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2
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348
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score
int64
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2.35k
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int64
-14,827
666,262,453B
offset_b
int64
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635M
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cross_references
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timestamp
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1999-12-11 03:00:00
2025-07-19 00:40:46
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32
A355501
Expansion of e.g.f. exp(3 * x * exp(x)).
[ "1", "3", "15", "90", "633", "5028", "44217", "424434", "4399953", "48858984", "577372809", "7221983838", "95192539641", "1317190650636", "19071213218745", "288112248054882", "4530217559806497", "73976635012027344", "1252091246140278153", "21926952634345281030", "396671314081806278601" ]
[ "nonn" ]
19
0
2
[ "A000248", "A187105", "A275707", "A295623", "A351763", "A355501" ]
null
Seiichi Manyama, Jul 04 2022
2022-07-06T05:39:45
oeisdata/seq/A355/A355501.seq
989342d8a75a200d3a48967023614e25
A355502
Inequivalent simultaneous colorings of the faces, vertices and edges of the cube under rotational symmetry using exactly n colors.
[ "1", "2802750", "105904482864", "187226450755016", "61150982606571900", "6737855626357107000", "342689297671355738880", "9659365383584921484480", "169366933728740293383600", "1995772772375467764487200" ]
[ "nonn", "fini" ]
35
1
2
[ "A355502", "A356685" ]
null
Marko Riedel, Aug 22 2022
2023-03-10T07:25:20
oeisdata/seq/A355/A355502.seq
a2590e9b0f6178cdac05ea9222f0faea
A355503
Total number of m-tuples (p_1, p_2, ..., p_m) of Dyck paths of semilength n-m, such that each p_i is never below p_{i-1} for m=0..n.
[ "1", "2", "3", "5", "11", "35", "164", "1120", "10969", "152849", "3029650", "85227078", "3400752392", "192644205130", "15470939367651", "1761760468965521", "284641456742538865", "65175288287611738435", "21159611204475209730138", "9743708333490185603430830", "6357930817596444858142966826" ]
[ "nonn" ]
27
0
2
[ "A000108", "A074962", "A078920", "A123352", "A355400", "A355503", "A368025" ]
null
Alois P. Heinz, Jul 04 2022
2024-11-16T17:27:32
oeisdata/seq/A355/A355503.seq
b256b9d4fa472d377e9bce5f5fc535bc
A355504
Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, among the decimal digits of n and a(n) (counted with multiplicity) there are as many even digits as odd digits.
[ "1", "0", "3", "2", "5", "4", "7", "6", "9", "8", "10", "20", "12", "22", "14", "24", "16", "26", "18", "28", "11", "21", "13", "23", "15", "25", "17", "27", "19", "29", "30", "40", "32", "42", "34", "44", "36", "46", "38", "48", "31", "41", "33", "43", "35", "45", "37", "47", "39", "49", "50", "60", "52", "62", "54", "64", "56", "66", "58", "68", "51", "61", "53", "63", "55", "65", "57", "67" ]
[ "nonn", "base" ]
23
0
3
[ "A227870", "A352546", "A352547", "A352760", "A355504" ]
null
Rémy Sigrist, Jul 05 2022
2022-07-09T12:14:31
oeisdata/seq/A355/A355504.seq
31bc8a0a6e5b073cf5cadae715d325d5
A355505
a(n) is the number of distinct cycles when iterating the function f_n(x), where f_n(x) is the sum of the digits in base n of x^2.
[ "2", "5", "3", "4", "4", "7", "4", "3", "4", "6", "4", "7", "4", "8", "6", "3", "3", "7", "5", "7", "9", "7", "4", "6", "4", "7", "5", "9", "5", "12", "7", "3", "9", "5", "8", "9", "5", "10", "9", "6", "4", "16", "8", "9", "8", "7", "5", "7", "9", "7", "7", "8", "4", "9", "8", "8", "11", "9", "4", "14", "7", "13", "11", "3", "8", "16", "7", "6", "9", "16", "8", "8", "5", "9", "9", "11", "13", "17", "7", "6", "6", "7", "5", "17", "6", "15", "11", "9", "4" ]
[ "base", "nonn" ]
57
2
1
[ "A004159", "A061903", "A159918", "A355505" ]
null
Wouter Zandsteeg, Jul 04 2022
2022-07-12T08:28:36
oeisdata/seq/A355/A355505.seq
57122b3b5ce0ff6dac9cf96ea1b9af96
A355506
a(n) is the least positive integer not occurring earlier in the sequence such that, if a(m) = a(n)+1, then |m - n| >= a(n).
[ "1", "2", "4", "6", "8", "3", "10", "12", "5", "14", "16", "7", "18", "20", "22", "9", "24", "26", "11", "28", "30", "32", "13", "34", "36", "15", "38", "40", "42", "17", "44", "46", "19", "48", "50", "21", "52", "54", "56", "23", "58", "60", "25", "62", "64", "66", "27", "68", "70", "29", "72", "74", "31", "76", "78", "80", "33", "82", "84", "35", "86", "88", "90", "37", "92", "94", "39", "96", "98", "41", "100", "102", "104", "43", "106" ]
[ "nonn" ]
28
1
2
[ "A136119", "A184119", "A353592", "A355506" ]
null
Ali Sada, Jul 04 2022
2025-05-09T02:58:57
oeisdata/seq/A355/A355506.seq
7d5cc27cbf03c9eb0e10b3082ed47852
A355507
Expansion of e.g.f. (1 - x)^(-x^4/24).
[ "1", "0", "0", "0", "0", "5", "15", "70", "420", "3024", "28350", "272250", "2875950", "33333300", "420840420", "5763671550", "84799915200", "1334007397800", "22343877115560", "396971840865600", "7456250728017000", "147612122975772000", "3071792315894841000", "67030983483724953000", "1530448652869851191400" ]
[ "nonn" ]
28
0
6
[ "A351493", "A355507", "A355610" ]
null
Seiichi Manyama, Jul 09 2022
2022-07-21T02:09:39
oeisdata/seq/A355/A355507.seq
67f339799625ca7e37757d64d7c51e63
A355508
E.g.f. satisfies log(A(x)) = x^2 * (exp(x * A(x)) - 1) * A(x).
[ "1", "0", "0", "6", "12", "20", "1830", "15162", "82376", "3326472", "59467050", "678585710", "20553790092", "563969783676", "10776243950654", "318310813941330", "10988438698692240", "303144002003606672", "9910024990673571666", "392381835437286982998", "14072003919511407720020" ]
[ "nonn" ]
40
0
4
[ "A349557", "A355508", "A356785", "A356892", "A356962" ]
null
Seiichi Manyama, Sep 07 2022
2022-09-12T03:05:03
oeisdata/seq/A355/A355508.seq
76a118822511f1a83eb50c175b1cdd25
A355509
Peaceable coexisting armies of knights: a(n) is the maximum number m such that m white knights and m black knights can coexist on an n X n chessboard without attacking each other.
[ "0", "2", "3", "6", "10", "14", "18", "24", "32", "40", "50", "60", "72", "84", "98", "112", "128", "144", "162", "180", "200", "220", "242", "264", "288", "312", "338", "364", "392", "420", "450", "480", "512", "544", "578", "612", "648", "684", "722", "760", "800", "840", "882", "924", "968", "1012", "1058", "1104", "1152", "1200", "1250", "1300", "1352", "1404" ]
[ "nonn", "easy" ]
35
1
2
[ "A002620", "A007590", "A052928", "A176222", "A250000", "A355509" ]
null
Aaron Khan, Jul 04 2022
2022-07-16T07:12:45
oeisdata/seq/A355/A355509.seq
32451b8012fb56485e0e0bcad0d94485
A355510
a(n) is the number of monic polynomials of degree n over GF(7) without linear factors.
[ "0", "0", "21", "112", "819", "5712", "39991", "279936", "1959552", "13716864", "96018048", "672126336", "4704884352", "32934190464", "230539333248", "1613775332736", "11296427329152", "79074991304064", "553524939128448", "3874674573899136", "27122722017293952" ]
[ "nonn", "easy" ]
36
0
3
null
null
Greyson C. Wesley, Jul 04 2022
2022-10-29T11:12:42
oeisdata/seq/A355/A355510.seq
c981246e6bb05b5feb23843194a0bc24
A355511
a(n) is the number of monic polynomials of degree n over GF(11) without linear factors.
[ "0", "0", "55", "440", "5170", "56408", "620950", "6830120", "75131485", "826446280", "9090909091", "100000000000", "1100000000000", "12100000000000", "133100000000000", "1464100000000000", "16105100000000000", "177156100000000000", "1948717100000000000", "21435888100000000000", "235794769100000000000" ]
[ "nonn" ]
14
0
3
[ "A355510", "A355511" ]
null
Greyson C. Wesley, Jul 04 2022
2022-09-07T11:12:16
oeisdata/seq/A355/A355511.seq
34eeb047cd3618927e109890fdc04680
A355512
Sum of numerator and denominator in the convergents of the approximation of log(2)/log(3) by a continued fraction.
[ "2", "3", "5", "13", "31", "106", "137", "791", "1719", "40328", "82375", "205078", "287453", "492531", "27376658", "27869189", "138853414", "444429431", "583282845", "1027712276", "15998966985", "17026679261", "169239080334", "355504839929", "1946763279979", "13982847799782", "15929611079761", "29912458879543", "135579446597933" ]
[ "nonn" ]
16
1
1
[ "A005663", "A005664", "A102525", "A355512", "A355513", "A355514", "A355515" ]
null
Hugo Pfoertner, Jul 05 2022
2024-08-02T11:50:49
oeisdata/seq/A355/A355512.seq
5b6ac672dbb6510298385d9f10120936
A355513
Sum of numerator and denominator in a rational approximation j/k of q = log(2)/log(3), such that abs(j/k - q) is a new minimum.
[ "2", "3", "5", "8", "13", "18", "31", "75", "106", "137", "517", "654", "791", "928", "1719", "21419", "23138", "24857", "26576", "28295", "30014", "31733", "33452", "35171", "36890", "38609", "40328", "82375", "205078", "287453", "492531", "14078321", "14570852", "15063383", "15555914", "16048445", "16540976", "17033507", "17526038", "18018569" ]
[ "nonn" ]
7
1
1
[ "A102525", "A355512", "A355513", "A355514", "A355515" ]
null
Hugo Pfoertner, Jul 05 2022
2022-07-05T10:35:12
oeisdata/seq/A355/A355513.seq
1388557411ff42559d13d860dda90af2
A355514
Sum of numerator and denominator in a rational approximation j/k of q = log(2)/log(3), such that q - j/k is a new minimum, i.e., q is approximated from below.
