Datasets:
christopher
/
oeis

Dataset card Data Studio Files
xet
Community
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348
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score
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2.31k
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int64
-14,827
666,262,453B
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635M
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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
32
A006801
Number of 2-dimensional directed compact animals of size n.
[ "1", "2", "5", "13", "34", "90", "239", "635", "1689", "4494", "11960", "31832", "84727", "225524", "600302", "1597904", "4253371", "11321838", "30137079", "80220557", "213535632", "568401380", "1513003529" ]
[ "nonn" ]
17
1
2
[ "A006801", "A187276" ]
[ "M1440" ]
N. J. A. Sloane.
2018-01-08T01:58:27
oeisdata/seq/A006/A006801.seq
e9f5abe5da9b14854c75e19bbc51691e
A006802
Log of e.g.f. for trees A000055(n-1).
[ "1", "0", "0", "0", "1", "-4", "12", "-30", "70", "-282", "2195", "-17680", "122815", "-752054", "4449773", "-30013564", "259850583", "-2638753310", "27217133989", "-269838173334", "2620588539506", "-26487374528378", "295615679025264", "-3658718423476721" ]
[ "sign" ]
9
1
6
[ "A000055", "A006802" ]
null
N. J. A. Sloane.
2012-03-30T16:45:04
oeisdata/seq/A006/A006802.seq
88751d9c08025a5f287b9e8a5fdfd333
A006803
Percolation series for hexagonal lattice.
[ "1", "0", "0", "-1", "0", "-3", "1", "-9", "6", "-29", "27", "-99", "112", "-351", "450", "-1275", "1782", "-4704", "6998", "-17531", "27324", "-65758", "106211", "-247669", "411291", "-935107", "1587391", "-3535398", "6108103", "-13373929", "23438144", "-50592067", "89703467", "-191306745", "342473589" ]
[ "sign" ]
24
0
6
[ "A006803", "A006809" ]
[ "M2232" ]
N. J. A. Sloane
2024-02-11T06:44:53
oeisdata/seq/A006/A006803.seq
58b6e7847db6d02759572a95c2b7e8e1
A006804
Percolation series for cubic lattice.
[ "3", "-3", "12", "-21", "55", "-114", "273", "-611", "1437", "-3300", "7714", "-17913" ]
[ "sign", "more" ]
10
0
1
null
[ "M2291" ]
N. J. A. Sloane.
2019-10-04T08:38:38
oeisdata/seq/A006/A006804.seq
5fa3d448d742c0dcf2ba120d6c1273d9
A006805
Percolation series for b.c.c. lattice.
[ "4", "-4", "0", "22", "-44", "32", "100", "-352", "492", "166", "-2268", "4914", "-3212", "-11083" ]
[ "sign", "more" ]
12
0
1
null
[ "M3219" ]
N. J. A. Sloane.
2019-10-04T08:33:29
oeisdata/seq/A006/A006805.seq
f89c1bdabacc6462cff932a491a111f9
A006806
Percolation series for f.c.c. lattice.
[ "6", "-6", "0", "0", "8", "27", "-78", "45", "21", "62", "0", "-584", "903", "-155", "66", "-998", "-2357", "9803", "-8273" ]
[ "sign", "more" ]
12
0
1
null
[ "M4054" ]
N. J. A. Sloane.
2019-10-04T08:11:50
oeisdata/seq/A006/A006806.seq
0fd61f153d1a0438c6408f5b7389e099
A006807
Percolation series for directed hexagonal lattice.
[ "3", "3", "6", "15", "26", "39", "192", "45" ]
[ "nonn", "more" ]
13
0
1
null
[ "M2283" ]
N. J. A. Sloane.
2019-10-04T09:09:26
oeisdata/seq/A006/A006807.seq
c639e82ff8c5b59ef87891abcb68dc86
A006808
Essentially a duplicate of A006727.
[ "2", "4", "8", "15", "28", "50", "90", "156" ]
[ "dead" ]
13
1
1
null
[ "M1104" ]
null
2018-09-05T05:49:23
oeisdata/seq/A006/A006808.seq
c0ba95da40065736869abceccc248635
A006809
Bond percolation series for hexagonal lattice.
