least number for which k^6 is n digits long and the sum of digits of k^6 is the maximum possible for a 6th power of that length (A373994(n)).
[ "1", "2", "3", "4", "6", "7", "12", "16", "23", "46", "64", "96", "143", "202", "277", "461", "547", "977", "1194", "2136", "2896", "3707", "5762", "9763", "13817", "16474", "25847", "43693", "51967", "72539", "121624", "172988", "271427", "463976", "681017", "751204", "1387617", "1732027", "3018897", "3515477", "6765526", "9258023" ]
[ "nonn", "base" ]
25
1
2
[ "A373994", "A379650", "A379869", "A380111", "A380193", "A380567" ]
null
Zhining Yang, Jan 26 2025
2025-03-25T08:55:22
oeisdata/seq/A380/A380567.seq
8641e5f2278d4b609a1c3e4ad50f2284
A380568
Choose two different numbers x and y from 2 to 9. a(n) is the number that consists solely of the digits x or y and is the smallest number divisible by both of them.
[ "24", "36", "288", "448", "2232", "2772", "3444", "3555", "3888", "4464", "5775", "6696", "8688", "33399", "37737", "44744", "76776", "7888888", "2222222292", "4444444944", "5555555595", "8888889888", "77777779779" ]
[ "nonn", "full", "fini", "base" ]
15
1
1
null
null
Seiichi Manyama, Jan 26 2025
2025-01-27T21:15:36
oeisdata/seq/A380/A380568.seq
68987e31de944b337705e6012469c05e
A380569
Numbers m such that the sum of cubes of nondivisors of m is prime.
[ "22", "82", "130", "144", "154", "178", "226", "274", "309", "322", "325", "514", "562", "565", "586", "670", "778", "1018", "1078", "1081", "1137", "1498", "1618", "1837", "1894", "1906", "1918", "1921", "2182", "2194", "2230", "2254", "2350", "2493", "2497", "2530", "2605", "2686", "2698", "2866", "3130", "3202", "3346", "3370", "3418", "3421", "3502" ]
[ "nonn" ]
15
1
1
[ "A024816", "A200981", "A380520", "A380569" ]
null
Michel Lagneau, Jan 27 2025
2025-02-09T04:58:58
oeisdata/seq/A380/A380569.seq
548f6ea2553139ceb031b0f3d697be21
A380570
Triangle T(n, k) read by rows: Row n gives the coefficients of the even powers in Product_{t=1..n}(2*x - (2*t - 1))*Product_{t=1..n}(2*x + (2*t - 1)).
[ "1", "4", "-1", "16", "-40", "9", "64", "-560", "1036", "-225", "256", "-5376", "31584", "-51664", "11025", "1024", "-42240", "561792", "-2764960", "4228884", "-893025", "4096", "-292864", "7358208", "-79036672", "351475696", "-515267064", "108056025", "16384", "-1863680", "78926848", "-1559683840", "14763100352", "-61460460880", "87512357916" ]
[ "sign", "tabl" ]
40
0
2
[ "A000302", "A001818", "A001824", "A001825", "A008956", "A380570", "A380612" ]
null
Thomas Scheuerle, Jan 27 2025
2025-02-05T22:17:38
oeisdata/seq/A380/A380570.seq
3af7c2b5e6ce57dce87f66e4ac83fbdb
A380571
Number of Dynkin systems on [n].
[ "1", "1", "2", "5", "19", "137", "3708", "1506404", "230328505024" ]
[ "nonn", "hard", "more" ]
33
0
3
[ "A000110", "A102894", "A380571", "A381471" ]
null
Peter J. Taylor, Feb 24 2025
2025-03-02T23:22:17
oeisdata/seq/A380/A380571.seq
3a57cd16b4ea0599428c58d950ef5362
A380572
Complement of A380509.
[ "1", "2", "3", "4", "5", "7", "8", "9", "10", "13", "14", "15", "17", "18", "22", "23", "24", "25", "27", "28", "32", "34", "35", "37", "39", "43", "44", "45", "48", "49", "50", "53", "57", "58", "59", "60", "62", "64", "67", "69", "70", "73", "77", "78", "79", "80", "84", "87", "88", "93", "95", "97", "98", "99", "100", "102", "104", "105", "108", "111", "112", "113", "114", "115", "122" ]
[ "nonn" ]
13
1
2
[ "A005097", "A006093", "A380509", "A380550", "A380572" ]
null
Davide Rotondo, Jan 27 2025
2025-01-31T04:23:12
oeisdata/seq/A380/A380572.seq
a5943a724fa06861ea4a142ce67d1eba
A380573
Number of distinct free polyominoes that are terraces in the first n levels of the stepped pyramid described in A245092.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "16", "17", "18", "19", "20", "21", "23", "24", "25", "26", "28", "29", "31", "32", "33", "34", "35", "36" ]
[ "nonn", "more" ]
42
1
2
[ "A000105", "A000203", "A175254", "A196020", "A235791", "A236104", "A237270", "A237271", "A237591", "A237593", "A239931", "A239934", "A245092", "A262626", "A347186", "A380573" ]
null
Omar E. Pol, Mar 15 2025
2025-04-09T22:51:48
oeisdata/seq/A380/A380573.seq
0784cf16f7ea06df376e13dced1ac3c3
A380574
For an integer k with prime factorization p_1*p_2*p_3* ... *p_m let k* = (p_1+1)*(p_2+1)*(p_3+1)* ... *(p_m+1); sequence gives k* such that k* is divisible by k.