[ "1", "3", "8", "13", "44", "75", "106", "243", "380", "517", "654", "791", "2510", "4229", "5948", "7667", "9386", "11105", "12824", "14543", "16262", "17981", "19700", "21419", "23138", "24857", "26576", "28295", "30014", "31733", "33452", "35171", "36890", "38609", "40328", "122703", "205078", "492531", "27869189", "166722603", "305576017" ]
[ "nonn" ]
7
1
2
[ "A102525", "A355240", "A355512", "A355513", "A355514", "A355515" ]
null
Hugo Pfoertner, Jul 05 2022
2022-07-05T10:34:55
oeisdata/seq/A355/A355514.seq
032a269482132f18768d68f462b3ca72
A355515
Sum of numerator and denominator in a rational approximation j/k of q = log(2)/log(3), such that j/k - q is a new minimum, i.e., q is approximated from above.
[ "2", "5", "18", "31", "137", "928", "1719", "42047", "82375", "287453", "779984", "1272515", "1765046", "2257577", "2750108", "3242639", "3735170", "4227701", "4720232", "5212763", "5705294", "6197825", "6690356", "7182887", "7675418", "8167949", "8660480", "9153011", "9645542", "10138073", "10630604", "11123135", "11615666", "12108197" ]
[ "nonn" ]
7
1
1
[ "A102525", "A355512", "A355513", "A355514", "A355515" ]
null
Hugo Pfoertner, Jul 05 2022
2022-07-05T10:34:41
oeisdata/seq/A355/A355515.seq
8e66502f46497cd44b8a7decc0e5d332
A355516
a(n) is the number of distinct integer values of Product_{k=1..n} (2 + 1/t_k) with integers t_k > 1.
[ "1", "2", "5", "11", "29", "70", "164", "392", "933" ]
[ "nonn", "hard", "more" ]
7
2
2
[ "A355243", "A355516", "A355626", "A355628" ]
null
Hugo Pfoertner and Markus Sigg, Jul 16 2022
2024-12-22T10:52:43
oeisdata/seq/A355/A355516.seq
d72601739a8e9bc1e2ddf71938767df8
A355517
Number of nonisomorphic systems enumerated by A334254; that is, the number of inequivalent closure operators on a set of n elements where all singletons are closed.
[ "1", "2", "1", "4", "50", "7443", "95239971" ]
[ "nonn", "hard", "more" ]
8
0
2
[ "A102896", "A193674", "A326960", "A326961", "A326979", "A334254", "A334255", "A355517" ]
null
Dmitry I. Ignatov, Jul 05 2022
2025-02-16T08:34:03
oeisdata/seq/A355/A355517.seq
0c824aacd15bf2aaab0e0dcacbd7a0c5
A355518
Primes that cannot be represented as 2*p - q where p, q and 2*p^2 - q^2 are prime.
[ "2", "3", "5", "13", "17", "37", "61", "137" ]
[ "nonn" ]
8
1
1
[ "A355518", "A355521" ]
null
J. M. Bergot and Robert Israel, Jul 05 2022
2022-07-18T19:37:47
oeisdata/seq/A355/A355518.seq
bacfb177437f757edeb5a6ca8b99d3a1
A355519
Number of valid brackets in an n-round tournament.
[ "1", "2", "5", "19", "123", "1457", "32924", "1452015", "126487061", "21898598245", "7558601003617", "5209629536999054", "7175576970776253311", "19758953061561609438197", "108796404018098314291373545", "1197986411771818785507163602609", "26381385902615283298043180284145933" ]
[ "nonn" ]
48
0
2
[ "A000108", "A107354", "A355519" ]
null
John P. D'Angelo, Jul 05 2022
2025-07-01T08:48:46
oeisdata/seq/A355/A355519.seq
9aac155c92964a98f1eb25bf729df68c
A355520
Number of length-n binary strings having a string attractor of size at most 2.
[ "2", "4", "8", "16", "32", "62", "116", "206", "350", "566", "886", "1334", "1974", "2846", "3978", "5472", "7398", "9854", "12964", "16804", "21524" ]
[ "nonn", "more" ]
27
1
1
[ "A339391", "A339668", "A355520" ]
null
Jeffrey Shallit, Jul 05 2022
2023-01-14T10:50:03
oeisdata/seq/A355/A355520.seq
dd60885740c24b226056d21a47fe33bb
A355521
Primes that cannot be represented as 2*p+q where p, q and (2*p^2+q^2)/3 are prime.
[ "2", "3", "5", "7", "13", "31", "37", "97", "211", "271" ]
[ "nonn" ]
4
1
1
[ "A355518", "A355521" ]
null
J. M. Bergot and Robert Israel, Jul 05 2022
2022-07-13T07:20:10
oeisdata/seq/A355/A355521.seq
ee9e89384f1b5b34207318b582a3de41
A355522
Triangle read by rows where T(n,k) is the number of reversed integer partitions of n with maximal difference k, if singletons have maximal difference 0.
[ "2", "2", "1", "3", "1", "1", "2", "3", "1", "1", "4", "3", "2", "1", "1", "2", "6", "3", "2", "1", "1", "4", "6", "6", "2", "2", "1", "1", "3", "10", "6", "5", "2", "2", "1", "1", "4", "11", "11", "6", "4", "2", "2", "1", "1", "2", "16", "13", "10", "5", "4", "2", "2", "1", "1", "6", "17", "19", "12", "9", "4", "4", "2", "2", "1", "1", "2", "24", "24", "18", "11", "8", "4", "4", "2", "2", "1", "1" ]
[ "nonn", "tabl" ]
10
2
1
[ "A000005", "A000041", "A001522", "A056239", "A064428", "A091602", "A115720", "A115994", "A179254", "A238352", "A238353", "A238354", "A238710", "A239455", "A279945", "A286469", "A286470", "A325404", "A352827", "A355522", "A355524", "A355526", "A355532" ]
null
Gus Wiseman, Jul 08 2022
2022-07-14T09:34:50
oeisdata/seq/A355/A355522.seq
a288923562a8eabee6811e97546b3f08
A355523
Number of distinct differences between adjacent prime indices of n.
[ "0", "0", "0", "1", "0", "1", "0", "1", "1", "1", "0", "2", "0", "1", "1", "1", "0", "2", "0", "2", "1", "1", "0", "2", "1", "1", "1", "2", "0", "1", "0", "1", "1", "1", "1", "2", "0", "1", "1", "2", "0", "2", "0", "2", "2", "1", "0", "2", "1", "2", "1", "2", "0", "2", "1", "2", "1", "1", "0", "2", "0", "1", "2", "1", "1", "2", "0", "2", "1", "2", "0", "2", "0", "1", "2", "2", "1", "2", "0", "2", "1", "1", "0", "3", "1", "1", "1", "2", "0", "2", "1", "2", "1", "1", "1", "2", "0", "2", "2", "2", "0", "2", "0", "2", "1" ]
[ "nonn" ]
18
1
12
[ "A001222", "A008578", "A056239", "A066312", "A238353", "A238710", "A252736", "A279945", "A286469", "A286470", "A287352", "A320348", "A325388", "A325406", "A351294", "A352827", "A355523", "A355524", "A355525", "A355533", "A355534", "A355536" ]
null
Gus Wiseman, Jul 10 2022
2025-01-20T10:21:28
oeisdata/seq/A355/A355523.seq
9d8425d63d679556cf387cc1ba34db87
A355524
Minimal difference between adjacent prime indices of n > 1, or 0 if n is prime.
[ "0", "0", "0", "0", "1", "0", "0", "0", "2", "0", "0", "0", "3", "1", "0", "0", "0", "0", "0", "2", "4", "0", "0", "0", "5", "0", "0", "0", "1", "0", "0", "3", "6", "1", "0", "0", "7", "4", "0", "0", "1", "0", "0", "0", "8", "0", "0", "0", "0", "5", "0", "0", "0", "2", "0", "6", "9", "0", "0", "0", "10", "0", "0", "3", "1", "0", "0", "7", "1", "0", "0", "0", "11", "0", "0", "1", "1", "0", "0", "0", "12", "0", "0", "4", "13", "8" ]
[ "nonn" ]
6
2
9
[ "A000005", "A056239", "A066312", "A077017", "A115720", "A115994", "A120944", "A130091", "A238353", "A238354", "A238710", "A286469", "A286470", "A287352", "A325161", "A351294", "A352822", "A355524", "A355525", "A355526", "A355527", "A355528", "A355530", "A355531", "A355532", "A355533", "A355534", "A355536" ]
null
Gus Wiseman, Jul 10 2022
2022-07-11T08:33:35
oeisdata/seq/A355/A355524.seq
b7c16a1debd97b63a8abd917d545bb2f
A355525
Minimal difference between adjacent prime indices of n, or k if n is the k-th prime.
[ "1", "2", "0", "3", "1", "4", "0", "0", "2", "5", "0", "6", "3", "1", "0", "7", "0", "8", "0", "2", "4", "9", "0", "0", "5", "0", "0", "10", "1", "11", "0", "3", "6", "1", "0", "12", "7", "4", "0", "13", "1", "14", "0", "0", "8", "15", "0", "0", "0", "5", "0", "16", "0", "2", "0", "6", "9", "17", "0", "18", "10", "0", "0", "3", "1", "19", "0", "7", "1", "20", "0", "21", "11", "0", "0", "1", "1", "22", "0", "0", "12" ]
[ "nonn" ]
8
2
2
[ "A000040", "A001522", "A013929", "A056239", "A066312", "A120944", "A130091", "A238352", "A238353", "A238709", "A279945", "A286469", "A286470", "A287352", "A325160", "A325161", "A325351", "A325352", "A351294", "A352822", "A352827", "A355524", "A355525", "A355526", "A355527", "A355528", "A355530", "A355531", "A355532", "A355533", "A355534", "A355536" ]
null
Gus Wiseman, Jul 10 2022
2022-07-11T08:33:43
oeisdata/seq/A355/A355525.seq
8975cb479ff3f94364da1e7726622f10
A355526
Maximal difference between adjacent prime indices of n, or k if n is the k-th prime.