[ "1", "3", "9", "25", "66", "168", "417", "1014", "2427", "5737", "13412", "31088", "71506", "163378", "371272", "839248", "1889019", "4235082", "9459687", "21067566", "46769977", "103574916", "228808544", "504286803", "1109344029", "2435398781", "5337497418", "11678931098" ]
[ "sign" ]
26
0
2
[ "A006736", "A006803", "A006809" ]
[ "M2796", "M2797" ]
N. J. A. Sloane, Simon Plouffe
2024-02-10T09:23:47
oeisdata/seq/A006/A006809.seq
eef8bb16a677b76e7dcc6ccdd5e2db5a
A006810
Bond percolation series for mean cluster size on directed cubic lattice.
[ "1", "3", "9", "27", "78", "225", "633", "1785", "4944", "13742", "37686", "103767", "282425", "772719" ]
[ "nonn", "more" ]
17
0
2
[ "A006727", "A006804", "A006809", "A006810", "A006811", "A006812", "A006813" ]
[ "M2805" ]
N. J. A. Sloane
2023-05-12T09:09:34
oeisdata/seq/A006/A006810.seq
1b4ac199a5d62469687964fb69e3dab9
A006811
Percolation series for b.c.c. lattice.
[ "4", "16", "64", "246", "944", "3532", "13252", "48825" ]
[ "nonn", "more" ]
13
1
1
null
[ "M3516" ]
N. J. A. Sloane.
2019-10-04T09:05:09
oeisdata/seq/A006/A006811.seq
e85924c2fb502e7ee60449ba013610a0
A006812
Percolation series for f.c.c. lattice.
[ "6", "36", "208", "1171", "6474", "35324", "190853" ]
[ "nonn", "more" ]
12
1
1
null
[ "M4221" ]
N. J. A. Sloane.
2019-10-04T08:08:17
oeisdata/seq/A006/A006812.seq
171a923729e24d5b6c27813119c46540
A006813
Percolation series for directed hexagonal lattice.
[ "3", "9", "21", "48", "105", "219", "459", "936" ]
[ "nonn", "more" ]
12
1
1
null
[ "M2778" ]
N. J. A. Sloane.
2019-10-04T08:33:09
oeisdata/seq/A006/A006813.seq
eeae546e7757bf66b3ca604862eac61b
A006814
Related to self-avoiding walks on square lattice.
[ "1", "6", "21", "76", "249", "814", "2521", "7824", "23473", "70590", "207345", "610356", "1765959", "511006", "14643993", "41958852", "118976633", "337823486", "951157365", "2681163492", "7505218171", "21030311474" ]
[ "nonn", "walk" ]
21
1
2
[ "A006814", "A006815", "A006816" ]
[ "M4145" ]
N. J. A. Sloane
2017-10-18T02:42:46
oeisdata/seq/A006/A006814.seq
e1eb09424116ebb2c833e7043629814f
A006815
Related to self-avoiding walks on square lattice.
[ "1", "6", "23", "84", "283", "930", "2921", "9096", "27507", "82930", "244819", "722116", "2096603", "6087290", "17458887", "50090544", "142317089", "404543142" ]
[ "nonn", "walk", "more" ]
15
1
2
[ "A006814", "A006815", "A006816" ]
[ "M4157" ]
N. J. A. Sloane
2017-08-09T21:47:28
oeisdata/seq/A006/A006815.seq
8b0abd14fa4d5546f6b4e1363278fdb6
A006816
Related to self-avoiding walks on square lattice.
[ "1", "6", "29", "108", "393", "1298", "4271", "13312", "41469", "125042", "376747", "1111144", "3274475", "9505054", "27573041", "79086964", "226727667", "644301026", "1830188555", "5162408200", "14556754485", "40811281170" ]
[ "nonn", "walk" ]
27
1
2
[ "A001411", "A006814", "A006815", "A006816" ]
[ "M4187" ]
N. J. A. Sloane
2018-12-30T03:43:13
oeisdata/seq/A006/A006816.seq
f8d72e19a07011e95e5e413f226805bc
A006817
Trails of length n on square lattice.