[ "1", "12", "36", "144", "432", "1296", "1728", "5184", "15552", "20736", "46656", "62208", "186624", "248832", "559872", "746496", "1679616", "2239488", "2985984", "6718464", "8957952", "20155392", "26873856", "35831808", "60466176", "80621568", "107495424", "241864704", "322486272", "429981696", "725594112", "967458816" ]
[ "nonn", "easy" ]
22
1
2
[ "A064476", "A064514", "A064515", "A064518", "A380574" ]
null
Chai Wah Wu, Mar 26 2025
2025-04-22T06:32:20
oeisdata/seq/A380/A380574.seq
92268193ad4b0b13e35d2f43836c554e
A380575
One half of the sum of the perimeters of the free polyominoes with n cells.
[ "2", "3", "8", "24", "71", "236", "835", "3182", "12302", "48834", "195035", "785280", "3167322", "12808531", "51834644", "209965222", "850817523", "3449091525" ]
[ "nonn", "more" ]
19
1
1
[ "A000105", "A342243", "A380287", "A380575" ]
null
Omar E. Pol, Feb 12 2025
2025-03-02T23:19:59
oeisdata/seq/A380/A380575.seq
d7d3fb462bb86077dd611b009f03f0e8
A380576
Total number of "block reversals" needed to transform all permutations of [n] into 12...n.
[ "0", "0", "1", "7", "42", "287", "2186", "18650", "176408", "1837189", "20908724", "258210463", "3440203098", "49202385314", "752012692572" ]
[ "nonn", "more" ]
19
0
4
[ "A300003", "A380576" ]
null
Alois P. Heinz, Mar 26 2025
2025-04-12T16:51:16
oeisdata/seq/A380/A380576.seq
3f3a35746083af2851d0504998558ded
A380577
a(n) is the number of distinct compositions of chess pieces with a collective material value of n that one color in a game can have, where 0 <= n <= 103.
[ "1", "1", "1", "3", "3", "4", "7", "7", "9", "13", "14", "17", "22", "24", "28", "35", "38", "41", "52", "54", "59", "72", "73", "79", "95", "95", "101", "117", "120", "122", "144", "139", "146", "166", "159", "165", "186", "174", "184", "195", "189", "199", "204", "197", "201", "208", "204", "194", "206", "194", "193", "195", "182", "182", "178", "177", "159", "177", "142", "154", "137", "145", "122", "135", "103", "121", "96", "104", "85", "96", "71", "77", "63", "73", "52", "60", "45", "48", "40", "41", "31", "39", "23", "26", "23", "22", "18", "18", "11", "15", "8", "10", "9", "6", "5", "4", "2", "5", "1", "1", "2", "0", "0", "1" ]
[ "nonn", "fini", "full" ]
9
0
4
[ "A278832", "A378248", "A380577" ]
null
Felix Huber, Mar 30 2025
2025-04-04T17:19:15
oeisdata/seq/A380/A380577.seq
0f4cd88216f9a3e46bace0f16e104b70
A380578
Number of nonisomorphic groups appearing as the group of units of the ring Z/kZ for every k such that phi(k) = n.
[ "1", "1", "0", "2", "0", "1", "0", "2", "0", "1", "0", "2", "0", "0", "0", "3", "0", "1", "0", "2", "0", "1", "0", "2", "0", "0", "0", "1", "0", "1", "0", "4", "0", "0", "0", "3", "0", "0", "0", "3", "0", "1", "0", "1", "0", "1", "0", "3", "0", "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "2", "0", "0", "0", "5", "0", "1", "0", "0", "0", "1", "0", "5", "0", "0", "0", "0", "0", "1", "0", "3", "0", "1", "0", "1", "0", "0", "0", "3", "0", "0", "0" ]
[ "nonn" ]
10
1
4
[ "A000010", "A000688", "A005277", "A007617", "A014197", "A049283", "A057635", "A380578" ]
null
Miles Englezou, Mar 26 2025
2025-04-01T23:08:55
oeisdata/seq/A380/A380578.seq
6adb1b47642c5938690da57b1a9981df
A380581
a(n) = [x^n] G(x)^n, where G(x) = Product_{k >= 1} 1/(1 - x^k)^(k^4) is the g.f. of A023873.