[ "1", "2", "0", "3", "1", "4", "0", "0", "2", "5", "1", "6", "3", "1", "0", "7", "1", "8", "2", "2", "4", "9", "1", "0", "5", "0", "3", "10", "1", "11", "0", "3", "6", "1", "1", "12", "7", "4", "2", "13", "2", "14", "4", "1", "8", "15", "1", "0", "2", "5", "5", "16", "1", "2", "3", "6", "9", "17", "1", "18", "10", "2", "0", "3", "3", "19", "6", "7", "2", "20", "1", "21", "11", "1", "7", "1", "4", "22", "2", "0", "12" ]
[ "nonn" ]
7
2
2
[ "A000005", "A000040", "A001522", "A013929", "A025475", "A047966", "A056239", "A066312", "A091602", "A238353", "A238709", "A238710", "A279945", "A286469", "A286470", "A287352", "A325160", "A325161", "A351294", "A352822", "A352827", "A355524", "A355525", "A355526", "A355527", "A355528", "A355530", "A355532", "A355533", "A355534", "A355536" ]
null
Gus Wiseman, Jul 10 2022
2022-07-11T08:33:48
oeisdata/seq/A355/A355526.seq
c9e76357f59dc13eee1484491cd2a566
A355527
Squarefree numbers having at least one pair of consecutive prime factors. Numbers n such that the minimal difference between adjacent prime indices of n is 1.
[ "6", "15", "30", "35", "42", "66", "70", "77", "78", "102", "105", "114", "138", "143", "154", "165", "174", "186", "195", "210", "221", "222", "231", "246", "255", "258", "282", "285", "286", "318", "323", "330", "345", "354", "366", "385", "390", "402", "426", "429", "435", "437", "438", "442", "455", "462", "465", "474", "498", "510", "534", "546", "555", "570" ]
[ "nonn" ]
9
1
1
[ "A000005", "A000040", "A001522", "A005117", "A013929", "A055932", "A056239", "A066312", "A120944", "A130091", "A238353", "A238354", "A286470", "A287352", "A325160", "A325161", "A352822", "A352827", "A355524", "A355525", "A355526", "A355527", "A355530", "A355531", "A355533", "A355534", "A355536" ]
null
Gus Wiseman, Jul 10 2022
2022-07-13T20:37:00
oeisdata/seq/A355/A355527.seq
144adf3c8c612db2c90b89e1d1877742
A355528
Minimal difference between adjacent 0-prepended prime indices of n > 1.
[ "1", "2", "0", "3", "1", "4", "0", "0", "1", "5", "0", "6", "1", "1", "0", "7", "0", "8", "0", "2", "1", "9", "0", "0", "1", "0", "0", "10", "1", "11", "0", "2", "1", "1", "0", "12", "1", "2", "0", "13", "1", "14", "0", "0", "1", "15", "0", "0", "0", "2", "0", "16", "0", "2", "0", "2", "1", "17", "0", "18", "1", "0", "0", "3", "1", "19", "0", "2", "1", "20", "0", "21", "1", "0", "0", "1", "1", "22", "0", "0", "1", "23" ]
[ "nonn" ]
9
2
2
[ "A000040", "A001522", "A005117", "A013929", "A056239", "A064428", "A066312", "A091602", "A112798", "A120944", "A238353", "A238354", "A286469", "A286470", "A287352", "A325161", "A352822", "A352827", "A355524", "A355525", "A355526", "A355527", "A355528", "A355530", "A355531", "A355532", "A355533", "A355534", "A355536" ]
null
Gus Wiseman, Jul 10 2022
2022-07-13T20:37:09
oeisdata/seq/A355/A355528.seq
296969367fe30f3572325bc2ba0e6b35
A355529
Numbers of which it is not possible to choose a different prime factor of each prime index (with multiplicity).
[ "2", "4", "6", "8", "9", "10", "12", "14", "16", "18", "20", "21", "22", "24", "25", "26", "27", "28", "30", "32", "34", "36", "38", "40", "42", "44", "45", "46", "48", "49", "50", "52", "54", "56", "57", "58", "60", "62", "63", "64", "66", "68", "70", "72", "74", "75", "76", "78", "80", "81", "82", "84", "86", "88", "90", "92", "94", "96", "98", "99", "100", "102", "104", "105", "106" ]
[ "nonn" ]
8
1
1
[ "A000720", "A001221", "A001222", "A001414", "A003963", "A056239", "A076610", "A112798", "A120383", "A318979", "A324850", "A335433", "A335448", "A355529", "A355535", "A355731", "A355732", "A355733", "A355739", "A355740", "A355741", "A355744", "A355745" ]
null
Gus Wiseman, Jul 24 2022
2022-07-24T14:13:39
oeisdata/seq/A355/A355529.seq
4a1f02bb91e18afa000b0a64fa02e66f
A355530
Squarefree numbers that are either even or have at least one pair of consecutive prime factors. Numbers n such that the minimal difference between adjacent 0-prepended prime indices of n is 1.
[ "2", "6", "10", "14", "15", "22", "26", "30", "34", "35", "38", "42", "46", "58", "62", "66", "70", "74", "77", "78", "82", "86", "94", "102", "105", "106", "110", "114", "118", "122", "130", "134", "138", "142", "143", "146", "154", "158", "165", "166", "170", "174", "178", "182", "186", "190", "194", "195", "202", "206", "210", "214", "218", "221", "222", "226", "230" ]
[ "nonn" ]
9
1
1
[ "A000005", "A000040", "A001522", "A005117", "A013929", "A055932", "A056239", "A066312", "A120944", "A238352", "A238354", "A279945", "A286469", "A286470", "A287352", "A325160", "A325161", "A352822", "A352827", "A355524", "A355525", "A355526", "A355527", "A355530", "A355531", "A355533", "A355534", "A355536" ]
null
Gus Wiseman, Jul 10 2022
2022-07-13T20:37:13
oeisdata/seq/A355/A355530.seq
7ee82329f3e64ae3929341d7bf25fdc4
A355531
Minimal augmented difference between adjacent reversed prime indices of n; a(1) = 0.
[ "0", "1", "2", "1", "3", "1", "4", "1", "1", "1", "5", "1", "6", "1", "2", "1", "7", "1", "8", "1", "2", "1", "9", "1", "1", "1", "1", "1", "10", "1", "11", "1", "2", "1", "2", "1", "12", "1", "2", "1", "13", "1", "14", "1", "1", "1", "15", "1", "1", "1", "2", "1", "16", "1", "3", "1", "2", "1", "17", "1", "18", "1", "1", "1", "3", "1", "19", "1", "2", "1", "20", "1", "21", "1", "1", "1", "2", "1", "22", "1", "1", "1" ]
[ "nonn" ]
10
1
3
[ "A001222", "A008578", "A013929", "A056239", "A112798", "A124010", "A129654", "A243055", "A243056", "A286470", "A307824", "A325351", "A325366", "A325394", "A355524", "A355525", "A355526", "A355528", "A355531", "A355533", "A355534", "A355535", "A355536" ]
null
Gus Wiseman, Jul 14 2022
2022-07-14T17:23:18
oeisdata/seq/A355/A355531.seq
b23ee4c8ef5de13c43c8969bdf64bae7
A355532
Maximal augmented difference between adjacent reversed prime indices of n; a(1) = 0.
[ "0", "1", "2", "1", "3", "2", "4", "1", "2", "3", "5", "2", "6", "4", "2", "1", "7", "2", "8", "3", "3", "5", "9", "2", "3", "6", "2", "4", "10", "2", "11", "1", "4", "7", "3", "2", "12", "8", "5", "3", "13", "3", "14", "5", "2", "9", "15", "2", "4", "3", "6", "6", "16", "2", "3", "4", "7", "10", "17", "2", "18", "11", "3", "1", "4", "4", "19", "7", "8", "3", "20", "2", "21", "12", "2", "8", "4", "5", "22", "3", "2" ]
[ "nonn" ]
8
1
3
[ "A000079", "A001221", "A001222", "A008578", "A056239", "A065119", "A066312", "A112798", "A124010", "A129654", "A243055", "A243056", "A286470", "A307824", "A325351", "A325366", "A325394", "A355524", "A355525", "A355526", "A355531", "A355532", "A355533", "A355534", "A355536" ]
null
Gus Wiseman, Jul 14 2022
2022-07-14T17:23:23
oeisdata/seq/A355/A355532.seq
dfe08b48043780ad5365fdb312a9ee13
A355533
Irregular triangle read by rows where row n lists the differences between adjacent prime indices of n; if n is prime(k), then row n is just (k).
[ "1", "2", "0", "3", "1", "4", "0", "0", "0", "2", "5", "0", "1", "6", "3", "1", "0", "0", "0", "7", "1", "0", "8", "0", "2", "2", "4", "9", "0", "0", "1", "0", "5", "0", "0", "0", "3", "10", "1", "1", "11", "0", "0", "0", "0", "3", "6", "1", "0", "1", "0", "12", "7", "4", "0", "0", "2", "13", "1", "2", "14", "0", "4", "0", "1", "8", "15", "0", "0", "0", "1", "0", "2", "0" ]
[ "nonn", "tabf" ]
13
2
2
[ "A001222", "A056239", "A066312", "A112798", "A124010", "A243056", "A286469", "A286470", "A287352", "A325160", "A325328", "A325351", "A325352", "A325368", "A325390", "A355523", "A355524", "A355525", "A355526", "A355531", "A355533", "A355534", "A355535", "A355536" ]
null
Gus Wiseman, Jul 12 2022
2022-07-14T17:23:27
oeisdata/seq/A355/A355533.seq
5d49bcc9f19170074013fd9843a2a0b2
A355534
Irregular triangle read by rows where row n lists the augmented differences of the reversed prime indices of n.
[ "1", "2", "1", "1", "3", "2", "1", "4", "1", "1", "1", "1", "2", "3", "1", "5", "2", "1", "1", "6", "4", "1", "2", "2", "1", "1", "1", "1", "7", "1", "2", "1", "8", "3", "1", "1", "3", "2", "5", "1", "9", "2", "1", "1", "1", "1", "3", "6", "1", "1", "1", "2", "4", "1", "1", "10", "2", "2", "1", "11", "1", "1", "1", "1", "1", "4", "2", "7", "1", "2", "3", "1", "2", "1", "1", "12", "8", "1", "5", "2", "3", "1", "1", "1" ]
[ "nonn", "tabf" ]
9
2
2
[ "A001222", "A056239", "A066312", "A091602", "A112798", "A124010", "A129654", "A243055", "A243056", "A252464", "A286470", "A287352", "A307824", "A325351", "A325352", "A325366", "A325394", "A355523", "A355524", "A355525", "A355526", "A355528", "A355531", "A355533", "A355534", "A355535", "A355536" ]
null
Gus Wiseman, Jul 12 2022
2022-07-14T17:23:31
oeisdata/seq/A355/A355534.seq
742eb7c52ff621c2982d3b735b702895
A355535
Odd numbers of which it is not possible to choose a different prime factor of each prime index.
