Datasets:
christopher
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oeis

Dataset card Data Studio Files
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score
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2.31k
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int64
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666,262,453B
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timestamp
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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
32
A006901
Number of caskets of order n.
[ "1", "2", "4", "10", "25", "76", "251", "968" ]
[ "nonn", "more" ]
15
1
2
[ "A006901", "A260019" ]
[ "M1213" ]
Simon Plouffe and N. J. A. Sloane.
2015-07-14T03:12:44
oeisdata/seq/A006/A006901.seq
d268dc7732561b2e12c08c6e8687ba68
A006902
a(n) = (2n)! * Sum_{k=0..n} (-1)^k * binomial(n,k) / (n+k)!.
[ "1", "1", "5", "47", "641", "11389", "248749", "6439075", "192621953", "6536413529", "248040482741", "10407123510871", "478360626529345", "23903857657114837", "1290205338991689821", "74803882225482661259", "4636427218380366565889", "305927317398343461908785", "21410426012751471702223333" ]
[ "nonn", "easy" ]
69
0
3
[ "A006902", "A047909", "A082545", "A267480" ]
[ "M4003" ]
Simon Plouffe and N. J. A. Sloane
2023-10-27T19:45:04
oeisdata/seq/A006/A006902.seq
49ce630311e1065efe910a41f150e463
A006903
Number of triangle-free trivalent (or cubic) graphs with 2n labeled nodes.
[ "1", "0", "0", "10", "3360", "1829520", "2010023400", "3622767548400", "9820308795897600", "38117776055769009600", "204209112522362230483200", "1465227517158776390187168000", "13730711637579303579659695248000" ]
[ "nonn", "nice" ]
22
0
4
[ "A006903", "A014371" ]
[ "M4763" ]
Simon Plouffe and N. J. A. Sloane
2021-12-19T02:15:04
oeisdata/seq/A006/A006903.seq
c8776a1273d3912b5a6bae89abfbfe6a
A006904
a(n) = a(n-1) + 2*a(n-2) + (-1)^n.
[ "1", "1", "4", "5", "14", "23", "52", "97", "202", "395", "800", "1589", "3190", "6367", "12748", "25481", "50978", "101939", "203896", "407773", "815566", "1631111", "3262244", "6524465", "13048954", "26097883", "52195792", "104391557" ]
[ "nonn", "easy" ]
29
4
3
null
[ "M3254" ]
Simon Plouffe and N. J. A. Sloane.
2023-06-28T20:46:58
oeisdata/seq/A006/A006904.seq
600c2f103d8085ce578930937f883a2c
A006905
Number of transitive relations on n labeled nodes.
[ "1", "2", "13", "171", "3994", "154303", "9415189", "878222530", "122207703623", "24890747921947", "7307450299510288", "3053521546333103057", "1797003559223770324237", "1476062693867019126073312", "1679239558149570229156802997", "2628225174143857306623695576671", "5626175867513779058707006016592954", "16388270713364863943791979866838296851", "64662720846908542794678859718227127212465" ]
[ "nonn", "nice" ]
62
0
2
[ "A000595", "A001173", "A006905", "A091073", "A340264" ]
[ "M2065" ]
Simon Plouffe and N. J. A. Sloane
2024-02-17T10:54:47
oeisdata/seq/A006/A006905.seq
c502dbf09c7cfda200e1a7b92d2ea9ee
A006906
a(n) is the sum of products of terms in all partitions of n.
[ "1", "1", "3", "6", "14", "25", "56", "97", "198", "354", "672", "1170", "2207", "3762", "6786", "11675", "20524", "34636", "60258", "100580", "171894", "285820", "480497", "791316", "1321346", "2156830", "3557353", "5783660", "9452658", "15250216", "24771526", "39713788", "64011924", "102199026", "163583054", "259745051" ]
[ "nonn", "nice", "easy" ]
76
0
3
[ "A000041", "A006906", "A007870", "A022629", "A022661", "A022693", "A077335", "A118851", "A163318", "A265758", "A302830", "A318127", "A322364", "A322365" ]
[ "M2575" ]
Simon Plouffe
2020-11-25T05:07:05
oeisdata/seq/A006/A006906.seq
cc6b87ba43a8d466f97b032372a4cfa2
A006907
Number of zeros in character table of symmetric group S_n.
[ "0", "0", "1", "4", "10", "29", "55", "153", "307", "588", "1018", "2230", "3543", "6878", "11216", "20615", "33355", "57980", "90194", "155176", "239327", "395473", "604113", "970294", "1453749", "2323476", "3425849", "5349414", "7905133", "11963861", "17521274", "26472001", "38054619", "56756488", "81683457", "119005220", "170498286", "247619748" ]
[ "nonn", "nice" ]
46
1
4
[ "A006907", "A006908", "A051748", "A051749" ]
[ "M3394" ]
Simon Plouffe and N. J. A. Sloane
2025-01-31T17:41:41
oeisdata/seq/A006/A006907.seq
f7b88d1ce169129a12e78a631f593f77
A006908
Number of nonzero elements in the character table of the symmetric group S_n.
[ "1", "4", "8", "21", "39", "92", "170", "331", "593", "1176", "2118", "3699", "6658", "11347", "19760", "32746", "54854", "90245", "149906", "237953", "387937", "608531", "970912", "1510331", "2380015", "3610620", "5634251", "8474110", "12934092", "19440955", "29291690", "43233800", "64825830", "94779612", "139820232" ]
[ "nonn", "nice" ]
32
1
2
[ "A006907", "A006908", "A061256" ]
[ "M3338" ]
Simon Plouffe and N. J. A. Sloane
2021-12-19T00:18:15
oeisdata/seq/A006/A006908.seq
0415742afaf4bfba71dc13f5590baa4d
A006909
Theta series of laminated lattice LAMBDA_10.
[ "1", "0", "336", "768", "4950", "6912", "22944", "27648", "75792", "72192", "181728", "158976", "393030", "317952", "682656", "557568", "1249686", "912384", "1881840", "1458432", "2979072", "2155776", "4254048", "3055104", "6251808", "4354560" ]
[ "nonn" ]
24
0
3
null
[ "M5439" ]
N. J. A. Sloane
2021-06-14T15:57:47
oeisdata/seq/A006/A006909.seq
3f46cc76d5e0344a78131581830844e2
A006910
Theta series of laminated lattice LAMBDA_11^{min}.
[ "1", "0", "432", "1632", "8700", "18048", "51072", "82880", "191926", "251648", "517568", "619104", "1204024", "1322368", "2326528", "2515904", "4396188", "4407552", "7238000", "7303456", "11911352", "11434752", "17948288", "17151936", "27144744", "25129984", "37714368", "35413888", "54674928", "48607872", "72122368" ]
[ "nonn" ]
19
0
3
null
[ "M5452" ]
N. J. A. Sloane.
2023-05-08T09:36:43
oeisdata/seq/A006/A006910.seq
0e0002cd654765a78c6c1e6448d6c298
A006911
Theta series of laminated lattice LAMBDA_11^{max}.
[ "1", "0", "438", "1536", "9372", "15360", "57896", "70656", "211638", "215040", "582648", "529920", "1316472", "1139712", "2619264", "2159616", "4815516", "3766272", "8165550", "6259200", "13070328", "9799680", "20203512", "14693376", "29739560", "21553152", "42530424", "30369792", "59881584", "41671680", "81197184" ]
[ "nonn" ]
17
0
3
null
[ "M5453" ]
N. J. A. Sloane.
2021-06-25T04:07:31
oeisdata/seq/A006/A006911.seq
99314e68999755030a39f4e428dafa89
A006912
Theta series of laminated lattice LAMBDA_12^{min}.
[ "1", "0", "624", "3456", "17544", "47616", "130752", "252672", "560904", "887808", "1692576", "2412672", "4280736", "5564928", "9068928", "11460864", "17948424", "21310464", "32009904", "37102464", "54842544", "61519872", "87013440", "96555264", "136860576", "146503680", "200463648", "216131328", "294879552" ]
[ "nonn" ]
14
0
3
null
[ "M5465" ]
N. J. A. Sloane.
2023-05-13T01:56:27
oeisdata/seq/A006/A006912.seq
9c3ea93a15c57e47f2aa24f4671000d9
A006913
Theta series of laminated lattice LAMBDA_12^{mid}.
[ "1", "0", "632", "3328", "18440", "44032", "139872", "236032", "589576", "829440", "1803600", "2250496", "4499360", "5196800", "9676480", "10694144", "18865928", "19884032", "34147224", "34636032", "57643440", "57413632", "92796192", "90131968", "143856544", "136744960", "213841936", "201703936", "309939520" ]
[ "nonn", "nice", "easy" ]
23
0
3
null
[ "M5467" ]
N. J. A. Sloane
2023-05-13T01:58:22
oeisdata/seq/A006/A006913.seq
8f00318af5def3ef7df0a2e3d6feed12
A006914
Theta series of laminated lattice LAMBDA_12^{max}.