[ "1", "1", "35", "397", "5075", "67126", "897911", "12144945", "165880531", "2280262825", "31522512910", "437730330357", "6101414176535", "85317965576325", "1196299277106675", "16813979471920522", "236812229975204563", "3341448338530887015", "47225228515043980715", "668417245247747877735", "9473101371364286661950", "134416752857691389968377", "1909344928242571795580255" ]
[ "nonn", "easy" ]
14
0
3
[ "A001160", "A023873", "A380290", "A380581", "A380582", "A380583" ]
null
Peter Bala, Jan 27 2025
2025-02-02T09:43:09
oeisdata/seq/A380/A380581.seq
f6f8e1840b7eb6438e5cc0515344a34a
A380582
a(n) = [x^n] G(x)^n, where G(x) = Product_{k >= 1} ((1 + x^k)/(1 - x^k))^(k^2) is the g.f. of A206622.
[ "1", "2", "24", "236", "2432", "25752", "277152", "3019088", "33186816", "367378814", "4089875024", "45741207228", "513537853952", "5784253405192", "65332622356032", "739706089046736", "8392732289277952", "95401363286044260", "1086232605119042424", "12386037358495697292", "141422619808922418432", "1616691574828234720352" ]
[ "nonn", "easy" ]
11
0
2
[ "A001158", "A015128", "A206622", "A380290", "A380581", "A380582", "A380583" ]
null
Peter Bala, Jan 27 2025
2025-01-29T22:31:43
oeisdata/seq/A380/A380582.seq
5d98820ee04f19263997cc5275339219
A380583
a(n) = [x^n] G(x)^n, where G(x) = Product_{k >= 1} ((1 + x^(2*k))/(1 - x^k))^(k^2).
[ "1", "1", "13", "82", "665", "5026", "40180", "319677", "2583401", "20965150", "171276238", "1405008925", "11571476120", "95601033542", "792038546739", "6577523807332", "54737967873385", "456368114019558", "3811136362823056", "31873576059000827", "266919720010452190", "2237944814420991135", "18784073017650350445" ]
[ "nonn", "easy" ]
15
0
3
[ "A380290", "A380581", "A380582", "A380583" ]
null
Peter Bala, Jan 27 2025
2025-01-31T04:26:49
oeisdata/seq/A380/A380583.seq
270ff2616cbbdfc0a4b97ce146502f98
A380584
Number of positive integers <= n that have the same sum of odd divisors as n.
[ "1", "2", "1", "3", "1", "2", "1", "4", "1", "2", "1", "3", "1", "2", "1", "5", "1", "2", "1", "3", "1", "2", "2", "4", "1", "2", "1", "3", "1", "3", "2", "6", "1", "2", "2", "3", "1", "2", "1", "4", "1", "3", "1", "3", "1", "4", "3", "5", "1", "2", "1", "3", "1", "2", "2", "4", "1", "2", "1", "5", "1", "4", "1", "7", "1", "4", "1", "3", "1", "5", "3", "4", "1", "2", "1", "3", "2", "2", "2", "5", "1", "2", "2", "5", "1", "2", "1", "4", "1", "2", "1", "6", "1", "6", "2", "6", "1", "2", "1", "3" ]
[ "nonn" ]
12
1
2
[ "A000593", "A263025", "A337557", "A380584", "A380653", "A380654" ]
null
Ilya Gutkovskiy, Jan 30 2025
2025-02-16T08:34:07
oeisdata/seq/A380/A380584.seq
50ed9aa7321a43916426b0abd17b754d
A380585
a(n) = floor(n^2 / 10^m) + (n^2 mod 10^m) where m is the number of decimal digits in n.
[ "0", "1", "4", "9", "7", "7", "9", "13", "10", "9", "1", "22", "45", "70", "97", "27", "58", "91", "27", "64", "4", "45", "88", "34", "81", "31", "82", "36", "91", "49", "9", "70", "34", "99", "67", "37", "108", "82", "58", "36", "16", "97", "81", "67", "55", "45", "37", "31", "27", "25", "25", "27", "31", "37", "45", "55", "67", "81", "97", "115", "36", "58", "82", "108", "136", "67", "99" ]
[ "nonn", "base", "look" ]
36
0
3
[ "A053816", "A055642", "A344851", "A358072", "A380585" ]
null
Giorgos Kalogeropoulos, Mar 27 2025
2025-04-10T17:14:19
oeisdata/seq/A380/A380585.seq
73b8c628c7711526238788ce5a5d2572
A380586
Split A377091 into sublists consisting of runs of terms with the same sign. Then a(n) is the maximum value of the first differences of the sorted terms within the n-th sublist.