[ "9", "21", "25", "27", "45", "49", "57", "63", "75", "81", "99", "105", "115", "117", "121", "125", "133", "135", "147", "153", "159", "171", "175", "189", "195", "207", "225", "231", "243", "245", "261", "273", "275", "279", "285", "289", "297", "315", "325", "333", "343", "345", "351", "357", "361", "363", "369", "371", "375", "387", "393", "399", "405", "423" ]
[ "nonn" ]
8
1
1
[ "A000720", "A001221", "A001222", "A001414", "A003963", "A056239", "A076610", "A112798", "A120383", "A289509", "A302796", "A327486", "A355529", "A355535", "A355731", "A355733", "A355739", "A355740", "A355741", "A355742", "A355744" ]
null
Gus Wiseman, Jul 22 2022
2022-07-24T14:13:43
oeisdata/seq/A355/A355535.seq
ec4259542941da23805192c5ea18f93c
A355536
Irregular triangle read by rows where row n lists the differences between adjacent prime indices of n; if n is prime, row n is empty.
[ "0", "1", "0", "0", "0", "2", "0", "1", "3", "1", "0", "0", "0", "1", "0", "0", "2", "2", "4", "0", "0", "1", "0", "5", "0", "0", "0", "3", "1", "1", "0", "0", "0", "0", "3", "6", "1", "0", "1", "0", "7", "4", "0", "0", "2", "1", "2", "0", "4", "0", "1", "8", "0", "0", "0", "1", "0", "2", "0", "5", "0", "5", "1", "0", "0", "2", "0", "0", "3", "6", "9", "0", "1", "1", "10", "0", "2", "0", "0", "0", "0", "0", "3", "1", "3", "0", "6" ]
[ "nonn", "tabf" ]
15
2
6
[ "A001222", "A056239", "A066312", "A112798", "A124010", "A129654", "A243055", "A243056", "A286470", "A287352", "A325328", "A325352", "A325368", "A325394", "A355523", "A355524", "A355526", "A355528", "A355531", "A355534", "A355536", "A358169" ]
null
Gus Wiseman, Jul 12 2022
2022-11-04T19:24:27
oeisdata/seq/A355/A355536.seq
6f00b3085ec4997b9fcb1a27ecb2df05
A355537
Number of ways to choose a sequence of prime factors, one of each integer from 2 to n.
[ "1", "1", "1", "1", "1", "2", "2", "2", "2", "4", "4", "8", "8", "16", "32", "32", "32", "64", "64", "128", "256", "512", "512", "1024", "1024", "2048", "2048", "4096", "4096", "12288", "12288", "12288", "24576", "49152", "98304", "196608", "196608", "393216", "786432", "1572864", "1572864", "4718592", "4718592", "9437184", "18874368", "37748736" ]
[ "nonn" ]
5
1
6
[ "A000005", "A000040", "A000096", "A000142", "A000720", "A001221", "A001222", "A001414", "A002110", "A003963", "A013939", "A056239", "A066843", "A070826", "A076610", "A112798", "A131818", "A327486", "A355537", "A355538", "A355731", "A355733", "A355741", "A355744", "A355745", "A355746", "A355747" ]
null
Gus Wiseman, Jul 20 2022
2022-07-21T07:40:35
oeisdata/seq/A355/A355537.seq
ee1514d52d0d63d3390009aec057b73d
A355538
Partial sum of A001221 (number of distinct prime factors) minus 1, ranging from 2 to n.
[ "0", "0", "0", "0", "0", "1", "1", "1", "1", "2", "2", "3", "3", "4", "5", "5", "5", "6", "6", "7", "8", "9", "9", "10", "10", "11", "11", "12", "12", "14", "14", "14", "15", "16", "17", "18", "18", "19", "20", "21", "21", "23", "23", "24", "25", "26", "26", "27", "27", "28", "29", "30", "30", "31", "32", "33", "34", "35", "35", "37", "37", "38", "39", "39", "40", "42", "42", "43", "44", "46", "46" ]
[ "nonn" ]
9
1
10
[ "A000005", "A000096", "A000142", "A000720", "A001221", "A001222", "A001414", "A002110", "A002541", "A003963", "A006218", "A013939", "A022559", "A056239", "A066843", "A070826", "A076610", "A077597", "A112798", "A131818", "A297155", "A305054", "A327486", "A355537", "A355538", "A355731", "A355733", "A355741", "A355744", "A355745", "A355746", "A355747" ]
null
Gus Wiseman, Jul 23 2022
2024-07-07T19:12:53
oeisdata/seq/A355/A355538.seq
8cd669f4e5631b8ba23ba1538dddcb67
A355539
a(1) = 1; for n >= 2, a(n) is the earliest occurrence k of the next distinct pair {x(k), y(k)}, where x(k) and y(k) denote the count of zero digits in A355318(k) and A355317(k), respectively.
[ "1", "6", "19", "97", "103", "110", "2065", "2515", "3261", "25562" ]
[ "nonn", "base", "more" ]
12
1
2
[ "A355317", "A355318", "A355539" ]
null
Xiaofeng Wang, Jul 06 2022
2022-08-24T10:00:31
oeisdata/seq/A355/A355539.seq
1092a03b27dec8217843db7c3ac39715
A355540
Triangle read by rows. Row n gives the coefficients of Product_{k=0..n} (x - k!) expanded in decreasing powers of x, with row 0 = {1}.
[ "1", "1", "-1", "1", "-2", "1", "1", "-4", "5", "-2", "1", "-10", "29", "-32", "12", "1", "-34", "269", "-728", "780", "-288", "1", "-154", "4349", "-33008", "88140", "-93888", "34560", "1", "-874", "115229", "-3164288", "23853900", "-63554688", "67633920", "-24883200", "1", "-5914", "4520189", "-583918448", "15971865420", "-120287210688", "320383261440", "-340899840000", "125411328000" ]
[ "sign", "tabl" ]
49
0
5
[ "A000110", "A000178", "A000522", "A003422", "A008276", "A039758", "A136457", "A203227", "A217757", "A349226", "A355540" ]
null
Thomas Scheuerle, Jul 06 2022
2022-07-10T16:12:56
oeisdata/seq/A355/A355540.seq
d834ad1fba9f0ee8844453d49105e764
A355541
Numbers k such that A061201(k) is divisible by k.
[ "1", "2", "7", "31", "1393", "5012", "7649", "50235", "147296", "426606", "611769", "3491681", "9324642", "11815109", "53962364", "82680301", "96789197", "230882246", "378444764", "1489280093", "1489280606", "3651325650", "5891877914", "5891877947", "5891877966", "58604540872" ]
[ "nonn", "more" ]
4
1
2
[ "A007425", "A045345", "A048290", "A050226", "A056550", "A061201", "A064605", "A064606", "A064607", "A064610", "A064611", "A064612", "A355541" ]
null
Amiram Eldar, Jul 06 2022
2022-07-07T02:07:08
oeisdata/seq/A355/A355541.seq
a7dadca3adbc458b0c28c982a24a92c8
A355542
Numbers k such that A272718(k) is divisible by k.
[ "1", "2", "3", "11", "13", "50", "81", "96", "395", "640", "59136", "65719", "632621", "1342813", "2137073", "2755370", "3446370", "10860093", "321939569", "1872591111", "8858043355" ]
[ "nonn", "more" ]
4
1
2
[ "A018804", "A045345", "A048290", "A050226", "A056550", "A064605", "A064606", "A064607", "A064610", "A064611", "A064612", "A272718", "A355542" ]
null
Amiram Eldar, Jul 06 2022
2022-07-07T02:07:19
oeisdata/seq/A355/A355542.seq
e49d1c904d691a164dfd1937a9805dac
A355543
Numbers k such that the sum of the squares of the odd divisors of k (A050999) is divisible by k.
[ "1", "65", "130", "175", "260", "350", "525", "1050", "1105", "2100", "2210", "4420", "5425", "8840", "10850", "16275", "20737", "21700", "30225", "32045", "32550", "41474", "60450", "64090", "65100", "70525", "82948", "86025", "103685", "120900", "128180", "130200", "141050", "171275", "172050", "200725", "207370", "207553", "211575" ]
[ "nonn" ]
8
1
2
[ "A007691", "A046762", "A050999", "A355543" ]
null
Amiram Eldar, Jul 06 2022
2022-07-07T08:12:55
oeisdata/seq/A355/A355543.seq
b8ac50a8bb71da4804ef6cfc21b40da7
A355544
Numbers k such that the arithmetic mean of the first k squarefree numbers is an integer.
[ "1", "3", "6", "37", "75", "668", "1075", "37732", "742767", "1811865", "3140083", "8937770", "108268896", "282951249", "633932500", "1275584757", "60455590365" ]
[ "nonn", "more" ]
10
1
2
[ "A005117", "A045345", "A048290", "A050226", "A056550", "A064605", "A064606", "A064607", "A064610", "A064611", "A064612", "A173143", "A355544" ]
null
Amiram Eldar, Jul 06 2022
2022-07-07T02:07:43
oeisdata/seq/A355/A355544.seq
24532fc4b078410c68b5ab1691937234
A355545
Primes p that satisfy q^(p-1) == 1 (mod p^2), i.e., are base-q Wieferich primes, for a prime q dividing p-1.
[ "1093", "3511", "20771", "1006003", "1747591", "5395561", "53471161" ]
[ "nonn", "hard", "more" ]
7
1
1
[ "A355545", "A355546" ]
null
Felix Fröhlich, Jul 06 2022
2022-07-07T02:09:45
oeisdata/seq/A355/A355545.seq
cc55f3ff53c3cd0988dcd92581e51369
A355546
Primes p that satisfy q^(p-1) == 1 (mod p^2), i.e., are base-q Wieferich primes, for a prime q dividing p+1.
[ "11", "1093", "3511", "7195291", "11642831", "13703077", "112955593", "5857727461" ]
[ "nonn", "hard", "more" ]
10
1
1
[ "A355545", "A355546" ]
null
Felix Fröhlich, Jul 06 2022
2022-07-10T16:07:27
oeisdata/seq/A355/A355546.seq
fc322de1ebac413e28cf216754e84494
A355547
Numbers k such that x^2 - s*x + p has noninteger roots with s sum of digits of k and p product of digits of k.
[ "1", "2", "3", "5", "6", "7", "8", "9", "111", "112", "113", "114", "115", "116", "117", "118", "119", "121", "123", "124", "125", "126", "127", "128", "129", "131", "132", "133", "135", "136", "137", "138", "139", "141", "142", "144", "145", "147", "148", "149", "151", "152", "153", "154", "155", "156", "157", "159", "161", "162", "163", "165", "167", "168", "169", "171" ]
[ "nonn", "base" ]
17
1
2
[ "A007953", "A007954", "A052382", "A355497", "A355547" ]
null
Stefano Spezia and Jean-Marc Rebert, Jul 06 2022
2022-07-12T08:40:03
oeisdata/seq/A355/A355547.seq
edebf7b5c515bec01ea0ec6b37e5af8d
A355548
a(n) is the smallest number k such that k occurs in the Reverse-and-Add trajectories of exactly n positive integers less than k.