[ "1", "0", "648", "3072", "20232", "36864", "158112", "202752", "646920", "712704", "2025648", "1926144", "4936608", "4460544", "10891584", "9160704", "20700936", "17031168", "38421864", "29703168", "63245232", "49201152", "104361696", "77285376", "157848480", "117227520", "240598512", "172849152", "340059456" ]
[ "nonn" ]
10
0
3
null
[ "M5468" ]
N. J. A. Sloane.
2021-06-19T13:19:56
oeisdata/seq/A006/A006914.seq
f02bd7961e61390d448ea26ea7e09d84
A006915
Theta series of laminated lattice LAMBDA_13^{min}.
[ "1", "0", "888", "6432", "36392", "110720", "336992", "696512", "1656202", "2779392", "5603904", "8392864", "15385200", "20978048", "35705728", "46190016", "74768920", "92015360", "142090040", "169094496", "255887536", "293745408", "427864224", "485217472", "696300464", "765363200", "1075013440", "1170251136" ]
[ "nonn" ]
19
0
3
null
[ "M5483" ]
N. J. A. Sloane
2023-05-08T09:36:16
oeisdata/seq/A006/A006915.seq
7986b39317ca66b2e84bc7b403dbc42b
A006916
Theta series of laminated lattice LAMBDA_13^{mid}.
[ "1", "0", "890", "6400", "36600", "110080", "337520", "698880", "1649610", "2780160", "5619792", "8387840", "15347280", "20974080", "35834560", "46174720", "74480280", "92062720", "142597450", "169132800", "254916880", "293647360", "429515280", "485235200", "693838000", "765358080", "1078906000", "1170170880" ]
[ "nonn" ]
24
0
3
null
[ "M5484" ]
N. J. A. Sloane
2023-05-08T09:36:20
oeisdata/seq/A006/A006916.seq
7069b2066b1605a93ffa2b48c64e6b61
A006917
Theta series of laminated lattice LAMBDA_13^{max}.
[ "1", "0", "906", "6144", "38424", "102400", "359344", "651264", "1743434", "2596864", "5956560", "7829504", "16232208", "19574784", "37960640", "43102208", "78860184", "85909504", "150986202", "157845504", "269942480", "274096128", "454718160", "452882432", "734667440", "714375168" ]
[ "nonn" ]
16
0
3
null
[ "M5485" ]
N. J. A. Sloane
2021-06-16T21:04:52
oeisdata/seq/A006/A006917.seq
08ff11566d1f816fc3c8769a1d141c6d
A006918
a(n) = binomial(n+3, 3)/4 for odd n, n*(n+2)*(n+4)/24 for even n.
[ "0", "1", "2", "5", "8", "14", "20", "30", "40", "55", "70", "91", "112", "140", "168", "204", "240", "285", "330", "385", "440", "506", "572", "650", "728", "819", "910", "1015", "1120", "1240", "1360", "1496", "1632", "1785", "1938", "2109", "2280", "2470", "2660", "2870", "3080", "3311", "3542", "3795", "4048", "4324", "4600", "4900", "5200", "5525", "5850", "6201", "6552", "6930" ]
[ "nonn", "nice", "easy" ]
202
0
3
[ "A000031", "A000094", "A001037", "A006918", "A028723", "A051168", "A115720", "A115994", "A117485", "A171238", "A173997", "A242093", "A257990", "A307373", "A325164", "A325168" ]
[ "M1349" ]
N. J. A. Sloane
2025-03-04T07:55:31
oeisdata/seq/A006/A006918.seq
773223f3a0e6f1e7965a417969d45b3b
A006919
Write down all the prime divisors in previous term.
[ "8", "222", "2337", "31941", "33371313", "311123771", "7149317941", "22931219729", "112084656339", "3347911118189", "11613496501723", "97130517917327", "531832651281459", "3331113965338635107", "3331113965338635107" ]
[ "nonn", "base", "nice" ]
21
1
1
[ "A006919", "A037271", "A037276", "A048985", "A048986", "A049065", "A056938" ]
[ "M4581" ]
N. J. A. Sloane
2022-10-07T15:47:24
oeisdata/seq/A006/A006919.seq
ae09bde4d551cdee61bc644551d91dfa
A006920
At each step, record how many 1's, 2's, etc. have been seen so far in the sequence.
[ "1", "1", "2", "21", "32", "331", "433", "4351", "53621", "647221", "7673221", "8883233", "891132333", "8101532334101", "101118423351110001", "141220533351220001001", "17142355335122101100101", "23162558335122102101101001", "30192751033612210211110100201", "3823295114361321021111110020101001" ]
[ "nonn", "base" ]
17
1
3
[ "A006920", "A333867" ]
[ "M2126" ]
N. J. A. Sloane, James Propp
2022-10-08T14:15:50
oeisdata/seq/A006/A006920.seq
37d8b995ae5de25de1b9a10a5d0e9026
A006921
Diagonals of Pascal's triangle mod 2 interpreted as binary numbers.
[ "1", "1", "3", "2", "7", "5", "13", "8", "29", "21", "55", "34", "115", "81", "209", "128", "465", "337", "883", "546", "1847", "1301", "3357", "2056", "7437", "5381", "14087", "8706", "29443", "20737", "53505", "32768", "119041", "86273", "226051", "139778", "472839", "333061", "859405", "526344", "1903901", "1377557", "3606327" ]
[ "nonn", "easy" ]
40
0
3
[ "A000079", "A006921", "A007318", "A011973", "A047999", "A101624", "A168081", "A257971", "A260022" ]
[ "M2252" ]
N. J. A. Sloane
2025-01-05T19:51:34
oeisdata/seq/A006/A006921.seq
de720c7dfd07a60c07a5d1e2eade8ecd
A006922
Expansion of 1/eta(q)^24; Fourier coefficients of T_{14}.
[ "1", "24", "324", "3200", "25650", "176256", "1073720", "5930496", "30178575", "143184000", "639249300", "2705114880", "10914317934", "42189811200", "156883829400", "563116739584", "1956790259235", "6599620022400", "21651325216200", "69228721526400", "216108718571250", "659641645039360", "1971466420726656" ]
[ "nonn", "easy", "nice" ]
88
-1
2
[ "A000041", "A000594", "A005758", "A006922", "A023021", "A048057", "A048100", "A048101", "A048110", "A048145", "A144064" ]
[ "M5160" ]
N. J. A. Sloane
2024-02-29T20:33:15
oeisdata/seq/A006/A006922.seq
92686973d7467785946e12c03ecdddc4
A006923
Number of connected trivalent graphs with 2n nodes and with girth exactly 3.
[ "0", "0", "1", "1", "3", "13", "63", "399", "3268", "33496", "412943", "5883727", "94159721", "1661723296", "31954666517", "663988090257", "14814445040728" ]
[ "nonn", "hard", "more" ]
28
0
5
[ "A002851", "A006923", "A006924", "A006925", "A006926", "A006927", "A014371", "A014372", "A014374", "A014375", "A014376", "A198303" ]
[ "M2944" ]
N. J. A. Sloane
2023-09-28T02:05:22
oeisdata/seq/A006/A006923.seq
d1ffc7b27864ab217f37d7bc03829eb9
A006924
Number of connected trivalent graphs with 2n nodes and girth exactly 4.
[ "0", "0", "0", "1", "2", "5", "20", "101", "743", "7350", "91763", "1344782", "22160335", "401278984", "7885687604", "166870266608", "3781101495300" ]
[ "nonn", "hard", "more" ]
32
0
5
[ "A002851", "A006923", "A006924", "A006925", "A006926", "A006927", "A014371", "A014372", "A014374", "A014375", "A014376", "A184944", "A184954", "A184964", "A184974", "A198303" ]
[ "M1526" ]
N. J. A. Sloane.
2014-05-01T02:40:01
oeisdata/seq/A006/A006924.seq
9165226bc7e2d0d22c2da887abd31c87
A006925
Number of connected trivalent graphs with 2n nodes and girth exactly 5.
[ "0", "0", "0", "0", "0", "1", "2", "8", "48", "450", "5751", "90553", "1612905", "31297357", "652159389", "14499780660", "342646718608" ]
[ "nonn", "hard", "more" ]
21
0
7
[ "A002851", "A006923", "A006924", "A006925", "A006926", "A006927", "A014371", "A014372", "A014374", "A014375", "A014376", "A184945", "A184955", "A198303" ]
[ "M1879" ]
N. J. A. Sloane.
2014-05-01T02:40:01
oeisdata/seq/A006/A006925.seq
ec1cc15aac0a9673fb647644f1ecb65b
A006926
Number of connected trivalent graphs with 2n nodes and girth exactly 6.
[ "0", "0", "0", "0", "0", "0", "0", "1", "1", "5", "32", "385", "7573", "181224", "4624480", "122089998", "3328899586", "93988909755" ]
[ "nonn", "hard", "more" ]
22
0
10
[ "A002851", "A006923", "A006924", "A006925", "A006926", "A006927", "A014371", "A014372", "A014374", "A014375", "A014376", "A185131", "A198303" ]
[ "M3969" ]
N. J. A. Sloane.
2014-05-01T02:40:01
oeisdata/seq/A006/A006926.seq
1fbbf63a07fb4f583ce754fa541dc7e5
A006927
Number of connected trivalent graphs with 2n nodes and girth exactly 7.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "3", "21", "545", "30368", "1782839", "95079080", "4686063107" ]
[ "nonn", "hard", "more" ]
18
0
14
[ "A002851", "A006923", "A006924", "A006925", "A006926", "A006927", "A014371", "A014372", "A014374", "A014375", "A014376", "A198303" ]
[ "M3086" ]
N. J. A. Sloane.
2014-05-01T02:40:01
oeisdata/seq/A006/A006927.seq
c2d67cf5a1f4bae1879ca14fb5274bf1
A006928
a(n) = length of (n+1)st run, with initial terms 1, 2.