[ "1", "4", "12", "36", "108", "316", "916", "2628", "7500", "21268", "60092", "169092", "474924", "1329188", "3715244", "10359636", "28856252", "80220244", "222847804", "618083972", "1713283628", "4742946484", "13123882524", "36274940740", "100226653420", "276669062116", "763482430316", "2105208491748", "5803285527724" ]
[ "nonn", "walk" ]
28
0
2
[ "A001997", "A006817", "A006818", "A006819", "A006851" ]
[ "M3450" ]
N. J. A. Sloane
2023-05-12T15:56:56
oeisdata/seq/A006/A006817.seq
136619dbd337f90ac2b7dd65eca32659
A006818
Trails of length n on hexagonal lattice.
[ "1", "6", "30", "150", "738", "3570", "17118", "81498", "385710", "1817046", "8528478", "39903462", "186198642", "866861394", "4027766490", "18681900270", "86518735722", "400136695074", "1848320799438", "8528448008214" ]
[ "nonn", "walk", "more" ]
19
0
2
null
[ "M4203" ]
N. J. A. Sloane.
2020-08-15T08:12:46
oeisdata/seq/A006/A006818.seq
5a477e4478adaef23c4bfadc40fe513f
A006819
Trails of length n on cubic lattice.
[ "1", "6", "30", "150", "750", "3726", "18438", "90966", "447918", "2201622", "10809006", "52999446", "259668942", "1271054982", "6218232414", "30399142614" ]
[ "nonn", "walk" ]
10
0
2
null
[ "M4204" ]
N. J. A. Sloane.
2015-07-08T04:01:57
oeisdata/seq/A006/A006819.seq
904096c43a6593beb325d1f61e7228eb
A006820
Number of connected regular simple graphs of degree 4 (or quartic graphs) with n nodes.
[ "1", "0", "0", "0", "0", "1", "1", "2", "6", "16", "59", "265", "1544", "10778", "88168", "805491", "8037418", "86221634", "985870522", "11946487647", "152808063181", "2056692014474", "29051272833609", "429668180677439", "6640165204855036", "107026584471569605", "1796101588825595008", "31333997930603283531", "567437240683788292989" ]
[ "nonn", "nice", "hard" ]
91
0
8
[ "A002851", "A005177", "A006820", "A006821", "A006822", "A014377", "A014378", "A014381", "A014382", "A014384", "A033301", "A033483", "A033886", "A058343", "A058348", "A068934", "A085549", "A129417", "A184943", "A184944", "A184945" ]
[ "M1617" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006820.seq
f3e82bee0828e6c63010a8706ab362ba
A006821
Number of connected regular graphs of degree 5 (or quintic graphs) with 2n nodes.
[ "1", "0", "0", "1", "3", "60", "7848", "3459383", "2585136675", "2807105250897", "4221456117363365", "8516994770090547979", "22470883218081146186209", "75883288444204588922998674", "322040154704144697047052726990" ]
[ "nonn", "nice", "hard", "more" ]
49
0
5
[ "A002851", "A005177", "A006820", "A006821", "A006822", "A014377", "A014378", "A014381", "A014382", "A014384", "A058275", "A068934", "A129419", "A129430", "A165626", "A165655", "A184953", "A184954", "A184955", "A205295" ]
[ "M3168" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006821.seq
6975afa14b517bc236b5e658e71bb9c2
A006822
Number of connected regular graphs of degree 6 (or sextic graphs) with n nodes.
[ "1", "0", "0", "0", "0", "0", "0", "1", "1", "4", "21", "266", "7849", "367860", "21609300", "1470293675", "113314233808", "9799685588936", "945095823831036", "101114579937187980", "11945375659139626688", "1551593789610509806552", "220716215902792573134799", "34259321384370620122314325", "5782740798229825207562109439" ]
[ "nonn", "nice", "hard" ]
51
0
10
[ "A002851", "A005177", "A006820", "A006821", "A006822", "A014377", "A014378", "A014381", "A014382", "A014384", "A058276", "A068934", "A165627", "A165656", "A184963", "A184964" ]
[ "M3579" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A006/A006822.seq
f082896a34a9dcfac207c1cbc1575d6b
A006823
Number of connected trivalent bipartite graphs with 2n nodes.