[ "0", "2", "4", "8", "16", "33", "55", "404", "44", "646", "99", "66", "848", "909", "888", "110", "88", "1090", "132", "176", "1089", "363", "3443", "10010", "121", "1881", "242", "1991", "4323", "3982", "1595", "726", "3553", "2992", "3663", "7447", "484", "1353", "46064", "6446", "5665", "10769", "3993", "2662", "4103", "2882", "968", "1111", "1837", "7667" ]
[ "nonn", "base" ]
9
0
2
[ "A298972", "A355548", "A355550" ]
null
Felix Fröhlich, Jul 06 2022
2022-07-07T05:03:16
oeisdata/seq/A355/A355548.seq
569c778a19fbd3e1c2e45208d8d5f9b7
A355549
Number of positive integers k with 1 < k < n such that n occurs in the Reverse-and-Multiply trajectory of k.
[ "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0" ]
[ "nonn", "base" ]
6
0
17
[ "A355549", "A355550" ]
null
Felix Fröhlich, Jul 06 2022
2022-07-07T02:10:18
oeisdata/seq/A355/A355549.seq
37d51dae81d877b38bde9eb1ad2799d9
A355550
a(n) is the smallest number k such that k occurs in the Reverse-and-Multiply trajectories of exactly n positive integers less than k.
[ "0", "4", "16", "1300", "976", "40300", "662704", "12251200" ]
[ "nonn", "base", "hard", "more" ]
9
0
2
[ "A355548", "A355549", "A355550" ]
null
Felix Fröhlich, Jul 06 2022
2022-07-07T05:03:22
oeisdata/seq/A355/A355550.seq
7998bf2f86443a096b320950e696996f
A355551
Number of ways to select 3 or more collinear points from a 3 X n grid.
[ "1", "2", "8", "23", "61", "144", "322", "689", "1439", "2954", "6004", "12123", "24385", "48932", "98054", "196325", "392899", "786078", "1572472", "3145295", "6290981", "12582392", "25165258", "50331033", "100662631", "201325874", "402652412", "805305539", "1610611849", "3221224524", "6442449934" ]
[ "nonn", "easy" ]
44
1
2
[ "A002662", "A355551", "A355552", "A355553" ]
null
Thomas Garrison, Jul 06 2022
2024-10-19T18:07:02
oeisdata/seq/A355/A355551.seq
bc1cee7f1d16d9861aa29156d0d5afab
A355552
Number of ways to select 3 or more collinear points from a 4 X n grid.
[ "5", "10", "23", "54", "117", "240", "497", "1006", "2027", "4074", "8169", "16356", "32741", "65506", "131039", "262110", "524253", "1048536", "2097113", "4194262", "8388563", "16777170", "33554385", "67108812", "134217677", "268435402", "536870855", "1073741766", "2147483589", "4294967232", "8589934529", "17179869118", "34359738299" ]
[ "nonn", "easy" ]
32
1
1
[ "A000982", "A355552", "A355553" ]
null
Thomas Garrison, Jul 14 2022
2023-01-17T04:35:14
oeisdata/seq/A355/A355552.seq
c0c8db578263a1eb0c78abc01e6db6ee
A355553
Number of ways to select 3 or more collinear points from an n X n grid.
[ "0", "0", "8", "54", "228", "708", "1980", "4890", "11528", "26004", "57384", "123786", "265596", "563664", "1192220", "2511474", "5279208", "11064216", "23156448", "48361110", "100859180", "209996772", "436635396", "906562842", "1879950384", "3893566872", "8054935784", "16645591974", "34363631412", "70872295524", "146036933100" ]
[ "nonn" ]
25
1
3
[ "A000982", "A355551", "A355552", "A355553" ]
null
Thomas Garrison, Jul 14 2022
2025-03-22T23:34:36
oeisdata/seq/A355/A355553.seq
451d47f8eb18b43f28ebf9d1e8042cde
A355554
Sexagesimal expansion of 180/Pi.
[ "57", "17", "44", "48", "22", "29", "22", "22", "7", "32", "46", "14", "58", "15", "20", "17", "32", "7", "4", "43", "35", "36", "12", "35", "9", "17", "4", "12", "9", "40", "27", "27", "26", "48", "25", "12", "52", "48", "52", "18", "21", "42", "13", "53", "32", "25", "44", "46", "54", "25", "56", "34", "21", "51", "6", "35", "33", "34", "49", "6", "43", "10", "36", "31", "50", "20", "31" ]
[ "nonn", "cons", "base" ]
26
1
1
[ "A000796", "A060707", "A072097", "A355554" ]
null
Carmine Suriano, Jan 17 2023
2023-02-03T20:51:52
oeisdata/seq/A355/A355554.seq
f477e36cc1dbd12ad831b2d1f47e3d75
A355555
a(n) is the first prime prime(j) such that prime(j) + prime(k) + prime(k+1) is prime for k = j+1..j+n but not k = j+n+1.
[ "2", "17", "5", "7", "53", "197", "848699", "2802313", "24281267", "54927644129", "29566753319" ]
[ "nonn", "more", "hard" ]
19
0
1
[ "A000040", "A355555" ]
null
J. M. Bergot and Robert Israel, Jul 06 2022
2022-07-13T07:20:27
oeisdata/seq/A355/A355555.seq
f30d54b03ecdb9cfe1d6b9dc49c4cb92
A355556
a(n) is the smallest position in the subtract-a-factorial game for which the value of the Sprague-Grundy function (or nim-value) is n.
[ "0", "1", "2", "6", "5050", "5056", "5064", "40520", "40696", "630373", "40348521", "483383076", "6302798387" ]
[ "nonn", "more" ]
9
0
3
[ "A014587", "A019307", "A297963", "A355556", "A355557" ]
null
Pontus von Brömssen, Jul 09 2022
2022-07-09T15:30:52
oeisdata/seq/A355/A355556.seq
73c111bc396a2186b5d89867eb736ce8
A355557
a(n) is the smallest position in the subtract-a-prime game for which the value of the Sprague-Grundy function (or nim-value) is n.
[ "0", "2", "4", "6", "8", "19", "21", "23", "43", "48", "67", "156" ]
[ "nonn", "more" ]
8
0
2
[ "A014589", "A019307", "A297963", "A355556", "A355557" ]
null
Pontus von Brömssen, Jul 09 2022
2024-04-09T15:07:36
oeisdata/seq/A355/A355557.seq
71d3429e003ce48988a5aafd3bf15487
A355558
The independence polynomial of the n-halved cube graph evaluated at -1.
[ "0", "-1", "-3", "-3", "25", "-135", "-2079", "1879969" ]
[ "sign", "more" ]
15
1
3
[ "A005864", "A288943", "A355226", "A355558" ]
null
Christopher Flippen, Jul 06 2022
2022-07-17T23:28:18
oeisdata/seq/A355/A355558.seq
d1f5b051d90432e74e0511c50d1dded9
A355559
The independence polynomial of the n-folded cube graph evaluated at -1.
[ "-1", "-3", "-1", "9", "131", "253", "25607" ]
[ "sign", "more" ]
20
2
2
[ "A058622", "A290888", "A355227", "A355559" ]
null
Christopher Flippen, Jul 06 2022
2022-10-13T13:08:02
oeisdata/seq/A355/A355559.seq
2b7a552d3e78c44ec12c0a2d6c032d27
A355560
Number of configurations of the 8 X 2 variant of the sliding block 15-puzzle that require a minimum of n moves to be reached, starting with the empty square in one of the corners.
[ "1", "2", "3", "6", "11", "20", "37", "68", "125", "227", "394", "672", "1151", "1983", "3373", "5703", "9508", "15640", "25293", "40732", "65032", "103390", "162830", "255543", "397013", "613104", "938477", "1431068", "2162964", "3255845", "4860428", "7223861", "10649867", "15628073", "22747718", "32963838", "47397514", "67825949", "96317070" ]
[ "nonn", "fini", "full" ]
16
0
2
[ "A090033", "A090034", "A090035", "A090036", "A090167", "A346736", "A355560" ]
null
Ben Whitmore, Jul 06 2022
2022-09-04T12:24:48
oeisdata/seq/A355/A355560.seq
80c1bb63ee4c7eb6aa8f77ff159ec3a1
A355561
Number of n-tuples (p_1, p_2, ..., p_n) of positive integers such that p_{i-1} <= p_i <= n^(i-1).
[ "1", "1", "2", "24", "3236", "7173370", "330736663032", "382149784071841422", "12983632019302863224103688", "14912674110246473369128526689667934", "654972005961623890774153743504185499487372010", "1228018869478731662593970252736815943512232438560622483276" ]
[ "nonn" ]
20
0
3
[ "A076113", "A090588", "A107354", "A355519", "A355561", "A355576" ]
null
Alois P. Heinz, Jul 06 2022
2022-07-08T19:06:05
oeisdata/seq/A355/A355561.seq
013475bed7f017b6df7d819dd20b576e
A355562
Number of blunt polypons with n cells.
[ "0", "1", "1", "2", "1", "5", "3", "10", "13", "31", "44", "103", "169", "360", "643", "1317", "2479", "5036", "9716", "19592", "38511", "77465", "153686", "309093", "617426", "1243392", "2496186", "5035612" ]
[ "nonn", "nice", "hard", "more" ]
8
1
4
[ "A057784", "A057785", "A355562" ]
null
Sean A. Irvine, Jul 06 2022
2022-07-07T02:04:47
oeisdata/seq/A355/A355562.seq
949fecaad75f3d034257df131f496126
A355563
a(n) is the number of numbers that divide the sum of the digits of their n-th powers.
[ "1", "9", "4", "9", "9", "7", "10", "14", "10", "12", "13", "10", "12", "19", "11", "15", "14", "15", "14", "16", "14", "13", "14", "12", "11", "23", "13", "11", "17", "15", "10", "16", "18", "18", "10", "13", "10", "17", "15", "16", "19", "12", "20", "19", "20", "17", "19", "21", "14", "27", "15", "18", "16", "16", "20", "10", "14", "20", "15", "11", "17", "23", "14", "15", "14", "19", "15" ]
[ "nonn", "base" ]
6
0
2
[ "A046019", "A355370", "A355563" ]
null
Mohammed Yaseen, Jul 07 2022
2022-07-14T17:25:33
oeisdata/seq/A355/A355563.seq
0cc3586d48fdd961209a9f03d000a562
A355564
Triangle read by rows: T(n,k) = n*(1+2*k) - k*(1+k), n >= 1, 0 <= k <= n-1.