[ "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", "1", "1", "2", "1", "2", "2", "1", "2", "3", "2", "2", "2", "3", "2", "2", "4", "2", "1", "3", "4", "1", "3", "1", "2", "1", "2", "1", "2", "2", "3", "2", "1", "3", "4", "2", "3", "4", "1", "3", "1", "3", "1", "1", "4", "1", "1", "1", "1", "1" ]
[ "nonn" ]
12
2
44
[ "A377091", "A379882", "A380510", "A380586", "A380587", "A380588" ]
null
Paolo Xausa, Jan 27 2025
2025-01-28T09:39:07
oeisdata/seq/A380/A380586.seq
6ef82721637879cf83ed86f37b1530b6
A380587
Split A377091 into sublists consisting of runs of terms with the same sign. Then a(n) is the maximum value of the first differences of the absolute value of the terms within the n-th sublist.
[ "1", "-1", "1", "-1", "1", "4", "1", "1", "1", "1", "4", "1", "4", "4", "1", "1", "1", "1", "1", "4", "1", "4", "4", "1", "4", "1", "4", "1", "1", "1", "1", "1", "4", "4", "1", "4", "1", "4", "1", "4", "1", "4", "4", "4", "4", "4", "4", "4", "9", "4", "9", "4", "4", "4", "9", "4", "4", "4", "-1", "4", "9", "-1", "1", "1", "4", "1", "4", "-1", "4", "4", "4", "9", "1", "4", "9", "4", "9", "9", "-1", "1", "1", "9", "-1", "1", "4", "4", "1", "4", "1", "4" ]
[ "sign" ]
11
2
6
[ "A377091", "A379882", "A380510", "A380586", "A380587", "A380588" ]
null
Paolo Xausa, Jan 27 2025
2025-01-28T09:39:32
oeisdata/seq/A380/A380587.seq
091f45f244cee1379daf0cbe29c188aa
A380588
Split A377091 into sublists consisting of runs of terms with the same sign. Then a(n) is max(b) - min(b), where b is the n-th sublist.
[ "0", "1", "1", "2", "1", "2", "7", "4", "5", "4", "5", "9", "7", "12", "7", "8", "9", "10", "9", "10", "14", "12", "22", "12", "13", "14", "15", "14", "15", "16", "17", "16", "17", "37", "19", "20", "19", "20", "21", "22", "21", "22", "23", "24", "50", "25", "26", "26", "27", "29", "29", "29", "29", "29", "32", "30", "5", "34", "26", "3", "34", "32", "1", "4", "32", "31", "33", "34", "3", "36", "32", "37", "38", "1", "39" ]
[ "nonn" ]
8
1
4
[ "A377091", "A379882", "A380510", "A380586", "A380587", "A380588" ]
null
Paolo Xausa, Jan 27 2025
2025-01-28T09:39:49
oeisdata/seq/A380/A380588.seq
e515a6f26b15cd1def04339b6c0b5558
A380589
Number of n-colorings of the Hypercube Graph Q5.
[ "0", "0", "2", "1185282", "130253748108", "2157531034816940", "7905235551766437150", "7365707045872206479742", "2337101560809838105414712", "327425229254999498091796728", "24489214732779742874109277530", "1119349138930999380736025706650", "34471067091433681765512048700932" ]
[ "nonn", "easy", "changed" ]
19
0
3
[ "A001477", "A002378", "A091940", "A140986", "A158348", "A334278", "A342128", "A380589" ]
null
Alois P. Heinz, Jan 27 2025
2025-07-06T18:57:21
oeisdata/seq/A380/A380589.seq
0174309aa4b7f7cfe9b7e4cfaddba7c5
A380590
Population of elementary triangular automaton rule 218 at generation n, starting from a lone 1 cell at generation 0.
[ "1", "4", "7", "16", "16", "22", "37", "46", "43", "52", "82", "106", "94", "136", "148", "181", "208", "208", "244", "286", "262", "343", "412", "460", "490", "499", "622", "703", "664", "790", "859", "922", "907", "940", "952", "1057", "1048", "1240", "1342", "1420", "1516", "1570", "1780", "1864", "1912", "2026", "2152", "2248", "2398", "2488", "2644", "2794" ]
[ "nonn" ]
21
0
2
[ "A372581", "A380012", "A380590", "A380670", "A381734", "A382971", "A382972", "A383028" ]
null
Paul Cousin, Apr 22 2025
2025-05-20T00:19:06
oeisdata/seq/A380/A380590.seq
9242de0d878533ed4a1f5efb76142410
A380591
a(n) is the number of dissections of a convex (n+2)-sided polygon by nonintersecting diagonals into triangles and quadrilaterals such that at least one of the dividing diagonals passes through a chosen vertex.
[ "0", "1", "5", "21", "90", "395", "1773", "8110", "37686", "177450", "844935", "4061762", "19687020", "96107358", "472132330", "2332304055", "11578595554", "57736664825", "289055592810", "1452381167325", "7321620080550", "37020073600755", "187699184460450", "954084756674088", "4861008765722340" ]
[ "nonn", "easy" ]
32
1
3
[ "A001002", "A217596", "A380591" ]
null
Muhammed Sefa Saydam, Jan 27 2025
2025-02-08T20:52:04
oeisdata/seq/A380/A380591.seq
cd58f4811651039fb60f27d68cf3e762
A380592
Number of ways that a European soccer league tournament with n teams can complete with all teams having the same number of points.