[ "1", "2", "1", "1", "2", "1", "2", "2", "1", "2", "2", "1", "1", "2", "1", "1", "2", "2", "1", "2", "1", "1", "2", "1", "2", "2", "1", "1", "2", "1", "1", "2", "1", "2", "2", "1", "2", "2", "1", "1", "2", "1", "2", "2", "1", "2", "1", "1", "2", "1", "1", "2", "2", "1", "2", "2", "1", "1", "2", "1", "2", "2", "1", "2", "2", "1", "1", "2", "1", "1", "2", "1", "2", "2", "1", "2", "1", "1", "2", "2", "1", "2", "2", "1", "1", "2", "1", "2", "2", "1", "2", "2", "1", "1", "2", "1", "1", "2", "2", "1", "2", "1", "1", "2", "1", "2", "2", "1" ]
[ "nonn", "easy", "nice" ]
32
1
2
[ "A000002", "A006928" ]
[ "M0070" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A006/A006928.seq
9c5b7e1db36665df34f32cb8db68d3e8
A006929
From analyzing an algorithm.
[ "1", "1", "1", "2", "2", "15", "39", "449", "2758" ]
[ "nonn" ]
8
1
4
null
[ "M0388" ]
N. J. A. Sloane, S. K. Bhaskar [ bhaskar(AT)umd5.umd.edu ]
2012-03-30T16:45:05
oeisdata/seq/A006/A006929.seq
cb70d968f0e5fd9d031e338d98328b02
A006930
Binomial transform of rooted tree numbers.
[ "1", "2", "5", "14", "42", "131", "420", "1376", "4589", "15537", "53293", "184881", "647752", "2289215", "8152147", "29226618", "105408688", "382193502", "1392377762", "5094356032", "18711122069", "68965586862", "255006331944", "945662753514", "3516281928159", "13106923073426", "48967229534156", "183326438562982" ]
[ "nonn" ]
15
0
2
[ "A000081", "A006930", "A051491" ]
null
N. J. A. Sloane.
2014-10-07T09:00:24
oeisdata/seq/A006/A006930.seq
4412dd7bc29972e6ebdfb8ce3aba5f2c
A006931
Least Carmichael number with n prime factors, or 0 if no such number exists.
[ "561", "41041", "825265", "321197185", "5394826801", "232250619601", "9746347772161", "1436697831295441", "60977817398996785", "7156857700403137441", "1791562810662585767521", "87674969936234821377601", "6553130926752006031481761", "1590231231043178376951698401" ]
[ "nonn" ]
50
3
1
[ "A002997", "A006931", "A074379", "A087788", "A112428", "A112429", "A112430", "A112431", "A112432", "A135717", "A135719", "A135720", "A135721", "A141711" ]
[ "M5463" ]
N. J. A. Sloane and Richard Pinch
2025-02-16T08:32:31
oeisdata/seq/A006/A006931.seq
778c12ae8a057f220761b863428bc505
A006932
Number of permutations of [n] with at least one strong fixed point (a permutation p of {1,2,...,n} is said to have j as a strong fixed point if p(k) < j for k < j and p(k) > j for k > j).
[ "1", "1", "3", "10", "43", "223", "1364", "9643", "77545", "699954", "7013079", "77261803", "928420028", "12085410927", "169413357149", "2544367949634", "40758600588283", "693684669653911", "12499734669634036", "237734433597317987", "4759174459355303521" ]
[ "nonn", "easy", "nice" ]
70
1
3
[ "A003149", "A006932", "A052186", "A145878" ]
[ "M2862" ]
N. J. A. Sloane
2021-07-13T19:47:34
oeisdata/seq/A006/A006932.seq
ca6e73856e74ad5b2e0a03480bece128
A006933
'Eban' numbers (the letter 'e' is banned!).
[ "2", "4", "6", "30", "32", "34", "36", "40", "42", "44", "46", "50", "52", "54", "56", "60", "62", "64", "66", "2000", "2002", "2004", "2006", "2030", "2032", "2034", "2036", "2040", "2042", "2044", "2046", "2050", "2052", "2054", "2056", "2060", "2062", "2064", "2066", "4000", "4002", "4004", "4006", "4030", "4032", "4034", "4036", "4040", "4042", "4044", "4046", "4050", "4052", "4054", "4056", "4060", "4062", "4064", "4066", "6000" ]
[ "word", "nonn" ]
73
1
1
[ "A006933", "A008520", "A008521", "A008523", "A008537", "A014254", "A072956", "A072957", "A082504", "A085513", "A089589", "A089590", "A287876" ]
[ "M1030" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A006/A006933.seq
5af2f72834fe5774c1ffeef164bc2ae5
A006934
A series for Pi.
[ "1", "1", "21", "671", "180323", "20898423", "7426362705", "1874409467055", "5099063967524835", "2246777786836681835", "2490122296790918386363", "1694873049836486741425113", "5559749161756484280905626951", "5406810236613380495234085140851", "12304442295910538475633061651918089" ]
[ "nonn" ]
50
0
3
[ "A006934", "A088802", "A123854", "A220412" ]
[ "M5119" ]
Simon Plouffe and N. J. A. Sloane
2019-06-02T11:26:17
oeisdata/seq/A006/A006934.seq
c59d325057ab70cee67c580523e97e41
A006935
Even pseudoprimes (or primes) to base 2: even n that divide 2^n - 2.
[ "2", "161038", "215326", "2568226", "3020626", "7866046", "9115426", "49699666", "143742226", "161292286", "196116194", "209665666", "213388066", "293974066", "336408382", "377994926", "410857426", "665387746", "667363522", "672655726", "760569694", "1066079026", "1105826338", "1423998226", "1451887438", "1610063326", "2001038066", "2138882626", "2952654706", "3220041826" ]
[ "nonn", "nice" ]
150
1
1
[ "A006935", "A015919", "A295740" ]
[ "M2190" ]
N. J. A. Sloane, Richard C. Schroeppel
2025-04-05T10:27:27
oeisdata/seq/A006/A006935.seq
591811d7f79f926873349a2831f117ab
A006936
Moebius transform of numbers of preferential arrangements.
[ "0", "1", "0", "2", "12", "74", "538", "4682", "47280", "545832", "7087186", "102247562", "1622632020", "28091567594", "526858343698", "10641342970366", "230283190930560", "5315654681981354", "130370767028589528", "3385534663256845322" ]
[ "nonn" ]
20
0
4
[ "A000670", "A006936" ]
null
N. J. A. Sloane
2017-12-15T06:26:39
oeisdata/seq/A006/A006936.seq
d743d93f321402484c382f6b32242db4
A006937
Convert the last term from decimal to binary! a(1)=10.
[ "10", "1010", "1111110010", "1000010001110100011000101111010", "1100100111110011010011100010101000011000101001000100011011011010001111011100010000001000010011100010" ]
[ "nonn", "base" ]
19
1
1
[ "A006937", "A008559" ]
[ "M4759" ]
N. J. A. Sloane
2025-01-19T03:30:13
oeisdata/seq/A006/A006937.seq
cae8f80b6c904e25e4fe191aefa12ab4
A006938
Convert the last term from decimal to binary! a(1)=3.
[ "3", "11", "1011", "1111110011", "1000010001110100011000101111011" ]
[ "nonn", "base" ]
43
1
1
[ "A006938", "A008559", "A260024", "A260025", "A260026", "A260027", "A260028", "A260029", "A260030" ]
[ "M4814" ]
N. J. A. Sloane
2025-01-18T16:35:34
oeisdata/seq/A006/A006938.seq
8195179a9b28c752779ceffdde75956e
A006939
Chernoff sequence: a(n) = Product_{k=1..n} prime(k)^(n-k+1).
[ "1", "2", "12", "360", "75600", "174636000", "5244319080000", "2677277333530800000", "25968760179275365452000000", "5793445238736255798985527240000000", "37481813439427687898244906452608585200000000", "7517370874372838151564668004911177464757864076000000000", "55784440720968513813368002533861454979548176771615744085560000000000" ]
[ "easy", "nonn", "nice" ]
92
0
2
[ "A000142", "A000178", "A000325", "A001221", "A001222", "A002110", "A005117", "A006939", "A007489", "A008302", "A022559", "A022915", "A051357", "A060389", "A071625", "A076954", "A118914", "A124010", "A130091", "A181796", "A181819", "A317829", "A336417", "A336419", "A336420", "A336426", "A336496" ]
[ "M2050" ]
N. J. A. Sloane
2024-05-31T20:57:44
oeisdata/seq/A006/A006939.seq
39ed23b94c5c150fb361f24f07f68b22
A006940
Rows of Pascal's triangle mod 3.