[ "1", "2", "4", "3", "7", "9", "4", "10", "14", "16", "5", "13", "19", "23", "25", "6", "16", "24", "30", "34", "36", "7", "19", "29", "37", "43", "47", "49", "8", "22", "34", "44", "52", "58", "62", "64", "9", "25", "39", "51", "61", "69", "75", "79", "81", "10", "28", "44", "58", "70", "80", "88", "94", "98", "100", "11", "31", "49", "65", "79", "91", "101", "109", "115", "119", "121" ]
[ "nonn", "easy", "tabl" ]
12
1
2
[ "A095832", "A212012", "A355564" ]
null
Lucas B. Vieira, Jul 07 2022
2022-08-30T14:27:39
oeisdata/seq/A355/A355564.seq
c0190f84c17a1ab8eea091769c3a9801
A355565
T(j,k) are the numerators s in the representation R = s/t + (2/Pi)*u/v of the resistance between two nodes separated by the distance vector (j,k) in an infinite square lattice of one-ohm resistors, where T(j,k), j >= 0, 0 <= k <= j, is a triangle read by rows.
[ "0", "1", "0", "2", "-1", "0", "17", "-4", "1", "0", "40", "-49", "6", "-1", "0", "401", "-140", "97", "-8", "1", "0", "1042", "-1569", "336", "-161", "10", "-1", "0", "11073", "-4376", "4321", "-660", "241", "-12", "1", "0", "29856", "-48833", "13342", "-9681", "1144", "-337", "14", "-1", "0", "325441", "-136488", "160929", "-33188", "18929", "-1820", "449", "-16", "1", "0" ]
[ "tabl", "frac", "sign" ]
54
0
4
[ "A025547", "A025550", "A089165", "A131406", "A211074", "A280079", "A280317", "A355565", "A355566", "A355567", "A355585", "A355586", "A355587", "A355588", "A355953", "A355955", "A356201", "A356202" ]
null
Hugo Pfoertner, Jul 07 2022
2022-09-09T14:50:53
oeisdata/seq/A355/A355565.seq
29c88c78ee7f8c8956df5f1ee5c12d60
A355566
T(j,k) are the numerators u in the representation R = s/t + (2/Pi)*u/v of the resistance between two nodes separated by the distance vector (j,k) in an infinite square lattice of one-ohm resistors, where T(j,k), j >= 0, 0 <= k <= j, is a triangle read by rows.
[ "0", "0", "1", "-2", "2", "4", "-12", "23", "2", "23", "-184", "40", "-118", "12", "176", "-940", "3323", "-1118", "499", "20", "563", "-24526", "1234", "-18412", "13462", "-626", "118", "6508", "-130424", "721937", "-71230", "327143", "-1312", "14369", "262", "88069", "-4924064", "191776", "-6601046", "2395676", "-888568", "131972", "-300766", "1624", "91072" ]
[ "tabl", "frac", "sign" ]
21
0
4
[ "A131406", "A350669", "A355565", "A355566", "A355567" ]
null
Hugo Pfoertner, Jul 07 2022
2022-08-01T23:16:11
oeisdata/seq/A355/A355566.seq
e1ce509ad6da8a91c77120975ebe0aca
A355567
T(j,k) are the denominators v in the representation R = s/t + (2/Pi)*u/v of the resistance between two nodes separated by the distance vector (j,k) in an infinite square lattice of one-ohm resistors, where T(j,k), j >= 0, 0 <= k <= j, is a triangle read by rows.
[ "1", "1", "1", "1", "1", "3", "1", "3", "3", "15", "3", "1", "15", "5", "105", "3", "15", "15", "35", "21", "315", "15", "1", "35", "105", "45", "45", "3465", "15", "105", "21", "315", "7", "693", "231", "45045", "105", "5", "315", "315", "495", "495", "15015", "585", "45045", "7", "315", "45", "3465", "3465", "45045", "45045", "15015", "385", "765765", "315", "35", "3465", "495", "45045", "6435", "15015", "45045", "765765", "9945", "14549535" ]
[ "nonn", "tabl", "frac" ]
8
0
6
[ "A131406", "A350670", "A355565", "A355566", "A355567" ]
null
Hugo Pfoertner, Jul 07 2022
2022-08-01T23:16:29
oeisdata/seq/A355/A355567.seq
d9b2e8de6d2826d204c9c237381cbf24
A355568
Numbers k > 4 in a Collatz trajectory reaching k after starting at k-1.
[ "8", "10", "16", "20", "26", "34", "40", "52", "92", "122", "160", "167", "184", "244", "251", "334", "377", "412", "433", "488", "502", "650", "668", "866", "890", "976", "1154", "1186", "1300", "1336", "1732", "1780", "2308", "3644", "4858", "7288" ]
[ "nonn", "more" ]
18
1
1
[ "A006370", "A006577", "A070991", "A070993", "A355239", "A355240", "A355568", "A355569" ]
null
Hugo Pfoertner, Jul 10 2022
2022-10-14T08:54:59
oeisdata/seq/A355/A355568.seq
08c4179852ce8465dc34614f19a2674a
A355569
Numbers k > 4 in a Collatz trajectory reaching k after starting at k+1.
[ "5", "8", "10", "13", "16", "17", "38", "40", "46", "53", "56", "58", "61", "70", "80", "88", "106", "107", "160", "251", "283", "377", "638", "650", "958", "976", "1367", "1438", "1822", "2158", "2429", "2734", "3238", "4102", "4616", "4858", "6154", "7288", "9232" ]
[ "nonn", "more" ]
14
1
1
[ "A006370", "A006577", "A070991", "A070993", "A355239", "A355240", "A355568", "A355569" ]
null
Hugo Pfoertner, Jul 10 2022
2022-10-14T08:54:53
oeisdata/seq/A355/A355569.seq
c5d2606c5c6996d65c0f1638cd4bd37e
A355570
Regular triangle of certain polynomial expansion coefficients for the n-th power series.
[ "1", "0", "1", "1", "-2", "2", "0", "5", "-10", "6", "1", "-10", "40", "-54", "24", "0", "21", "-140", "336", "-336", "120", "1", "-42", "462", "-1764", "3024", "-2400", "720", "0", "85", "-1470", "8442", "-22176", "29520", "-19440", "5040", "1", "-170", "4580", "-38178", "144648", "-288000", "313200", "-176400", "40320", "0", "341", "-14080", "166452", "-875952", "2451240", "-3920400", "3603600", "-1774080", "362880" ]
[ "sign", "tabl" ]
15
2
5
[ "A000142", "A202365", "A355570" ]
null
Michel Marcus, Jul 07 2022
2022-08-24T08:51:14
oeisdata/seq/A355/A355570.seq
d0662d2083a09c00baadbe2db61fcf70
A355571
Complement of A007956: numbers not of the form P(k)/k where P(n) is the product of the divisors of n.
[ "4", "9", "12", "16", "18", "20", "24", "25", "28", "30", "32", "36", "40", "42", "44", "45", "48", "49", "50", "52", "54", "56", "60", "63", "66", "68", "70", "72", "75", "76", "78", "80", "81", "84", "88", "90", "92", "96", "98", "99", "100", "102", "104", "105", "108", "110", "112", "114", "116", "117", "120", "121", "124", "126", "128", "130", "132", "135", "136", "138", "140", "147", "148", "150", "152" ]
[ "nonn" ]
17
1
1
[ "A001248", "A007304", "A007956", "A030514", "A050997", "A052485", "A054753", "A065036", "A085986", "A106543", "A355571" ]
null
Luca Onnis, Jul 07 2022
2022-07-15T20:40:18
oeisdata/seq/A355/A355571.seq
e29bcc16614109f622aaf16f9fdd59c1
A355572
Largest LCM of partitions of n into odd parts.
[ "1", "1", "3", "3", "5", "5", "7", "15", "15", "21", "21", "35", "35", "45", "105", "105", "105", "105", "165", "165", "315", "315", "385", "385", "495", "1155", "1155", "1365", "1365", "1365", "1365", "3465", "3465", "4095", "4095", "5005", "5005", "6435", "15015", "15015", "15015", "15015", "19635", "19635", "45045", "45045", "45045", "45045", "58905", "58905", "69615", "69615" ]
[ "nonn" ]
16
1
3
[ "A000793", "A051593", "A159685", "A355572", "A355573" ]
null
Torsten Muetze, Jul 07 2022
2022-07-13T07:23:42
oeisdata/seq/A355/A355572.seq
b6a5113f0097eae2b3dd1a7b1fca5a73
A355573
Largest LCM of partitions of n with a nonzero even number of even parts.
[ "2", "2", "4", "6", "6", "12", "12", "20", "30", "30", "60", "60", "84", "84", "140", "210", "210", "420", "420", "420", "420", "840", "840", "1260", "1260", "1540", "2310", "2520", "4620", "4620", "5460", "5460", "9240", "9240", "13860", "13860", "16380", "16380", "27720", "30030", "32760", "60060", "60060", "60060", "60060", "120120", "120120", "180180", "180180", "180180", "180180" ]
[ "nonn" ]
14
4
1
[ "A000793", "A051593", "A159685", "A355572", "A355573" ]
null
Torsten Muetze, Jul 07 2022
2022-07-13T07:23:26
oeisdata/seq/A355/A355573.seq
1c6751e06622d1a4bbd3bd6f150df766
A355574
Number of nonnegative integers k with n digits such that x^2 - s*x + p has only integer roots, where s and p denote the sum and product of the digits of k respectively.
[ "2", "90", "223", "2686", "31601", "370894", "4220160", "46962379", "512600193" ]
[ "nonn", "base", "hard", "more" ]
20
1
1
[ "A007953", "A007954", "A063945", "A355497", "A355547", "A355574" ]
null
Stefano Spezia, Jul 07 2022
2025-02-26T08:54:33
oeisdata/seq/A355/A355574.seq
0c24e516da10a62758284438a71c7b28
A355575
a(n) = n! * Sum_{k=0..floor(n/3)} k^(n - 3*k)/k!.
[ "1", "0", "0", "6", "24", "120", "1080", "10080", "120960", "1874880", "34473600", "738460800", "17982518400", "489858969600", "14834839219200", "498452777222400", "18583796335104000", "768773914900992000", "35220800475250790400", "1779227869201400217600", "98469904378626772992000" ]
[ "nonn" ]
123
0
4
[ "A292889", "A345747", "A352945", "A354436", "A355575" ]
null
Seiichi Manyama, Sep 17 2022
2024-11-24T23:08:33
oeisdata/seq/A355/A355575.seq
c8f07a2be55fa81b8ad8c5edc65e4d24
A355576
Number A(n,k) of n-tuples (p_1, p_2, ..., p_n) of positive integers such that p_{i-1} <= p_i <= k^(i-1); square array A(n,k), n>=0, k>=0, read by antidiagonals.