[ "1", "3", "27", "1083", "296081", "696779523", "16503494334993", "3439079361325736243" ]
[ "nonn", "hard", "more" ]
35
1
2
[ "A007080", "A053764", "A380592" ]
null
Ruediger Jehn, Jan 27 2025
2025-03-25T19:52:02
oeisdata/seq/A380/A380592.seq
dfc59a60b81d31bc8b63a934ff994e98
A380593
Starting position of the first occurrence of the longest monochromatic arithmetic progression of difference n in the Rudin-Shapiro sequence (A020987).
[ "7", "14", "28", "28", "31", "43", "95", "56", "43", "62", "453", "86", "99", "190", "39", "112", "495", "86", "366", "124", "81", "321", "203", "172", "1006", "81", "233", "380", "2019", "78", "993", "224", "980", "990", "888", "172", "1084", "732", "4057", "248", "2007", "162", "164", "642", "1215", "406", "1729", "344", "1398", "2012", "1988", "162", "1765" ]
[ "nonn" ]
24
1
1
[ "A020985", "A020987", "A364995", "A380593" ]
null
Gandhar Joshi, Jan 27 2025
2025-02-12T21:40:11
oeisdata/seq/A380/A380593.seq
618d917db34a37738d4a2bb7015869f8
A380594
a(n) is the number of positive integers having 2*n primitive roots.
[ "6", "4", "4", "6", "2", "8", "0", "4", "2", "2", "2", "8", "0", "2", "0", "4", "0", "4", "0", "12", "0", "2", "0", "12", "0", "2", "4", "0", "0", "2", "0", "6", "0", "0", "0", "10", "0", "0", "0", "2", "2", "6", "0", "4", "0", "2", "0", "12", "0", "2", "0", "0", "0", "4", "0", "6", "0", "0", "0", "10", "0", "0", "0", "6", "2", "2", "0", "0", "0", "0", "0", "16", "0", "0", "0", "0", "0", "2", "0", "8", "4", "2", "0", "6", "0" ]
[ "nonn" ]
17
1
1
[ "A007617", "A010554", "A033949", "A046144", "A231772", "A378506", "A378508", "A380594", "A380604" ]
null
David James Sycamore, Michael De Vlieger, and Amiram Eldar, Jan 27 2025
2025-03-31T23:12:02
oeisdata/seq/A380/A380594.seq
bc2ea7215a6674870e6f1ae52d8dfc01
A380595
a(n) is the first nonsquarefree number k such that the n consecutive nonsquarefree numbers starting with k are in arithmetic progression.
[ "4", "4", "16", "28", "28", "5050", "6348", "144946", "3348550", "221167422", "221167422", "47255689915", "82462576220", "1043460553364", "79180770078548", "3215226335143218", "23742453640900972", "125781000834058568" ]
[ "nonn", "hard", "more" ]
16
1
1
[ "A013929", "A045882", "A376267", "A380595" ]
null
Robert Israel, Jan 27 2025
2025-01-29T22:13:44
oeisdata/seq/A380/A380595.seq
c598e1ad373249a36fbae4ab5637f7ca
A380596
Numbers with embedded palindromes as proper substrings of the term.
[ "100", "110", "111", "112", "113", "114", "115", "116", "117", "118", "119", "122", "133", "144", "155", "166", "177", "188", "199", "200", "211", "220", "221", "222", "223", "224", "225", "226", "227", "228", "229", "233", "244", "255", "266", "277", "288", "299", "300", "311", "322", "330", "331", "332", "333", "334", "335", "336", "337", "338", "339", "344", "355", "366", "377", "388", "399" ]
[ "nonn", "base" ]
22
1
1
[ "A002113", "A044821", "A380596" ]
null
James S. DeArmon, Jan 27 2025
2025-03-06T11:52:49
oeisdata/seq/A380/A380596.seq
4217fdea3220561b2d0ef2e24fc68f60
A380597
Smallest side length of a square board on which Harary's generalized tic-tac-toe (or animal tic-tac-toe) for the free polyomino with binary code A246521(n+1) is a first-player win, or 0 if it is a draw for all board sizes.
[ "1", "2", "3", "4", "4", "0", "5", "3", "7", "0", "0", "0", "7", "7", "6", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "nonn", "tabf", "more" ]
7
1
2
[ "A000105", "A246521", "A380597", "A380598" ]
null
Pontus von Brömssen, Jan 27 2025
2025-01-29T12:47:06
oeisdata/seq/A380/A380597.seq
ddb696724945b09ac62f5c0a1ec7e6c3
A380598
Number of moves required for the first player to win Harary's generalized tic-tac-toe (or animal tic-tac-toe) for the free polyomino with binary code A246521(n+1) on a square board of side length A380597(n), or 0 if it is a draw for all board sizes.