[ "1", "1", "2", "5", "13", "38", "149", "703", "4132", "29579", "245627", "2291589", "23466857", "259974248", "3087698618", "39075020582", "524492748500", "7439833931266", "111179110620163", "1745593888011626", "28726140345832290", "494406533261250407", "8881990236308687928", "166255686198172837111", "3237191621055524796848", "65467841616499410561220" ]
[ "nonn", "hard", "nice" ]
41
3
3
[ "A006823", "A006824", "A008325", "A008326" ]
[ "M1450" ]
N. J. A. Sloane and Brendan McKay
2025-02-16T08:32:31
oeisdata/seq/A006/A006823.seq
459d1a807c9fd97a3493543121798948
A006824
Number of connected regular bipartite graphs of degree 4 with 2n nodes.
[ "1", "1", "4", "14", "129", "1980", "62611", "2806490", "158937213", "10773251972", "855658082615", "78558949838723", "8251166737356319", "982806379842257309", "131756174189661102281", "19748565896506014747623", "3289970433888731383271400", "605948436052375098046655323", "122796503871896458570959144266" ]
[ "nonn", "hard", "nice" ]
21
4
3
[ "A006823", "A006824", "A006825", "A008326", "A333730" ]
[ "M3493" ]
N. J. A. Sloane
2020-04-03T21:53:21
oeisdata/seq/A006/A006824.seq
4c4de601685702cae8f6788cbed08d92
A006825
Number of connected regular bipartite graphs of degree 5 with 2n nodes.
[ "1", "1", "4", "41", "1981", "304495", "78322915", "27033154060", "11934777413004", "6593485023087880", "4485517185017428244", "3707462300996566329965", "3680029088808677189795063", "4341813441626419937873317841", "6033239205199247162872884404386", "9792722283774374706204648839780148" ]
[ "nonn", "hard" ]
18
5
3
[ "A006823", "A006824", "A006825", "A008326", "A333731" ]
[ "M3679" ]
N. J. A. Sloane
2020-04-03T21:54:13
oeisdata/seq/A006/A006825.seq
ba91a1c90c6f184e8bb5e14a753dcc7f
A006826
Erroneous version of A003182.
[ "1", "3", "5", "10", "30", "210", "16353" ]
[ "dead" ]
5
0
2
null
[ "M2469" ]
null
2010-06-01T03:00:00
oeisdata/seq/A006/A006826.seq
9cb5ec383176947e9f79a8e528fef025
A006827
Number of partitions of 2n with all subsums different from n.
[ "1", "2", "5", "8", "17", "24", "46", "64", "107", "147", "242", "302", "488", "629", "922", "1172", "1745", "2108", "3104", "3737", "5232", "6419", "8988", "10390", "14552", "17292", "23160", "27206", "36975", "41945", "57058", "65291", "85895", "99384", "130443", "145283", "193554", "218947", "281860", "316326", "413322", "454229", "594048" ]
[ "nonn", "nice" ]
52
1
2
[ "A002219", "A006827", "A035470", "A046663", "A058695", "A064914", "A078408", "A237258", "A305551", "A321142", "A321451", "A321452", "A321453", "A357976", "A365543", "A365663", "A366320", "A367094", "A371731", "A371736", "A371782", "A371783", "A371792", "A371794", "A371795" ]
[ "M1351" ]
N. J. A. Sloane
2024-04-20T00:00:04
oeisdata/seq/A006/A006827.seq
49b51463983200ebb3446b5561894de6
A006828
From fundamental unit of Z[ (-d)^{1/4} ], where d runs over positive integers not of the form 4*k^4.