[ "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "2", "1", "0", "1", "1", "3", "7", "1", "0", "1", "1", "4", "24", "44", "1", "0", "1", "1", "5", "58", "541", "516", "1", "0", "1", "1", "6", "115", "3236", "35649", "11622", "1", "0", "1", "1", "7", "201", "12885", "713727", "6979689", "512022", "1", "0", "1", "1", "8", "322", "39656", "7173370", "627642640", "4085743032", "44588536", "1", "0" ]
[ "nonn", "tabl" ]
27
0
13
[ "A000012", "A001477", "A081436", "A107354", "A109055", "A109056", "A109057", "A109058", "A109059", "A109060", "A109061", "A354608", "A355561", "A355576" ]
null
Alois P. Heinz, Jul 07 2022
2022-09-21T10:39:52
oeisdata/seq/A355/A355576.seq
656b0b024913bff6507b7ea5f575aa42
A355577
Primes p such that 5*p+6, 5*p+12, 5*p+18 and 5*p+24 are all primes.
[ "7", "11", "127", "347", "659", "1019", "2689", "4663", "4817", "5233", "8387", "13997", "18257", "19051", "19181", "23909", "24109", "28211", "34483", "38287", "39761", "41203", "44647", "45767", "51829", "57089", "64019", "70207", "72671", "73091", "96821", "100237", "101021", "101119", "102607", "102967", "104231", "120779", "121171", "126851", "127541", "130547", "135727" ]
[ "nonn" ]
10
1
1
null
null
J. M. Bergot and Robert Israel, Jul 08 2022
2022-07-13T13:18:19
oeisdata/seq/A355/A355577.seq
7b9a76d250f355072ae98db441014509
A355578
Numbers whose sum of 3-smooth divisors sets a new record.
[ "1", "2", "3", "4", "6", "8", "12", "16", "18", "24", "32", "36", "48", "64", "72", "96", "108", "144", "192", "216", "288", "324", "384", "432", "576", "648", "768", "864", "972", "1152", "1296", "1536", "1728", "1944", "2304", "2592", "2916", "3072", "3456", "3888", "4608", "5184", "5832", "6912", "7776", "8748", "9216", "10368", "11664", "13824", "15552", "17496" ]
[ "nonn" ]
18
1
2
[ "A000203", "A002093", "A003586", "A072079", "A309015", "A355578", "A355579" ]
null
Amiram Eldar, Jul 08 2022
2022-07-08T15:56:00
oeisdata/seq/A355/A355578.seq
61bc0e26507112b0c0c756b8f8af6c25
A355579
Numbers k such that A072079(k)/k sets a new record.
[ "1", "2", "4", "6", "12", "24", "36", "48", "72", "144", "288", "432", "864", "1728", "2592", "3456", "5184", "10368", "20736", "31104", "41472", "62208", "124416", "248832", "373248", "746496", "1492992", "2239488", "2985984", "4478976", "8957952", "17915904", "26873856", "53747712", "107495424", "161243136", "214990848", "322486272" ]
[ "nonn" ]
10
1
2
[ "A000203", "A003586", "A004394", "A072079", "A355578", "A355579" ]
null
Amiram Eldar, Jul 08 2022
2022-07-09T15:29:03
oeisdata/seq/A355/A355579.seq
bec9583cbb529ba9cfc843d045e9f1e6
A355580
Powerful 3-smooth numbers: numbers of the form 2^i * 3^j with i, j != 1.
[ "1", "4", "8", "9", "16", "27", "32", "36", "64", "72", "81", "108", "128", "144", "216", "243", "256", "288", "324", "432", "512", "576", "648", "729", "864", "972", "1024", "1152", "1296", "1728", "1944", "2048", "2187", "2304", "2592", "2916", "3456", "3888", "4096", "4608", "5184", "5832", "6561", "6912", "7776", "8192", "8748", "9216", "10368", "11664" ]
[ "nonn", "easy" ]
11
1
2
[ "A000244", "A001694", "A003586", "A007283", "A008776", "A151821", "A355580", "A355581" ]
null
Amiram Eldar, Jul 08 2022
2022-07-10T03:56:33
oeisdata/seq/A355/A355580.seq
51d4c16cdd1197f76a65b19c80aa5f60
A355581
Exponentially-odd 3-smooth numbers: number of the form 2^i * 3^j where i and j are either 0 or odd.
[ "1", "2", "3", "6", "8", "24", "27", "32", "54", "96", "128", "216", "243", "384", "486", "512", "864", "1536", "1944", "2048", "2187", "3456", "4374", "6144", "7776", "8192", "13824", "17496", "19683", "24576", "31104", "32768", "39366", "55296", "69984", "98304", "124416", "131072", "157464", "177147", "221184", "279936", "354294", "393216", "497664" ]
[ "nonn", "easy" ]
10
1
2
[ "A002023", "A003586", "A013711", "A092810", "A268335", "A355580", "A355581" ]
null
Amiram Eldar, Jul 08 2022
2022-07-10T03:56:36
oeisdata/seq/A355/A355581.seq
ae3b1774036911c4269f4d7c41be1e9a
A355582
a(n) is the largest 5-smooth divisor of n.
[ "1", "2", "3", "4", "5", "6", "1", "8", "9", "10", "1", "12", "1", "2", "15", "16", "1", "18", "1", "20", "3", "2", "1", "24", "25", "2", "27", "4", "1", "30", "1", "32", "3", "2", "5", "36", "1", "2", "3", "40", "1", "6", "1", "4", "45", "2", "1", "48", "1", "50", "3", "4", "1", "54", "5", "8", "3", "2", "1", "60", "1", "2", "9", "64", "5", "6", "1", "4", "3", "10", "1", "72", "1", "2", "75", "4", "1", "6", "1", "80" ]
[ "nonn", "mult", "easy" ]
24
1
2
[ "A006519", "A007814", "A007949", "A038500", "A051037", "A060904", "A065331", "A112765", "A132741", "A165725", "A355582", "A355583", "A355584", "A379005", "A379006" ]
null
Amiram Eldar, Jul 08 2022
2025-04-20T03:30:55
oeisdata/seq/A355/A355582.seq
a6133e42e914c67842b98a6d3a928fc1
A355583
a(n) is the number of the 5-smooth divisors of n.
[ "1", "2", "2", "3", "2", "4", "1", "4", "3", "4", "1", "6", "1", "2", "4", "5", "1", "6", "1", "6", "2", "2", "1", "8", "3", "2", "4", "3", "1", "8", "1", "6", "2", "2", "2", "9", "1", "2", "2", "8", "1", "4", "1", "3", "6", "2", "1", "10", "1", "6", "2", "3", "1", "8", "2", "4", "2", "2", "1", "12", "1", "2", "3", "7", "2", "4", "1", "3", "2", "4", "1", "12", "1", "2", "6", "3", "1", "4", "1", "10", "5", "2", "1", "6", "2", "2" ]
[ "nonn", "mult", "easy" ]
15
1
2
[ "A000005", "A007814", "A007949", "A051037", "A072078", "A112765", "A355582", "A355583", "A355584" ]
null
Amiram Eldar, Jul 08 2022
2022-12-25T02:11:21
oeisdata/seq/A355/A355583.seq
b354d15fdf06e01e5fa5df8482238779
A355584
a(n) is the sum of the 5-smooth divisors of n.
[ "1", "3", "4", "7", "6", "12", "1", "15", "13", "18", "1", "28", "1", "3", "24", "31", "1", "39", "1", "42", "4", "3", "1", "60", "31", "3", "40", "7", "1", "72", "1", "63", "4", "3", "6", "91", "1", "3", "4", "90", "1", "12", "1", "7", "78", "3", "1", "124", "1", "93", "4", "7", "1", "120", "6", "15", "4", "3", "1", "168", "1", "3", "13", "127", "6", "12", "1", "7", "4", "18", "1", "195", "1", "3", "124", "7" ]
[ "nonn", "mult", "easy" ]
17
1
2
[ "A000203", "A007814", "A007949", "A038712", "A051037", "A072079", "A112765", "A355582", "A355583", "A355584" ]
null
Amiram Eldar, Jul 08 2022
2022-12-25T02:11:17
oeisdata/seq/A355/A355584.seq
a252616dd004fa95be8bc26bc2ef51f4
A355585
T(j,k) are the numerators s in the representation R = s/t + (2*sqrt(3)/Pi)*u/v of the resistance between two nodes separated by the distance (j,k) in an infinite triangular lattice of one-ohm resistors, where T(j,k), j >= 0, 0 <= k <= floor(j/2) is an irregular triangle read by rows.
[ "0", "1", "8", "-2", "27", "-5", "928", "-70", "16", "11249", "-2671", "123", "46872", "-34354", "5992", "-438", "1792225", "-445535", "28075", "-10303", "23152256", "-5824226", "1168304", "-178754", "38336", "100685835", "-25547957", "5343755", "-885717", "101355", "3970817992", "-338056246", "72962904", "-12914726", "1825464", "-386166" ]
[ "tabf", "frac", "sign" ]
38
0
3
[ "A084768", "A307012", "A355565", "A355566", "A355567", "A355585", "A355586", "A355587", "A355588" ]
null
Hugo Pfoertner, Jul 09 2022
2022-09-19T13:59:56
oeisdata/seq/A355/A355585.seq
5f9761f9fa0e714ab2ff221871830482
A355586
T(j,k) are the denominators t in the representation R = s/t + (2*sqrt(3)/Pi)*u/v of the resistance between two nodes separated by the distance (j,k) in an infinite triangular lattice of one-ohm resistors, where T(j,k), j >= 0, 0 <= k <= floor(j/2) is an irregular triangle read by rows.
[ "1", "3", "3", "3", "1", "1", "3", "1", "1", "3", "3", "1", "1", "3", "3", "1", "3", "3", "1", "3", "3", "3", "3", "3", "3", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "3", "3", "1", "1", "1", "1", "1", "3", "3", "1", "1", "1", "1", "3", "3", "1", "3", "1", "1", "1", "3", "3", "3", "3", "3", "1", "1", "1", "1", "1", "1", "1", "3", "3", "1", "1", "3", "1", "1", "1", "3", "1", "3", "1", "1", "3", "3", "1", "1", "3", "3", "3", "3", "1" ]
[ "nonn", "tabf", "frac" ]
7
0
2
[ "A355585", "A355586", "A355587", "A355588" ]
null
Hugo Pfoertner, Jul 09 2022
2022-07-22T16:44:25
oeisdata/seq/A355/A355586.seq
c3b18024e380f924525c90b4ee72c7ef
A355587
T(j,k) are the numerators u in the representation R = s/t + (2*sqrt(3)/Pi)*u/v of the resistance between two nodes separated by the distance (j,k) in an infinite triangular lattice of one-ohm resistors, where T(j,k), j >= 0, 0 <= k <= floor(j/2) is an irregular triangle read by rows.