[ "1", "2", "3", "3", "4", "0", "4", "5", "8", "0", "0", "0", "10", "9", "6", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "nonn", "tabf", "more" ]
8
1
2
[ "A000105", "A246521", "A380597", "A380598" ]
null
Pontus von Brömssen, Jan 27 2025
2025-01-29T12:47:17
oeisdata/seq/A380/A380598.seq
3118e8ba053b08b22c8632bae7fb27ed
A380599
Decimal expansion of the smallest number greater than 1 whose binary and ternary expansions have the same succession of digits.
[ "9", "3", "8", "2", "7", "9", "2", "2", "4", "8", "5", "7", "3", "0", "9", "2", "7", "2", "7", "5", "3", "6", "9", "6", "6", "3", "3", "6", "4", "2", "8", "3", "3", "1", "2", "2", "6", "3", "2", "0", "2", "9", "4", "1", "8", "6", "1", "0", "0", "8", "3", "0", "7", "4", "7", "4", "3", "8", "3", "4", "0", "1", "1", "5", "4", "8", "6", "1", "1", "4", "4", "3", "0", "2", "8", "9", "5", "3", "0", "8", "6", "6", "0", "5", "7", "7", "8", "9", "6", "8", "1", "8", "4", "3", "3", "3", "6", "5", "8", "1", "0", "6", "3", "9", "7" ]
[ "base", "cons", "nonn" ]
12
1
1
[ "A379651", "A380599" ]
null
Robert G. Wilson v, Jan 27 2025
2025-01-29T11:50:28
oeisdata/seq/A380/A380599.seq
5e7355f531a8c961b5fb7fc71d048e50
A380600
Irregular table T(n, k), n > 0, k = 1..A000005(n) read by rows: the n-th row lists the numbers of the form n * (d-1) / d with d a positive divisor of n.
[ "0", "0", "1", "0", "2", "0", "2", "3", "0", "4", "0", "3", "4", "5", "0", "6", "0", "4", "6", "7", "0", "6", "8", "0", "5", "8", "9", "0", "10", "0", "6", "8", "9", "10", "11", "0", "12", "0", "7", "12", "13", "0", "10", "12", "14", "0", "8", "12", "14", "15", "0", "16", "0", "9", "12", "15", "16", "17", "0", "18", "0", "10", "15", "16", "18", "19", "0", "14", "18", "20", "0", "11", "20", "21", "0", "22" ]
[ "nonn", "tabf", "easy" ]
21
1
5
[ "A000005", "A027750", "A046666", "A060681", "A072513", "A094471", "A258324", "A380600" ]
null
Rémy Sigrist, Feb 02 2025
2025-04-01T08:56:31
oeisdata/seq/A380/A380600.seq
5baca930e6d0b11983bdc4be5fd8f33c
A380601
Decimal expansion of the asymptotic mean of the ratio A322483(k)/A000005(k).
[ "8", "5", "9", "8", "0", "6", "7", "7", "9", "3", "3", "0", "3", "4", "3", "6", "3", "3", "1", "1", "2", "4", "4", "7", "6", "7", "5", "9", "4", "9", "4", "1", "8", "3", "2", "4", "6", "6", "5", "1", "5", "8", "0", "9", "5", "5", "1", "3", "8", "5", "6", "6", "1", "1", "2", "7", "7", "1", "5", "4", "6", "4", "8", "9", "4", "9", "1", "3", "4", "3", "3", "0", "8", "5", "8", "7", "6", "9", "4", "9", "7", "3", "4", "2", "3", "7", "6", "4", "8", "4", "8", "5", "9", "3", "5", "3", "5", "2", "4", "5", "4", "4", "8", "4", "5" ]
[ "nonn", "cons" ]
6
0
1
[ "A000005", "A308043", "A322483", "A361060", "A361062", "A380601", "A380602" ]
null
Amiram Eldar, Jan 27 2025
2025-01-28T01:48:44
oeisdata/seq/A380/A380601.seq
3f2abde87c845b6eb80bb04e5b78e793
A380602
Decimal expansion of the asymptotic mean of the ratio A000005(k)/A322483(k).
[ "1", "2", "3", "5", "8", "7", "9", "7", "7", "7", "5", "2", "6", "1", "7", "3", "5", "4", "8", "7", "1", "0", "9", "3", "8", "0", "5", "3", "1", "8", "9", "4", "5", "1", "1", "0", "4", "4", "7", "7", "5", "2", "7", "5", "0", "3", "7", "0", "3", "0", "5", "4", "8", "6", "3", "8", "6", "2", "9", "3", "6", "8", "6", "8", "4", "7", "1", "1", "0", "0", "2", "2", "9", "1", "4", "5", "9", "3", "3", "4", "8", "6", "7", "0", "3", "7", "8", "3", "8", "5", "6", "5", "2", "3", "6", "6", "0", "9", "4", "4", "9", "6", "9", "1", "7" ]
[ "nonn", "cons" ]
5
1
2
[ "A000005", "A307869", "A322483", "A361059", "A361061", "A380601", "A380602" ]
null
Amiram Eldar, Jan 27 2025
2025-01-28T01:48:59
oeisdata/seq/A380/A380602.seq
243433655eed6e6fe346cdeff3af565c
A380603
Expansion of e.g.f. exp(2*x*G(x)^2) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.