[ "1", "11", "121", "1001", "11011", "121121", "1002001", "11022011", "121212121", "1000000001", "11000000011", "121000000121", "1001000001001", "11011000011011", "121121000121121", "1002001001002001", "11022011011022011", "121212121121212121", "1000000002000000001", "11000000022000000011", "121000000212000000121" ]
[ "nonn" ]
16
0
2
[ "A006940", "A007318" ]
[ "M4806" ]
N. J. A. Sloane
2018-11-22T02:40:26
oeisdata/seq/A006/A006940.seq
18f7dc14db583b2d6c820854439777a3
A006941
Expansion of Pi in base 8.
[ "3", "1", "1", "0", "3", "7", "5", "5", "2", "4", "2", "1", "0", "2", "6", "4", "3", "0", "2", "1", "5", "1", "4", "2", "3", "0", "6", "3", "0", "5", "0", "5", "6", "0", "0", "6", "7", "0", "1", "6", "3", "2", "1", "1", "2", "2", "0", "1", "1", "1", "6", "0", "2", "1", "0", "5", "1", "4", "7", "6", "3", "0", "7", "2", "0", "0", "2", "0", "2", "7", "3", "7", "2", "4", "6", "1", "6", "6", "1", "1", "6", "3", "3", "1", "0", "4", "5", "0", "5", "1", "2", "0", "2", "0", "7", "4", "6", "1", "6", "1", "5", "0", "0", "2", "3" ]
[ "nonn", "base", "cons", "easy" ]
61
1
1
[ "A000796", "A004601", "A004602", "A004603", "A004604", "A004605", "A004606", "A004608", "A006941", "A007514", "A060707", "A062964", "A068436", "A068437", "A068438", "A068439", "A068440" ]
[ "M2208" ]
N. J. A. Sloane
2022-10-03T11:59:20
oeisdata/seq/A006/A006941.seq
999d024ad1d338fa43ab3e68731e6f30
A006942
Number of segments used to represent n on calculator display, variant 5: digits '6', '7' and '9' use 6, 3 and 6 segments, respectively.
[ "6", "2", "5", "5", "4", "5", "6", "3", "7", "6", "8", "4", "7", "7", "6", "7", "8", "5", "9", "8", "11", "7", "10", "10", "9", "10", "11", "8", "12", "11", "11", "7", "10", "10", "9", "10", "11", "8", "12", "11", "10", "6", "9", "9", "8", "9", "10", "7", "11", "10", "11", "7", "10", "10", "9", "10", "11", "8", "12", "11", "12", "8", "11", "11", "10", "11", "12", "9", "13", "12", "9", "5", "8", "8", "7", "8", "9" ]
[ "base", "nonn", "nice", "easy" ]
78
0
1
[ "A000120", "A006942", "A010371", "A063720", "A074458", "A165244", "A216261", "A234691", "A234692", "A277116", "A302552", "A328330", "A331529" ]
[ "M4049" ]
N. J. A. Sloane
2021-06-02T08:01:47
oeisdata/seq/A006/A006942.seq
c2a0226198990975c74b6b4425f5e986
A006943
Rows of Sierpiński's triangle (Pascal's triangle mod 2).
[ "1", "11", "101", "1111", "10001", "110011", "1010101", "11111111", "100000001", "1100000011", "10100000101", "111100001111", "1000100010001", "11001100110011", "101010101010101", "1111111111111111", "10000000000000001", "110000000000000011" ]
[ "nonn", "easy", "base" ]
112
0
2
[ "A001317", "A006943", "A080176", "A249183" ]
[ "M4802" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A006/A006943.seq
b1e73e880dcbaccdc8e05e4f9c5b2d60
A006944
Number of letters in the n-th ordinal number (in American English).
[ "5", "6", "5", "6", "5", "5", "7", "6", "5", "5", "8", "7", "10", "10", "9", "9", "11", "10", "10", "9", "11", "12", "11", "12", "11", "11", "13", "12", "11", "9", "11", "12", "11", "12", "11", "11", "13", "12", "11", "8", "10", "11", "10", "11", "10", "10", "12", "11", "10", "8", "10", "11", "10", "11", "10", "10", "12", "11", "10", "8", "10", "11", "10", "11", "10", "10", "12", "11", "10", "10", "12", "13", "12", "13", "12", "12" ]
[ "nonn", "word", "nice", "easy" ]
55
1
1
[ "A005589", "A006944", "A006969", "A196278" ]
[ "M3744" ]
N. J. A. Sloane
2022-07-12T13:01:05
oeisdata/seq/A006/A006944.seq
c3af95370d5d869ee4e54de8c1b22d9e
A006945
Smallest odd composite number that requires n Miller-Rabin primality tests.
[ "9", "2047", "1373653", "25326001", "3215031751", "2152302898747", "3474749660383", "341550071728321", "341550071728321", "3825123056546413051", "3825123056546413051", "3825123056546413051", "318665857834031151167461", "3317044064679887385961981" ]
[ "nonn", "hard", "more" ]
55
1
1
[ "A006945", "A089105", "A089825" ]
[ "M4673" ]
N. J. A. Sloane
2025-04-05T10:27:31
oeisdata/seq/A006/A006945.seq
34f63ee91a3a8a5f628891ec238537c6
A006946
Independence number of De Bruijn graph of order n on two symbols.
[ "1", "2", "3", "7", "13", "28", "55", "114", "227", "466", "931", "1891", "3781" ]
[ "nonn", "more", "hard" ]
56
1
2
[ "A000031", "A006946", "A333077", "A333078" ]
[ "M0834" ]
N. J. A. Sloane, Herb Taylor
2025-02-16T08:32:31
oeisdata/seq/A006/A006946.seq
039d9144d1da744f97966569580023f7
A006947
Two-rowed truncated monotone triangles.
[ "2", "7", "35", "219", "1594", "12935", "113945", "1070324", "10586856", "109259633", "1168384157", "12877168147", "145656436074", "1685157199175", "19886174611045", "238819338399054", "2913166800256664", "36036122671902718", "451429953643336590", "5720172601392931006" ]
[ "nonn" ]
16
1
1
null
[ "M1797" ]
N. J. A. Sloane.
2017-09-05T03:42:20
oeisdata/seq/A006/A006947.seq
8d7c7d8981572d70ffa96f672381574b
A006948
Number of zero-entropy permutations of length n.
[ "1", "2", "4", "12", "30", "90", "244", "776", "2218", "6946", "20468" ]
[ "nonn", "more" ]
18
1
2
null
[ "M1255" ]
Ethan Coven (ecoven(AT)wesleyan.edu)
2023-01-01T04:28:03
oeisdata/seq/A006/A006948.seq
dc1e1a714d9ae9884e88a1a9ff51c0d0
A006949
A well-behaved cousin of the Hofstadter sequence: a(n) = a(n - 1 - a(n-1)) + a(n - 2 - a(n-2)) for n > 2 with a(0) = a(1) = a(2) = 1.
[ "1", "1", "1", "2", "2", "2", "3", "4", "4", "4", "4", "5", "6", "6", "7", "8", "8", "8", "8", "8", "9", "10", "10", "11", "12", "12", "12", "13", "14", "14", "15", "16", "16", "16", "16", "16", "16", "17", "18", "18", "19", "20", "20", "20", "21", "22", "22", "23", "24", "24", "24", "24", "25", "26", "26", "27", "28", "28", "28", "29", "30", "30", "31", "32", "32", "32", "32", "32", "32", "32", "33", "34", "34", "35", "36", "36" ]
[ "nonn" ]
91
0
4
[ "A006949", "A120511", "A240807", "A240808", "A241235", "A244478", "A244479", "A244483" ]
[ "M0230" ]
N. J. A. Sloane, Jeffrey Shallit
2024-01-29T01:52:58
oeisdata/seq/A006/A006949.seq
011571d52d7ba3df8af08060351db517
A006950
G.f.: Product_{k>=1} (1 + x^(2*k - 1)) / (1 - x^(2*k)).
[ "1", "1", "1", "2", "3", "4", "5", "7", "10", "13", "16", "21", "28", "35", "43", "55", "70", "86", "105", "130", "161", "196", "236", "287", "350", "420", "501", "602", "722", "858", "1016", "1206", "1431", "1687", "1981", "2331", "2741", "3206", "3740", "4368", "5096", "5922", "6868", "7967", "9233", "10670", "12306", "14193", "16357", "18803", "21581" ]
[ "nonn" ]
190
0
4
[ "A000122", "A000700", "A006950", "A010054", "A015128", "A046682", "A085642", "A106459", "A121373", "A163203", "A316384" ]
[ "M0524" ]
N. J. A. Sloane, Warren D. Smith
2025-03-19T13:19:53
oeisdata/seq/A006/A006950.seq
d412a96b00de4b04c36dabf8e8b4294a
A006951
Number of conjugacy classes in GL(n,2).