[ "0", "-1", "2", "-2", "1", "36", "1", "-485", "-27", "-98", "23", "-86", "-13", "16", "577", "-16", "-13823", "14439374", "-9", "1", "-91167", "25899588", "-95", "-4443", "-125", "-1414178", "57", "330206", "-74879", "1975104", "6913", "67", "-33", "64926", "1351", "-571878", "-267790150327167", "3745", "-159" ]
[ "sign", "more" ]
22
1
3
[ "A006828", "A006829", "A006830", "A006831" ]
[ "M0203" ]
N. J. A. Sloane
2024-04-24T11:37:40
oeisdata/seq/A006/A006828.seq
0b6718413174a7dcdd15aa970d3823e8
A006829
From fundamental unit of Z[ (-n)^{1/4} ].
[ "1", "0", "-2", "2", "4", "-26", "2", "198", "12", "96", "-14", "28", "2", "4", "-204", "7", "58332", "11821890", "6", "36", "440140", "-8909082", "46", "1405", "12", "220224", "2", "-411912", "57396", "28184", "-360", "-74", "-4", "-77790", "-390", "289258", "-183064217333724" ]
[ "sign", "more" ]
15
1
3
[ "A006828", "A006829", "A006830", "A006831" ]
[ "M0342" ]
N. J. A. Sloane.
2020-06-23T06:19:19
oeisdata/seq/A006/A006829.seq
99abe213931352759725a94486960e0b
A006830
From fundamental unit of Z[ (-n)^1/4 ].
[ "-1", "1", "1", "-1", "-4", "9", "-2", "0", "-1", "-45", "4", "3", "2", "-7", "0", "-1", "-36792", "-11320425", "-2", "-24", "-267972", "352849", "-10", "0", "17", "135531", "-12", "189709", "-21012", "-371631", "-1008", "32", "8", "34255", "0", "-71847", "147714465189436", "840", "78" ]
[ "sign", "more" ]
14
1
5
[ "A006828", "A006829", "A006830", "A006831" ]
[ "M3349" ]
N. J. A. Sloane.
2020-06-23T06:19:11
oeisdata/seq/A006/A006830.seq
bc9594e1775efbca2b8f6f60b9796bd2
A006831
From fundamental unit of Z[ (-n)^{1/4} ].
[ "1", "-1", "0", "0", "2", "2", "1", "-66", "-3", "6", "1", "-10", "-2", "4", "51", "-1", "11512", "4956000", "0", "8", "81146", "1629810", "-3", "-281", "-13", "-126466", "7", "-39122", "2218", "217672", "663", "-6", "-4", "-6768", "65", "-6356", "-54441051012990", "-68", "-29" ]
[ "sign", "more" ]
15
1
5
[ "A006828", "A006829", "A006830", "A006831" ]
[ "M0204" ]
N. J. A. Sloane.
2020-06-23T06:18:18
oeisdata/seq/A006/A006831.seq
c95ac40f7c30192ce6a564c4254c9d1f
A006832
Discriminants of totally real cubic fields.
[ "49", "81", "148", "169", "229", "257", "316", "321", "361", "404", "469", "473", "564", "568", "621", "697", "733", "756", "761", "785", "788", "837", "892", "940", "961", "985", "993", "1016", "1076", "1101", "1129", "1229", "1257", "1300", "1304", "1345", "1369", "1373", "1384", "1396", "1425", "1436", "1489", "1492", "1509", "1524" ]
[ "nonn", "changed" ]
28
1
1
[ "A006832", "A023679", "A278790" ]
[ "M5296" ]
N. J. A. Sloane
2025-04-18T09:53:33
oeisdata/seq/A006/A006832.seq
70591bd8e3698e64cf2936dff01c6320
A006833
Decimal expansion of neutron-to-electron mass ratio.
[ "1", "8", "3", "8", "6", "8", "3", "6", "6", "2" ]
[ "nonn", "cons" ]
9
4
2
null
[ "M4471" ]
N. J. A. Sloane
2024-05-14T12:06:04
oeisdata/seq/A006/A006833.seq
26b785ec133ae1dbd88d34984593bbd4
A006834
Decimal expansion of neutron-to-proton mass ratio.