[ "0", "0", "-2", "1", "-24", "5", "-280", "64", "-14", "-3400", "808", "-111", "-212538", "51929", "-9054", "1989", "-2708944", "673429", "-127303", "15576", "-244962336", "61623224", "-12361214", "1891328", "-405592", "-3195918288", "810930216", "-169618717", "28113999", "-3217136", "-42013225014", "2146081719", "-2315951182", "81986531", "-57942922", "12257507" ]
[ "tabf", "frac", "sign" ]
16
0
3
[ "A355585", "A355586", "A355587", "A355588" ]
null
Hugo Pfoertner, Jul 09 2022
2022-09-19T14:03:15
oeisdata/seq/A355/A355587.seq
ad461f6094e35379bb4a193ed0611adc
A355588
T(j,k) are the denominators v in the representation R = s/t + (2*sqrt(3)/Pi)*u/v of the resistance between two nodes separated by the distance (j,k) in an infinite triangular lattice of one-ohm resistors, where T(j,k), j >= 0, 0 <= k <= floor(j/2) is an irregular triangle read by rows.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "5", "5", "5", "5", "5", "5", "5", "5", "35", "35", "35", "35", "35", "35", "35", "35", "35", "35", "35", "7", "35", "7", "35", "35", "7", "35", "35", "35", "35", "35", "55", "385", "385", "385", "55", "55", "385", "11", "55", "385", "385", "385", "385", "55", "5005", "455", "5005", "5005", "455", "5005", "5005", "5005", "5005", "5005", "5005", "5005", "5005", "1001", "143", "1001" ]
[ "nonn", "tabf", "frac" ]
8
0
13
[ "A355585", "A355586", "A355587", "A355588" ]
null
Hugo Pfoertner, Jul 09 2022
2022-07-22T16:44:13
oeisdata/seq/A355/A355588.seq
bf7a3fb42f168c7751e250c41165d2e1
A355589
a(n) is the least distance of two nodes on the same grid line in an infinite triangular lattice of one-ohm resistors for which the resistance measured between the two nodes is greater than n ohms.
[ "1", "38", "8632", "1991753", "459625866" ]
[ "nonn", "hard", "more" ]
14
0
2
[ "A355585", "A355589", "A355955" ]
null
Hugo Pfoertner, Jul 23 2022
2022-07-25T16:07:21
oeisdata/seq/A355/A355589.seq
c34160c2f17d71d2af97c59747f54779
A355590
a(n) = (product of the first n primes) - (sum of the first n primes).
[ "1", "0", "1", "20", "193", "2282", "29989", "510452", "9699613", "223092770", "6469693101", "200560489970", "7420738134613", "304250263526972", "13082761331669749", "614889782588491082", "32589158477190044349", "1922760350154212638630", "117288381359406970982769", "7858321551080267055878522" ]
[ "nonn" ]
20
0
4
[ "A000040", "A002110", "A007504", "A059841", "A355590" ]
null
Des MacHale and Bernard Schott, Jul 08 2022
2022-07-11T16:10:53
oeisdata/seq/A355/A355590.seq
de7311cbbf6f02703ddbef733d9ecb71
A355591
a(n) = (product of the first n odd primes) - (sum of the first n odd primes).
[ "1", "0", "7", "90", "1129", "14976", "255199", "4849770", "111546337", "3234846488", "100280244907", "3710369067210", "152125131763369", "6541380665834736", "307444891294245379", "16294579238595021986", "961380175077106319097", "58644190679703485491136", "3929160775540133527938979" ]
[ "nonn" ]
30
0
3
[ "A000040", "A059841", "A070826", "A071148", "A355590", "A355591" ]
null
Des MacHale and Bernard Schott, Jul 12 2022
2023-07-14T15:20:40
oeisdata/seq/A355/A355591.seq
1de5520811ab3fe875ba03c28f79bc2d
A355592
Positions of records in A357299: integers m such that the number of divisors whose first digit equals the first digit of m sets a new record.
[ "1", "10", "100", "108", "120", "180", "1008", "1260", "1680", "10010", "10080", "15120", "100320", "100800", "110880", "166320", "196560", "1003200", "1004640", "1005480", "1028160", "1053360", "1081080", "1441440", "1884960", "10024560", "10090080", "10533600", "10810800", "12252240", "17297280", "100069200", "100124640", "100212840", "100245600" ]
[ "nonn", "base" ]
29
1
2
[ "A206287", "A342833", "A355592", "A357299", "A357300" ]
null
Bernard Schott, Sep 24 2022
2022-09-26T17:47:48
oeisdata/seq/A355/A355592.seq
2ef4ca8d464f023d0a4c5a907b75a367
A355593
a(n) is the number of alternating integers that divide n.
[ "1", "2", "2", "3", "2", "4", "2", "4", "3", "4", "1", "6", "1", "4", "3", "5", "1", "6", "1", "5", "4", "2", "2", "7", "3", "2", "4", "5", "2", "7", "1", "6", "2", "3", "3", "9", "1", "3", "2", "6", "2", "7", "2", "3", "5", "3", "2", "8", "3", "6", "2", "4", "1", "8", "2", "7", "2", "4", "1", "9", "2", "2", "6", "6", "3", "4", "2", "4", "4", "7", "1", "11", "1", "3", "4", "5", "2", "5", "1", "7", "5", "3", "2", "9", "3", "3", "4", "4", "2", "11", "2", "5", "2", "4", "2", "10", "1", "6", "3", "7" ]
[ "nonn", "base" ]
42
1
2
[ "A030141", "A332268", "A355302", "A355593", "A355594", "A355595", "A355596" ]
null
Bernard Schott, Jul 08 2022
2024-01-06T09:21:33
oeisdata/seq/A355/A355593.seq
c24e5ecc2de2b26241a582a7ee003d99
A355594
a(n) is the smallest integer that has exactly n alternating divisors.
[ "1", "2", "4", "6", "16", "12", "24", "48", "36", "96", "72", "144", "210", "180", "420", "360", "504", "864", "630", "1080", "1512", "2160", "1260", "3150", "1890", "2520", "5040", "6300", "3780", "10080", "12600", "9450", "7560", "32760", "15120", "18900", "22680", "30240", "88830", "37800", "45360", "75600", "105840", "90720", "151200", "162540", "254520" ]
[ "nonn", "base" ]
54
1
2
[ "A005179", "A030141", "A355303", "A355593", "A355594", "A355595", "A355596" ]
null
Bernard Schott, Jul 08 2022
2023-01-26T10:14:31
oeisdata/seq/A355/A355594.seq
71cb3aa22bd06ea5377d4b8818f32a5e
A355595
Positions of records in A355593: Integers whose number of alternating divisors sets a new record.
[ "1", "2", "4", "6", "12", "24", "36", "72", "144", "180", "360", "504", "630", "1080", "1260", "1890", "2520", "3780", "7560", "15120", "18900", "22680", "30240", "37800", "45360", "75600", "90720", "151200", "162540", "226800", "317520", "325080", "650160", "763560", "1137780", "1243620", "1527120", "2275560", "3054240", "3738420", "4551120", "6826680", "7476840", "14953680", "17445960", "21818160", "26168940", "36363600", "43636320", "52337880" ]
[ "nonn", "base" ]
14
1
2
[ "A030141", "A355304", "A355593", "A355594", "A355595" ]
null
Bernard Schott, Jul 08 2022
2022-07-11T16:10:57
oeisdata/seq/A355/A355595.seq
c94180d7889e0f36b6181572b6cd0f24
A355596
Numbers all of whose divisors are alternating numbers (A030141).
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "14", "16", "18", "21", "23", "25", "27", "29", "32", "36", "41", "43", "47", "49", "50", "54", "58", "61", "63", "67", "69", "81", "83", "87", "89", "94", "98", "101", "103", "107", "109", "123", "125", "127", "129", "141", "145", "147", "149", "161", "163", "167", "181", "183", "189", "214", "218", "250", "254", "290", "298" ]
[ "nonn", "base" ]
16
1
2
[ "A030141", "A062687", "A190217", "A329419", "A337941", "A355593", "A355594", "A355595", "A355596" ]
null
Bernard Schott, Jul 12 2022
2022-07-14T12:08:35
oeisdata/seq/A355/A355596.seq
6c94baa08009b7f1835f4352173c5480
A355597
a(1) = 2. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).
[ "2", "5", "7", "19", "127", "911", "7331", "167149", "387749", "17153317", "432383657", "10459192927" ]
[ "nonn", "hard", "more" ]
5
1
1
[ "A249162", "A355597", "A355598", "A355599", "A355600", "A355601", "A355602" ]
null
Felix Fröhlich, Jul 09 2022
2022-07-16T01:30:50
oeisdata/seq/A355/A355597.seq
39e458e881fd527e4841a102fff051b7
A355598
a(1) = 3. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).
[ "3", "17", "131", "659", "503", "9833", "49603", "327317", "13900147", "144229223", "5872276013" ]
[ "nonn", "hard", "more" ]
6
1
1
[ "A249162", "A355597", "A355598", "A355599", "A355600", "A355601", "A355602" ]
null
Felix Fröhlich, Jul 09 2022
2023-07-23T18:59:39
oeisdata/seq/A355/A355598.seq
90bdebc298354d1c28eb29c6891ed577
A355599
a(1) = 29. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).
[ "29", "41", "313", "1499", "941", "12011", "6287", "52301", "50077", "137743", "1274353", "46303409", "89018221", "687655393", "7462816891" ]
[ "nonn", "hard", "more" ]
4
1
1
[ "A249162", "A355597", "A355598", "A355599", "A355600", "A355601", "A355602" ]
null
Felix Fröhlich, Jul 09 2022
2022-07-16T01:31:16
oeisdata/seq/A355/A355599.seq
c74a4b18f5e38b172d683e92b85e2b1e
A355600
a(1) = 37. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).
[ "37", "691", "19181", "5849", "18503", "37853", "478741", "18401827", "571007279", "5860639859" ]
[ "nonn", "hard", "more" ]
4
1
1
[ "A249162", "A355597", "A355598", "A355599", "A355600", "A355601", "A355602" ]
null
Felix Fröhlich, Jul 09 2022
2022-07-16T01:31:35
oeisdata/seq/A355/A355600.seq
3ab860c6e02645c7ab547c91c0333015