[ "1", "1", "3", "6", "14", "27", "60", "117", "246", "490", "1002", "1998", "4053", "8088", "16284", "32559", "65330", "130626", "261726", "523374", "1047690", "2095314", "4192479", "8384808", "16773552", "33546736", "67101273", "134202258", "268420086", "536839446", "1073710914", "2147420250", "4294904430", "8589807438" ]
[ "nonn" ]
75
0
3
[ "A006951", "A006952", "A049314", "A049315", "A049316", "A070933", "A100471", "A100883", "A218698", "A264685", "A264687", "A279784", "A279786", "A323433", "A323582", "A323583" ]
[ "M2577" ]
N. J. A. Sloane
2022-09-08T08:44:35
oeisdata/seq/A006/A006951.seq
ae5b6a501b9f0813942c2afbba87f64f
A006952
Number of conjugacy classes in GL(n,3).
[ "1", "2", "8", "24", "78", "232", "720", "2152", "6528", "19578", "58944", "176808", "531128", "1593288", "4781952", "14345792", "43043622", "129130584", "387411144", "1162232520", "3486755688", "10460266224", "31380972784", "94142915640", "282429275616", "847287817866", "2541865038832", "7625595108432" ]
[ "nonn" ]
50
0
2
[ "A006951", "A006952", "A049314", "A049315", "A049316", "A304082" ]
[ "M1842" ]
N. J. A. Sloane
2022-09-08T08:44:35
oeisdata/seq/A006/A006952.seq
f57e10df3c90d7fe9c6ab92a2acc79e5
A006953
a(n) = denominator of Bernoulli(2n)/(2n).
[ "12", "120", "252", "240", "132", "32760", "12", "8160", "14364", "6600", "276", "65520", "12", "3480", "85932", "16320", "12", "69090840", "12", "541200", "75852", "2760", "564", "2227680", "132", "6360", "43092", "6960", "708", "3407203800", "12", "32640", "388332", "120", "9372", "10087262640" ]
[ "nonn", "frac", "easy", "nice" ]
84
1
1
[ "A001067", "A006953" ]
[ "M2039" ]
Simon Plouffe and N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A006/A006953.seq
ae82d2678adddef7b721ba1e7fbe7848
A006954
Denominators of Bernoulli numbers B_0, B_1, B_2, B_4, B_6, ...
[ "1", "2", "6", "30", "42", "30", "66", "2730", "6", "510", "798", "330", "138", "2730", "6", "870", "14322", "510", "6", "1919190", "6", "13530", "1806", "690", "282", "46410", "66", "1590", "798", "870", "354", "56786730", "6", "510", "64722", "30", "4686", "140100870", "6", "30", "3318", "230010", "498", "3404310", "6", "61410", "272118", "1410", "6", "4501770" ]
[ "nonn", "frac" ]
33
0
2
[ "A000367", "A002445", "A006954", "A027762" ]
[ "M1689", "N0667" ]
N. J. A. Sloane, Simon Plouffe
2024-11-01T02:07:09
oeisdata/seq/A006/A006954.seq
50672ab4e2e24dd9d41ae06a5de9a78d
A006955
Denominator of (2n+1) B_{2n}, where B_n are the Bernoulli numbers.
[ "1", "2", "6", "6", "10", "6", "210", "2", "30", "42", "110", "6", "546", "2", "30", "462", "170", "6", "51870", "2", "330", "42", "46", "6", "6630", "22", "30", "798", "290", "6", "930930", "2", "102", "966", "10", "66", "1919190", "2", "30", "42", "76670", "6", "680862", "2", "690", "38874", "470", "6", "46410", "2", "330", "42", "106", "6", "1919190" ]
[ "nonn", "frac", "easy", "nice" ]
32
0
2
[ "A000367", "A002427", "A002445", "A006955", "A006956", "A050925", "A050932", "A123125" ]
[ "M1562" ]
Simon Plouffe and N. J. A. Sloane
2021-12-17T11:26:52
oeisdata/seq/A006/A006955.seq
2fa3b4711ed63fe786cd74024f5ae762
A006956
Denominator of (2n+1)(2n+2) B_{2n}, where B_n are the Bernoulli numbers. Also denominators of the asymptotic expansion of the polygamma function psi'''(z).
[ "1", "1", "1", "1", "3", "1", "1", "15", "1", "5", "21", "5", "1", "21", "1", "1", "231", "5", "1", "1365", "1", "55", "21", "1", "1", "663", "11", "5", "57", "5", "1", "15015", "1", "17", "483", "1", "11", "25935", "1", "5", "21", "935", "1", "7917", "1", "23", "19437", "5", "1", "3315", "1", "55", "21", "1", "1", "191919", "253", "2465", "21", "5", "1", "1734915", "1", "1", "17157", "17", "1" ]
[ "nonn", "frac" ]
18
3
5
[ "A002427", "A006955", "A006956", "A076549" ]
[ "M2211" ]
Simon Plouffe
2018-05-08T15:11:54
oeisdata/seq/A006/A006956.seq
e559bd80baf1aca50c0348928ee8ec4c
A006957
Self-convolution of numbers of preferential arrangements.
[ "1", "2", "7", "32", "185", "1310", "11067", "109148", "1234045", "15752858", "224169407", "3518636504", "60381131265", "1124390692886", "22577494959427", "486212633129300", "11177317486573445", "273173247028616594", "7072436847620016327", "193351544314753174736", "5565941751233499986185" ]
[ "nonn" ]
44
0
2
[ "A000670", "A006957", "A217388", "A217389" ]
null
N. J. A. Sloane
2024-12-27T13:35:45
oeisdata/seq/A006/A006957.seq
63e20883e87d43ec219bccc33b084808
A006958
Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused).
[ "1", "2", "4", "9", "20", "46", "105", "242", "557", "1285", "2964", "6842", "15793", "36463", "84187", "194388", "448847", "1036426", "2393208", "5526198", "12760671", "29466050", "68041019", "157115917", "362802072", "837759792", "1934502740", "4467033943", "10314998977", "23818760154", "55000815222", "127004500762" ]
[ "nonn", "nice" ]
160
1
2
[ "A006958", "A075125", "A161492", "A275761", "A275762", "A276994" ]
[ "M1175" ]
N. J. A. Sloane, Simon Plouffe
2025-04-02T05:14:30
oeisdata/seq/A006/A006958.seq
a1df2ab0bb636e720141d8a43bb8408c
A006959
Number of labeled M-type rooted trees on n nodes.
[ "1", "6", "65", "1092", "25272", "749034", "27108440", "1159194472", "57190952440", "3197759266112", "199831490658912", "13802087001056704", "1044075809166477232", "85847947926743165952", "7623428923066363040672", "727116625218755662644416" ]
[ "nonn", "eigen", "nice" ]
34
1
2
[ "A006959", "A052315" ]
[ "M4274" ]
Simon Plouffe and N. J. A. Sloane
2015-01-31T11:52:21
oeisdata/seq/A006/A006959.seq
e81d81a997584453b35963b27ad8f5c0
A006960
Reverse and Add! sequence starting with 196.
[ "196", "887", "1675", "7436", "13783", "52514", "94039", "187088", "1067869", "10755470", "18211171", "35322452", "60744805", "111589511", "227574622", "454050344", "897100798", "1794102596", "8746117567", "16403234045", "70446464506", "130992928913", "450822227944", "900544455998", "1800098901007", "8801197801088", "17602285712176" ]
[ "nonn", "base", "nice", "easy" ]
102
0
1
[ "A004086", "A006960", "A016016", "A023108", "A023109", "A033665", "A056964" ]
[ "M5410" ]
N. J. A. Sloane, Simon Plouffe
2025-02-16T08:32:31
oeisdata/seq/A006/A006960.seq
073de64866d32be493f030fb01b06c78
A006961
Number of mappings from n points to themselves with in-degree <= 2.
[ "1", "1", "3", "6", "15", "31", "75", "164", "388", "887", "2092", "4884", "11599", "27443", "65509", "156427", "375263", "901353", "2171313", "5237581", "12658815", "30633725", "74238228", "180106656", "437437445", "1063425655", "2587564434", "6301175326", "15356071604", "37448674536" ]
[ "nonn", "easy", "nice" ]
20
0
3
[ "A001190", "A006961" ]
[ "M2584" ]
Simon Plouffe
2015-12-04T02:48:19
oeisdata/seq/A006/A006961.seq
4f7187b6b8efaac4f51e2a9d2a309bc4
A006962
Supersingular primes of the elliptic curve X_0 (11).
[ "2", "19", "29", "199", "569", "809", "1289", "1439", "2539", "3319", "3559", "3919", "5519", "9419", "9539", "9929", "11279", "11549", "13229", "14489", "17239", "18149", "18959", "19319", "22279", "24359", "27529", "28789", "32999", "33029", "36559", "42899", "45259", "46219", "49529", "51169", "52999", "55259" ]
[ "nonn" ]
50
1
1
[ "A006571", "A006962" ]
[ "M2115" ]
N. J. A. Sloane
2018-01-16T02:37:32
oeisdata/seq/A006/A006962.seq
67bc0d1f4b79851eaf7d05be3e54a4bd
A006963
Number of planar embedded labeled trees with n nodes: (2*n-3)!/(n-1)! for n >= 2, a(1) = 1.