[ "1", "2", "12", "140", "2512", "61392", "1905184", "71781824", "3183563520", "162497556224", "9383803201024", "604888546242048", "43056560538093568", "3354362248463544320", "283895464602180231168", "25938521255822517813248", "2544584391277895815069696", "266765818037212169468706816", "29764238411096397030375424000" ]
[ "nonn" ]
8
0
2
[ "A001764", "A251573", "A380511", "A380603" ]
null
Seiichi Manyama, Jan 28 2025
2025-01-28T08:38:32
oeisdata/seq/A380/A380603.seq
4f3926d214758fc0d360fde327d729aa
A380604
Numbers k such that there is no number i such that A046144(i) = 2*k.
[ "7", "13", "15", "17", "19", "21", "23", "25", "28", "29", "31", "33", "34", "35", "37", "38", "39", "43", "45", "47", "49", "51", "52", "53", "55", "57", "58", "59", "61", "62", "63", "67", "68", "69", "70", "71", "73", "74", "75", "76", "77", "79", "83", "85", "87", "91", "92", "93", "94", "97", "98", "99", "101", "103", "104", "105", "107", "109", "111", "112", "113", "114", "115", "117", "118" ]
[ "nonn" ]
15
1
1
[ "A046144", "A378508", "A380594", "A380604" ]
null
David James Sycamore, Jan 28 2025
2025-02-01T14:43:40
oeisdata/seq/A380/A380604.seq
512fb720f745efa6f72a2ed3aa05d101
A380605
Expansion of e.g.f. exp(2*x*G(x)^3) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
[ "1", "2", "16", "260", "6544", "224672", "9797824", "518778752", "32332764160", "2319086302208", "188178044545024", "17043816700333568", "1704575787500099584", "186577340672207974400", "22185432394552519868416", "2847773562263558405439488", "392481896442656581445287936", "57805399208817471918851883008" ]
[ "nonn" ]
8
0
2
[ "A002293", "A251574", "A380515", "A380605", "A380606" ]
null
Seiichi Manyama, Jan 28 2025
2025-01-28T08:38:29
oeisdata/seq/A380/A380605.seq
13cdc6fd2e7893a78192f4ff8c7a5b33
A380606
Expansion of e.g.f. exp(3*x*G(x)^3) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
[ "1", "3", "27", "459", "11817", "411183", "18090459", "963856071", "60351513777", "4344290172891", "353515902334299", "32093341598006307", "3215888732193019353", "352572962113533923271", "41981774097966848444763", "5395346708265250105968927", "744369113570455426540767201", "109733083289828610273889269939" ]
[ "nonn" ]
8
0
2
[ "A002293", "A251574", "A380515", "A380605", "A380606" ]
null
Seiichi Manyama, Jan 28 2025
2025-01-28T08:38:25
oeisdata/seq/A380/A380606.seq
5d7c0b162a805a2f051a2da17401bef3
A380607
a(0) = 1, a(n) = 5*binomial(6*(n-1),n-1), for n > 0.
[ "1", "5", "30", "330", "4080", "53130", "712530", "9738960", "134891640", "1886744970", "26589681300", "376970137830", "5370413979840", "76816421507280", "1102478371452150", "15868672192650600", "228978369822304080", "3311260421942706570" ]
[ "nonn" ]
23
0
2
[ "A004355", "A380607" ]
null
Karol A. Penson, Jan 28 2025
2025-02-02T08:48:44
oeisdata/seq/A380/A380607.seq
25f7428f1924e8e7368722dea3fe4183
A380608
a(n) is the number of distinct ways to cut a hexagon with edges of size n into diamonds with integer sides.
[ "2", "37", "6330", "12807773" ]
[ "nonn", "more" ]
10
0
1
[ "A045846", "A380608" ]
null
Craig Knecht, Jan 28 2025
2025-02-07T00:46:35
oeisdata/seq/A380/A380608.seq
de067a2b7942116cb50e5797bef1893b
A380609
Primes a single step away from a cycle under the mapping p-> gpf(2*p+1).