[ "1", "1", "3", "20", "210", "3024", "55440", "1235520", "32432400", "980179200", "33522128640", "1279935820800", "53970627110400", "2490952020480000", "124903451312640000", "6761440164390912000", "393008709555221760000", "24412776311194951680000", "1613955767240110694400000" ]
[ "nonn", "easy", "nice" ]
129
1
3
[ "A000407", "A001761", "A001813", "A006963", "A173333" ]
[ "M3076" ]
Simon Plouffe and N. J. A. Sloane
2024-01-19T08:18:55
oeisdata/seq/A006/A006963.seq
e6acf6859cb1cbf864451c56e1c00341
A006964
Number of directed rooted trees with n nodes.
[ "1", "3", "15", "82", "495", "3144", "20875", "142773", "1000131", "7136812", "51702231", "379234623", "2810874950", "21020047557", "158398829121", "1201617201230", "9169060501023", "70329406653879", "541949364313821", "4193569906262874", "32571403998781956", "253842927519362734", "1984442128649393178" ]
[ "nonn", "eigen" ]
56
1
2
[ "A006964", "A038059", "A242249" ]
[ "M2994" ]
Simon Plouffe
2019-01-23T02:33:05
oeisdata/seq/A006/A006964.seq
d2d204e8ee1efd7ce97cd37127e56a8d
A006965
Number of directed trees with n nodes.
[ "1", "2", "6", "25", "114", "591", "3298", "19532", "120687", "771373", "5061741", "33943662", "231751331", "1606587482", "11283944502", "80157645245", "575105238243", "4162624144308", "30365913761136", "223075674659696", "1649166676341180", "12262121068089094", "91649977839972636", "688288656744067230" ]
[ "nonn" ]
34
1
2
[ "A006965", "A038060", "A335362" ]
[ "M1677" ]
Simon Plouffe
2020-11-01T07:45:28
oeisdata/seq/A006/A006965.seq
e558d77162d8536ddaa261f16b766684
A006966
Number of lattices on n unlabeled nodes.
[ "1", "1", "1", "1", "2", "5", "15", "53", "222", "1078", "5994", "37622", "262776", "2018305", "16873364", "152233518", "1471613387", "15150569446", "165269824761", "1901910625578", "23003059864006" ]
[ "nonn", "hard", "more", "nice", "core" ]
72
0
5
[ "A006966", "A006981", "A006982", "A055512", "A058116", "A058142" ]
[ "M1486" ]
N. J. A. Sloane
2025-01-08T09:32:00
oeisdata/seq/A006/A006966.seq
a7fc17b8accf3b332593944c4bb522de
A006967
Number of graceful permutations of length n.
[ "1", "1", "2", "4", "4", "8", "24", "32", "40", "120", "296", "648", "1328", "3200", "9912", "25592", "55920", "143192", "510696", "1451296", "3497344", "10451824", "38570704", "118914992", "315235872", "1014824752", "3963684496", "13166130152", "37846301904", "130507967088", "533318630936", "1884550215976", "5800121391936" ]
[ "nonn", "nice", "hard" ]
91
0
3
[ "A006967", "A084894" ]
[ "M3229" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A006/A006967.seq
2dba524ca87205e8cfe234b87acf64b7
A006968
Number of letters in Roman numeral representation of n.
[ "1", "2", "3", "2", "1", "2", "3", "4", "2", "1", "2", "3", "4", "3", "2", "3", "4", "5", "3", "2", "3", "4", "5", "4", "3", "4", "5", "6", "4", "3", "4", "5", "6", "5", "4", "5", "6", "7", "5", "2", "3", "4", "5", "4", "3", "4", "5", "6", "4", "1", "2", "3", "4", "3", "2", "3", "4", "5", "3", "2", "3", "4", "5", "4", "3", "4", "5", "6", "4", "3", "4", "5", "6", "5", "4", "5", "6", "7", "5", "4", "5", "6", "7", "6", "5", "6", "7", "8", "6", "2", "3", "4", "5", "4", "3", "4", "5", "6", "4", "1", "2", "3", "4", "3", "2" ]
[ "nonn", "base", "nice", "easy" ]
64
1
2
[ "A002963", "A006968", "A036746", "A036786", "A036787", "A036788", "A061493", "A092196", "A160676", "A160677", "A199921" ]
[ "M0417" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A006/A006968.seq
28f40a1641f7da60bb2432df2633aa8e
A006969
Number of characters in French ordinal numbers.
[ "7", "8", "9", "9", "9", "7", "8", "8", "8", "7", "7", "8", "9", "11", "9", "8", "12", "12", "12", "9", "15", "14", "15", "15", "15", "13", "14", "14", "14", "9", "16", "15", "16", "16", "16", "14", "15", "15", "15", "11", "18", "17", "18", "18", "18", "16", "17", "17", "17", "12", "19", "18" ]
[ "nonn", "word" ]
45
1
1
[ "A006944", "A006969", "A007005", "A167507", "A196278" ]
[ "M4334" ]
N. J. A. Sloane, Simon Plouffe
2021-08-14T15:11:04
oeisdata/seq/A006/A006969.seq
5a789dcb5f0c4b6918c62c122ff36a0e
A006970
Euler pseudoprimes: composite numbers n such that 2^((n-1)/2) == +-1 (mod n).
[ "341", "561", "1105", "1729", "1905", "2047", "2465", "3277", "4033", "4681", "5461", "6601", "8321", "8481", "10261", "10585", "12801", "15709", "15841", "16705", "18705", "25761", "29341", "30121", "31621", "33153", "34945", "41041", "42799" ]
[ "nonn", "nice" ]
62
1
1
null
[ "M5442" ]
N. J. A. Sloane, Robert G. Wilson v, Richard Pinch
2025-02-16T08:32:31
oeisdata/seq/A006/A006970.seq
a380c405b8975c3d931bf7ec46071245
A006971
Composite numbers k such that k == +-1 (mod 8) and 2^((k-1)/2) == 1 (mod k).
[ "561", "1105", "1729", "1905", "2047", "2465", "4033", "4681", "6601", "8321", "8481", "10585", "12801", "15841", "16705", "18705", "25761", "30121", "33153", "34945", "41041", "42799", "46657", "52633", "62745", "65281", "74665", "75361", "85489", "87249", "90751", "113201", "115921", "126217", "129921", "130561", "149281", "158369" ]
[ "nonn" ]
37
1
1
[ "A001567", "A006971", "A047713", "A244626", "A244628", "A270697", "A270698" ]
[ "M5461" ]
Richard Pinch
2023-11-06T07:17:14
oeisdata/seq/A006/A006971.seq
45f1542887a4764c5de7a84f4950b7bc
A006972
Lucas-Carmichael numbers: squarefree composite numbers k such that p | k => p+1 | k+1.
[ "399", "935", "2015", "2915", "4991", "5719", "7055", "8855", "12719", "18095", "20705", "20999", "22847", "29315", "31535", "46079", "51359", "60059", "63503", "67199", "73535", "76751", "80189", "81719", "88559", "90287", "104663", "117215", "120581", "147455", "152279", "155819", "162687", "191807", "194327", "196559", "214199" ]
[ "nonn" ]
113
1
1
[ "A006972", "A024556", "A056729", "A216925", "A216926", "A216927", "A216929", "A217002", "A217003", "A217091", "A322702" ]
[ "M5450" ]
Richard Pinch and Jeffrey Shallit
2024-03-29T11:43:46
oeisdata/seq/A006/A006972.seq
c10a4c3c28ea82e49e6e58c456445333
A006973
Dimensions of representations by Witt vectors.
[ "0", "1", "2", "9", "24", "130", "720", "8505", "35840", "412776", "3628800", "42030450", "479001600", "7019298000", "82614884352", "1886805545625", "20922789888000", "374426276224000", "6402373705728000", "134987215801622184", "2379913632645120000" ]
[ "nonn", "easy", "nice" ]
55
1
3
[ "A006973", "A137852", "A156792" ]
[ "M1921" ]
Simon Plouffe
2021-06-12T23:20:21
oeisdata/seq/A006/A006973.seq
005fa66e0576619166d043e6ca935756
A006974
Coefficients of Chebyshev T polynomials: a(n) = A053120(n+8, n), n >= 0.
[ "1", "9", "50", "220", "840", "2912", "9408", "28800", "84480", "239360", "658944", "1770496", "4659200", "12042240", "30638080", "76873728", "190513152", "466944000", "1133117440", "2724986880", "6499598336", "15386804224", "36175872000", "84515225600", "196293427200", "453437816832" ]
[ "nonn", "easy" ]
53
0
2
[ "A003472", "A006974", "A039991", "A053120" ]
[ "M4631" ]
Simon Plouffe
2024-04-27T17:21:36
oeisdata/seq/A006/A006974.seq
828458a6fda4622c301f3098cbe4eeaa
A006975
Negated coefficients of Chebyshev T polynomials: a(n) = -A053120(n+10, n), n >= 0.
[ "1", "11", "72", "364", "1568", "6048", "21504", "71808", "228096", "695552", "2050048", "5870592", "16400384", "44843008", "120324096", "317521920", "825556992", "2118057984", "5369233408", "13463453696", "33426505728", "82239815680", "200655503360", "485826232320" ]
[ "nonn", "easy" ]
66
0
2
[ "A006975", "A039991", "A053120", "A054849", "A069038" ]
[ "M4796" ]
Simon Plouffe
2024-06-27T04:45:47
oeisdata/seq/A006/A006975.seq
afbb0a82e04f864fef269871527f89d0
A006976
Coefficients of Chebyshev T polynomials: a(n) = A053120(n+12, n), n >= 0.
[ "1", "13", "98", "560", "2688", "11424", "44352", "160512", "549120", "1793792", "5637632", "17145856", "50692096", "146227200", "412778496", "1143078912", "3111714816", "8341487616", "22052208640", "57567870976", "148562247680", "379364311040", "959384125440" ]
[ "nonn", "easy" ]
54
0
2
[ "A002409", "A006976", "A039991", "A053120" ]
[ "M4907" ]
Simon Plouffe
2024-09-26T18:56:14
oeisdata/seq/A006/A006976.seq
c93acec8fb2a64829e64ae908ab5068c
A006977
Cellular automaton with Rule 230: 000, 001, 010, 011, ..., 111 -> 0,1,1,0,0,1,1,1.
[ "1", "3", "5", "15", "23", "59", "93", "239", "375", "955", "1501", "3823", "6007", "15291", "24029", "61167", "96119", "244667", "384477", "978671", "1537911", "3914683", "6151645", "15658735", "24606583", "62634939", "98426333", "250539759", "393705335", "1002159035", "1574821341", "4008636143", "6299285367" ]
[ "nonn", "easy" ]
50
0
2
[ "A006977", "A266178", "A266179", "A266180", "A292680", "A292681", "A292682" ]
[ "M2497" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A006/A006977.seq
86c42da865fa8b651e185242d61cbcdd
A006978
Successive states of the Rule 110 cellular automaton defined by 000, 001, 010, 011, ..., 111 -> 0,1,1,1,0,1,1,0 when started with a single ON cell.
[ "1", "3", "7", "13", "31", "49", "115", "215", "509", "775", "1805", "3359", "7985", "12659", "29655", "54909", "130759", "197581", "460383", "855793", "2038675", "3227319", "7562237", "14149127", "33304077", "50625055", "118279729", "220060275", "523730647", "830325757", "1942439431", "3595423245", "8571017759", "12951092785" ]
[ "nonn" ]
36
1
2
[ "A006978", "A070887", "A117999" ]
[ "M2642" ]
N. J. A. Sloane.
2025-02-16T08:32:31
oeisdata/seq/A006/A006978.seq
711f5dc24631023dedf3ab1c16b4edc4
A006979
a(n) is the number of compositions of n in which the maximum part size is 5.
[ "0", "0", "0", "0", "0", "1", "2", "5", "12", "28", "63", "139", "303", "653", "1394", "2953", "6215", "13008", "27095", "56201", "116143", "239231", "491326", "1006420", "2056633", "4193706", "8534653", "17337764", "35162804", "71205504", "143990366", "290795624", "586566102", "1181834852", "2378701408" ]
[ "nonn" ]
26
0
7
[ "A006979", "A048003" ]
[ "M1410" ]
Simon Plouffe
2023-11-20T15:05:06
oeisdata/seq/A006/A006979.seq
28d9e5b38894cd4d9542abc3ac194347
A006980
Compositions: 6th column of A048004.
[ "1", "2", "5", "12", "28", "64", "143", "315", "687", "1485", "3186", "6792", "14401", "30391", "63872", "133751", "279177", "581040", "1206151", "2497895", "5161982", "10646564", "21919161", "45052841", "92461171", "189489255", "387830160", "792810956", "1618840800", "3301999647" ]
[ "nonn", "easy" ]
30
6
2
[ "A006980", "A048004" ]
[ "M1411" ]
Simon Plouffe
2024-02-07T09:31:32
oeisdata/seq/A006/A006980.seq
becb304863f6dc667ff1859a4edf00e5
A006981
a(n) is the number of unlabeled modular lattices on n nodes.
[ "1", "1", "1", "1", "2", "4", "8", "16", "34", "72", "157", "343", "766", "1718", "3899", "8898", "20475", "47321", "110024", "256791", "601991", "1415768", "3340847", "7904700", "18752943", "44588803", "106247120", "253644319", "606603025", "1453029516", "3485707007", "8373273835", "20139498217", "48496079939", "116905715114", "282098869730" ]
[ "nonn" ]
77
0
5
[ "A006966", "A006981", "A006982", "A342132" ]
[ "M1133" ]
N. J. A. Sloane
2021-04-18T01:48:00
oeisdata/seq/A006/A006981.seq
5c0bdce210a1900d2d6eb4534d5f3316
A006982
Number of unlabeled distributive lattices on n nodes.
[ "1", "1", "1", "1", "2", "3", "5", "8", "15", "26", "47", "82", "151", "269", "494", "891", "1639", "2978", "5483", "10006", "18428", "33749", "62162", "114083", "210189", "386292", "711811", "1309475", "2413144", "4442221", "8186962", "15077454", "27789108", "51193086", "94357143", "173859936", "320462062", "590555664", "1088548290", "2006193418", "3697997558", "6815841849", "12563729268", "23157428823", "42686759863", "78682454720", "145038561665", "267348052028", "492815778109", "908414736485" ]
[ "hard", "nonn", "nice" ]
56
0
5
[ "A006966", "A006981", "A006982", "A343161" ]
[ "M0700" ]
N. J. A. Sloane
2021-09-18T08:56:15
oeisdata/seq/A006/A006982.seq
72dcb626f511133eeaf00c8a86591790
A006983
Number of simple perfect squared squares of order n up to symmetry.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "8", "12", "26", "160", "441", "1152", "3001", "7901", "20566", "54541", "144161", "378197", "990981", "2578081", "6674067", "17086918" ]
[ "nonn", "hard", "more", "nice" ]
177
1
22
[ "A002839", "A002881", "A002962", "A006983", "A014530", "A129947", "A181340", "A181735", "A217149", "A217155", "A217156", "A228953", "A349205", "A349206", "A349207", "A349208", "A349209", "A349210" ]
[ "M4482" ]
N. J. A. Sloane
2025-03-13T09:45:49
oeisdata/seq/A006/A006983.seq
6413fec3bbbbb531929b19bc7bdccc98
A006984
Greatest minimal norm of sublattice of index n in hexagonal lattice.
[ "1", "1", "3", "4", "3", "4", "7", "7", "9", "7", "7", "12", "13", "12", "13", "16", "13", "13", "19", "16", "21", "19", "19", "21", "25", "21", "27", "28", "21", "27", "31", "28", "27", "28", "31", "36", "37", "31", "39", "37", "37", "36", "43", "39", "39", "39", "39", "48", "49", "43", "43" ]
[ "nonn", "nice" ]
25
1
3
[ "A001615", "A003050", "A003051", "A006984" ]
[ "M2298" ]
N. J. A. Sloane, Mira Bernstein
2023-09-19T05:01:22
oeisdata/seq/A006/A006984.seq
0b78278579f3963c62fdafc24e978aa5
A006985
Fibonacci tower: a(n) = F(a(n-1)+2) (there is no room for next term).
[ "1", "2", "3", "5", "13", "610" ]
[ "nonn", "nice", "easy" ]
26
0
2
null
[ "M0742" ]
N. J. A. Sloane
2021-04-10T22:18:33
oeisdata/seq/A006/A006985.seq
61c9a19a6bb21223a5d8d62592f3f065
A006986
Erroneous version of A038119.
[ "1", "1", "2", "7", "23", "114", "625", "3974" ]
[ "dead" ]
4
1
3
null
null
null
1999-12-11T03:00:00
oeisdata/seq/A006/A006986.seq
23d451de88ba5f802ef908e3d1161d32
A006987
Binomial coefficients: C(n,k), 2 <= k <= n-2, sorted, duplicates removed.
[ "6", "10", "15", "20", "21", "28", "35", "36", "45", "55", "56", "66", "70", "78", "84", "91", "105", "120", "126", "136", "153", "165", "171", "190", "210", "220", "231", "252", "253", "276", "286", "300", "325", "330", "351", "364", "378", "406", "435", "455", "462", "465", "495", "496", "528", "560", "561", "595", "630", "666", "680", "703", "715", "741", "780", "792", "816", "820" ]
[ "nonn" ]
70
1
1
[ "A002808", "A006987", "A007318" ]
[ "M4084" ]
N. J. A. Sloane, Robert G. Wilson v
2018-12-13T02:47:21
oeisdata/seq/A006/A006987.seq
acb13de87737488dc9a5ab1c2d31cd68
A006988
a(n) = (10^n)-th prime.
[ "2", "29", "541", "7919", "104729", "1299709", "15485863", "179424673", "2038074743", "22801763489", "252097800623", "2760727302517", "29996224275833", "323780508946331", "3475385758524527", "37124508045065437", "394906913903735329", "4185296581467695669", "44211790234832169331" ]
[ "nonn", "nice" ]
97
0
1
[ "A006880", "A006988", "A033844", "A099260", "A119780", "A274767" ]
[ "M2151" ]
N. J. A. Sloane, Robert G. Wilson v
2025-02-16T08:32:31
oeisdata/seq/A006/A006988.seq
97997889552ae0517424749bd13fd701
A006989
Log of g.f. of numbers of preferential arrangements.