[ "2", "17", "31", "37", "67", "71", "73", "97", "103", "137", "149", "157", "181", "199", "211", "227", "241", "269", "283", "313", "337", "367", "379", "409", "487", "541", "563", "577", "587", "607", "617", "643", "661", "769", "787", "857", "877", "907", "929", "937", "977", "997", "1039", "1093", "1151", "1187", "1237", "1453", "1543", "1567", "1579", "1621" ]
[ "nonn" ]
23
1
1
[ "A006530", "A076565", "A287865", "A380609" ]
null
Johannes M.V.A. Koelman, Jan 28 2025
2025-02-16T19:36:35
oeisdata/seq/A380/A380609.seq
95df46d2435c6898be356ae7b318ab1e
A380610
Irregular triangle read by rows: T(n,k) is the number of non-isomorphic formulas in conjunctive normal form (CNF) with n variables and k distinct nonempty clauses up to permutations of the variables and clauses, 0 <= k < 3^n.
[ "1", "1", "2", "1", "1", "5", "16", "31", "38", "31", "16", "5", "1", "1", "9", "73", "500", "2676", "11390", "39256", "111252", "263014", "524677", "890602", "1294240", "1617050", "1741208", "1617050", "1294240", "890602", "524677", "263014", "111252", "39256", "11390", "2676", "500", "73", "9", "1", "1", "14", "238", "4320", "72225", "1039086", "12712546", "133231940", "1211353657" ]
[ "nonn", "tabf" ]
44
0
3
[ "A000244", "A371830", "A380518", "A380610", "A380630" ]
null
Frank Schwidom, Jan 28 2025
2025-02-26T06:32:22
oeisdata/seq/A380/A380610.seq
3e7ff0199fe13b3ddceada7ecc684464
A380611
Irregular triangle read by rows: T(r,c) is the product of the number of standard Young tableaux (A117506) and the number of semistandard Young tableaux (A262030) for partitions of r.
[ "1", "1", "3", "1", "10", "16", "1", "35", "135", "40", "45", "1", "126", "896", "875", "756", "375", "96", "1", "462", "5250", "10206", "8400", "2450", "14336", "2800", "875", "1701", "175", "1", "1716", "28512", "90552", "74250", "65856", "257250", "48000", "74088", "55566", "102900", "8100", "10976", "5488", "288", "1", "6435", "147147", "686400", "567567", "931392", "3244032", "606375", "194040", "2910600", "1448832", "2673000", "202125", "666792", "846720", "1029000", "491520", "19845", "24696", "65856", "14400", "441", "1" ]
[ "nonn", "tabf" ]
34
0
3
[ "A000041", "A000312", "A047874", "A059304", "A088218", "A117506", "A262030", "A365643", "A380611" ]
null
Wouter Meeussen, Jan 28 2025
2025-01-29T22:15:35
oeisdata/seq/A380/A380611.seq
d1dc00e4d4bd6b4170ffd395ade2f459
A380612
a(n) = (-1)^n*Product_{k=1..n} (2*k + 1)*(2*k - 3).
[ "1", "3", "-15", "315", "-14175", "1091475", "-127702575", "21070924875", "-4656674397375", "1327152203251875", "-473793336560919375", "207047688077121766875", "-108700036240488927609375", "67502722505343624045421875", "-48939473816374127432930859375", "40962339584305144661363129296875" ]
[ "sign", "easy" ]
35
0
2
[ "A001147", "A380570", "A380612" ]
null
Thomas Scheuerle, Jan 28 2025
2025-02-02T16:30:45
oeisdata/seq/A380/A380612.seq
b017ceace324a2f8537f9e1cfea27f38
A380613
Expansion of Product_{k>=1} (1 + x^k)^prime(k)#.
[ "1", "2", "7", "42", "291", "2970", "36950", "597100", "11070875", "248103940", "7018494836", "215718595582", "7881561212732", "320881902092122", "13754717161317416", "643588827524430916", "33926485821837232397", "1992916854095359256932", "121393059052727838936847", "8107963745977267426512386", "574571379331620422000295082" ]
[ "nonn" ]
8
0
2
[ "A002110", "A061152", "A261052", "A380497", "A380613", "A380614" ]
null
Ilya Gutkovskiy, Jan 28 2025
2025-02-16T08:34:07
oeisdata/seq/A380/A380613.seq
5143a00623dc364c1f8bb6f9c7c92141
A380614
Product_{n>=1} (1 + x^n)^a(n) = Sum_{n>=0} prime(n)# * x^n.
[ "2", "5", "20", "155", "1860", "24970", "444060", "8583935", "202071920", "5992773714", "186947632200", "7001535728810", "288868991951760", "12455290280871150", "587972068547997856", "31327583556949986095", "1856116108295418943020", "113366872636395467452840", "7619343577986975410930880", "541957669076266404650853414" ]
[ "nonn" ]
7
1
1
[ "A002110", "A168246", "A305871", "A380498", "A380613", "A380614" ]
null
Ilya Gutkovskiy, Jan 28 2025
2025-02-16T08:34:07
oeisdata/seq/A380/A380614.seq
4b9b8b0fe11a6d2e15b7867f0061e20d