[ "1", "0", "2", "4", "34", "196", "1826", "17172", "199074", "2510116", "35862562", "559572916", "9577862306", "177417693636", "3546104002338", "75961485384532", "1737273637523362", "42235881659123812", "1087865420946370082", "29589907884231535860", "847576876148087333538", "25501591020532799366404" ]
[ "nonn" ]
25
0
3
[ "A000670", "A006989" ]
null
N. J. A. Sloane
2021-01-05T03:01:58
oeisdata/seq/A006/A006989.seq
ab67f2aac59605cb7c3e0c96d1f1ce22
A006990
Largest prime <= n!.
[ "2", "5", "23", "113", "719", "5039", "40289", "362867", "3628789", "39916787", "479001599", "6227020777", "87178291199", "1307674367953", "20922789887947", "355687428095941", "6402373705727959", "121645100408831899", "2432902008176639969", "51090942171709439969", "1124000727777607679927" ]
[ "nonn" ]
37
2
1
[ "A000142", "A006990", "A007917" ]
[ "M1541" ]
N. J. A. Sloane, Robert G. Wilson v
2017-11-08T19:34:24
oeisdata/seq/A006/A006990.seq
a1fd38fd3d9421e75f8123979227b5d8
A006991
Primitive congruent numbers.
[ "5", "6", "7", "13", "14", "15", "21", "22", "23", "29", "30", "31", "34", "37", "38", "39", "41", "46", "47", "53", "55", "61", "62", "65", "69", "70", "71", "77", "78", "79", "85", "86", "87", "93", "94", "95", "101", "102", "103", "109", "110", "111", "118", "119", "127", "133", "134", "137", "138", "141", "142", "143", "145", "149", "151", "154", "157", "158", "159" ]
[ "nonn" ]
108
1
1
[ "A003273", "A006991", "A072068", "A072069", "A072070", "A072071" ]
[ "M3748" ]
N. J. A. Sloane, Robert G. Wilson v
2024-08-06T13:03:56
oeisdata/seq/A006/A006991.seq
ba03dc03df9ce2d34a3935b0af627d58
A006992
Bertrand primes: a(n) is largest prime < 2*a(n-1) for n > 1, with a(1) = 2.
[ "2", "3", "5", "7", "13", "23", "43", "83", "163", "317", "631", "1259", "2503", "5003", "9973", "19937", "39869", "79699", "159389", "318751", "637499", "1274989", "2549951", "5099893", "10199767", "20399531", "40799041", "81598067", "163196129", "326392249", "652784471", "1305568919", "2611137817" ]
[ "nonn", "nice" ]
118
1
1
[ "A006992", "A007917", "A055496", "A163961", "A185231", "A229607", "A295262" ]
[ "M0675" ]
N. J. A. Sloane, Robert G. Wilson v
2025-02-16T08:32:31
oeisdata/seq/A006/A006992.seq
f839490160974acda62da40ecd1f89cc
A006993
n! in base n.
[ "1", "10", "20", "120", "440", "3200", "20460", "116600", "612700", "3628800" ]
[ "nonn", "base", "fini", "full" ]
26
1
2
null
[ "M4684" ]
N. J. A. Sloane, L. J. Upton
2017-11-08T19:31:16
oeisdata/seq/A006/A006993.seq
6d594233395dda8137ed14a800217ca9
A006994
Number of letters in n (in Russian).
[ "4", "3", "3", "6", "4", "5", "4", "6", "6", "6", "11", "10", "10", "12", "10", "11", "10", "12", "12", "8", "12", "11", "11", "14", "12", "13", "12", "14", "14", "8", "12", "11", "11", "14", "12", "13", "12", "14", "14", "5", "9", "8", "8", "11", "9", "10", "9", "11", "11", "9", "13", "12", "12" ]
[ "nonn", "word" ]
21
1
1
null
[ "M3208" ]
Mira Bernstein
2022-01-21T00:46:34
oeisdata/seq/A006/A006994.seq
a4c88ac9f91519e2493c1975bda3c4d6
A006995
Binary palindromes: numbers whose binary expansion is palindromic.
[ "0", "1", "3", "5", "7", "9", "15", "17", "21", "27", "31", "33", "45", "51", "63", "65", "73", "85", "93", "99", "107", "119", "127", "129", "153", "165", "189", "195", "219", "231", "255", "257", "273", "297", "313", "325", "341", "365", "381", "387", "403", "427", "443", "455", "471", "495", "511", "513", "561", "585", "633", "645", "693", "717", "765", "771", "819", "843" ]
[ "nonn", "base", "easy", "nice", "hear" ]
240
1
3
[ "A000051", "A002113", "A005408", "A006995", "A016041", "A048700", "A048701", "A057148", "A117697", "A145799", "A154809", "A164126", "A178225", "A206913", "A206914", "A241491", "A244162", "A261678", "A262556" ]
[ "M2403" ]
N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein, L. J. Upton
2024-06-11T01:41:24
oeisdata/seq/A006/A006995.seq
e47c9a75926658df97f455db36f5f332
A006996
a(n) = C(2n,n) mod 3.
[ "1", "2", "0", "2", "1", "0", "0", "0", "0", "2", "1", "0", "1", "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "1", "0", "1", "2", "0", "0", "0", "0", "1", "2", "0", "2", "1", "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", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "1", "0", "1", "2", "0", "0", "0", "0", "1", "2", "0", "2", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "nonn", "easy" ]
42
0
2
null
[ "M0021" ]
N. J. A. Sloane, James Propp
2024-07-15T05:33:27
oeisdata/seq/A006/A006996.seq
10eb3709838e33e423471078e9d6a133
A006997
Partitioning integers to avoid arithmetic progressions of length 3.
[ "0", "0", "1", "0", "0", "1", "1", "2", "2", "0", "0", "1", "0", "0", "1", "1", "2", "2", "1", "2", "2", "3", "3", "4", "3", "3", "4", "0", "0", "1", "0", "0", "1", "1", "2", "2", "0", "0", "1", "0", "0", "1", "1", "2", "2", "1", "2", "2", "3", "3", "4", "3", "3", "4", "1", "2", "2", "3", "3", "4", "3", "3", "4", "4", "5", "5", "4", "5", "5", "6", "6", "7", "4", "5", "5", "4", "5", "5", "6", "6", "7", "0", "0", "1", "0", "0", "1" ]
[ "nonn", "easy" ]
43
0
8
[ "A005836", "A006997", "A100480" ]
[ "M0185" ]
N. J. A. Sloane, James Propp
2025-04-09T14:14:57
oeisdata/seq/A006/A006997.seq
86e3a6671bf6b76ad86b9ca2029dab8c
A006998
Partitioning integers to avoid arithmetic progressions of length 3.
[ "0", "1", "2", "4", "6", "8", "12", "14", "16", "24", "26", "28", "32", "40", "48", "52", "54", "56", "64", "72", "80", "96", "100", "104", "108", "110", "112", "128", "136", "144", "160", "176", "192", "200", "204", "208", "216", "218", "220", "224", "240", "256", "272", "280", "288", "320", "336", "352", "384", "392", "400", "408", "412", "416", "432", "434", "436", "440" ]
[ "nonn", "look" ]
24
0
3
[ "A006997", "A006998", "A006999" ]
[ "M0990" ]
N. J. A. Sloane, James Propp
2021-06-10T16:02:41
oeisdata/seq/A006/A006998.seq
4a2d4e49d322564dc3a2ff2b9b5eb81b
A006999
Partitioning integers to avoid arithmetic progressions of length 3.
[ "0", "1", "2", "4", "7", "11", "17", "26", "40", "61", "92", "139", "209", "314", "472", "709", "1064", "1597", "2396", "3595", "5393", "8090", "12136", "18205", "27308", "40963", "61445", "92168", "138253", "207380", "311071", "466607", "699911", "1049867", "1574801", "2362202", "3543304", "5314957", "7972436" ]
[ "nonn", "easy" ]
63
0
3
[ "A003312", "A005428", "A006999", "A016789", "A061418", "A061419", "A073941", "A083286", "A152009" ]
[ "M1047" ]
N. J. A. Sloane, D. R. Hofstadter, and James Propp, Jul 15 1977
2023-07-30T18:46:38
oeisdata/seq/A006/A006999.seq
f57c25d12d0eed38969acea686367df0
A007000
Number of partitions of n into Fibonacci parts (with 2 types of 1).
[ "1", "2", "4", "7", "11", "17", "25", "35", "49", "66", "88", "115", "148", "189", "238", "297", "368", "451", "550", "665", "799", "956", "1136", "1344", "1583", "1855", "2167", "2520", "2920", "3373", "3882", "4455", "5097", "5814", "6617", "7509", "8502", "9604", "10823", "12173", "13662", "15302", "17110", "19093", "21271", "23657", "26266" ]
[ "nonn" ]
45
0
2
[ "A000045", "A003107", "A007000" ]
[ "M1045" ]
N. J. A. Sloane, Mira Bernstein
2023-10-29T21:51:01
oeisdata/seq/A007/A007000.seq
612ec73cd2126416db7f564c94f49fb9