[ "1", "0", "0", "1", "3", "7", "8", "4", "1", "9" ]
[ "nonn", "cons" ]
12
1
5
null
[ "M2611" ]
N. J. A. Sloane
2024-05-14T12:13:29
oeisdata/seq/A006/A006834.seq
e5d9f4e662813225962d9fa15f27c55d
A006835
Percolation series for directed square lattice.
[ "1", "0", "-1", "-3", "-8", "-21", "-56", "-154", "-434", "-1252", "-3675", "-10954", "-33044", "-100676", "-309569", "-957424", "-2987846", "-9330274", "-29522921", "-92459524", "-298142956", "-922424269", "-3098690837", "-9042937179", "-34187149573", "-79544646085" ]
[ "sign" ]
13
0
4
null
[ "M2742" ]
N. J. A. Sloane and Simon Plouffe
2012-03-30T18:36:10
oeisdata/seq/A006/A006835.seq
e30a53ab990b62c5310e95936a793c94
A006836
Percolation series for directed hexagonal lattice.
[ "1", "0", "0", "-1", "-2", "-5", "-10", "-20", "-41", "-86", "-182", "-393", "-853", "-1887", "-4208", "-9445", "-21350", "-48612", "-111307", "-255236", "-590543", "-1362919", "-3182137", "-7362611", "-17377129", "-40125851", "-96106251", "-219681825", "-539266908", "-1200140540" ]
[ "sign" ]
17
0
5
[ "A006739", "A006836" ]
[ "M1379" ]
N. J. A. Sloane.
2019-10-04T07:41:57
oeisdata/seq/A006/A006836.seq
2ef4f0335fa8a7b1e50a92a0d5fe5f47
A006837
Percolation series for directed cubic lattice.
[ "0", "1", "0", "3", "1", "0", "21", "-34", "101", "-249", "921", "-2524", "5613", "-8914", "6206" ]
[ "sign" ]
7
2
4
null
[ "M2207" ]
N. J. A. Sloane.
2012-03-30T16:45:04
oeisdata/seq/A006/A006837.seq
84e1be4691a1c3d46f4a8cc2f925feb2
A006838
Percolation series for directed b.c.c. lattice.
[ "0", "0", "1", "0", "0", "4", "0", "-1", "0", "28", "-1", "-118", "294", "-184", "-441", "1486", "-273", "-6464", "8969" ]
[ "sign" ]
9
2
6
null
[ "M3188" ]
N. J. A. Sloane.
2012-03-30T16:45:04
oeisdata/seq/A006/A006838.seq
e6d0aaabf90816ec8e175aac8000c572
A006839
Minimum of largest partial quotient of continued fraction for k/n, (k,n) = 1.
[ "1", "1", "1", "2", "1", "4", "2", "1", "3", "2", "2", "2", "1", "3", "2", "3", "2", "2", "2", "4", "1", "3", "3", "2", "2", "2", "2", "4", "2", "2", "2", "3", "3", "1", "3", "3", "2", "4", "3", "2", "2", "4", "2", "2", "2", "2", "2", "3", "2", "2", "3", "3", "3", "5", "1", "2", "3", "2", "3", "3", "2", "3", "2", "2", "2", "3", "2", "2", "2", "2", "2", "3", "2", "2", "2", "2", "3", "3", "2", "2", "2", "3", "3", "3", "3", "3", "3", "3", "1", "3", "2", "3", "2", "3", "3", "4", "2", "2", "2", "2", "2", "3", "3", "2", "2", "2", "3", "2" ]
[ "nonn" ]
35
1
4
[ "A006839", "A141822" ]
[ "M0164" ]
N. J. A. Sloane
2023-11-01T18:30:44
oeisdata/seq/A006/A006839.seq
b743fd9ecdb9876830f59e837feb3254
A006840
Number of 2n-bead black-white reversible complementable necklaces with n black beads.
[ "1", "1", "2", "3", "7", "13", "35", "85", "257", "765", "2518", "8359", "28968", "101340", "361270", "1297879", "4707969", "17179435", "63068876", "232615771", "861725794", "3204236779", "11955836258", "44748176653", "167959144032", "632058070310", "2384235077576", "9013628451275" ]
[ "nonn" ]
50
0
3
[ "A006840", "A045629", "A259341" ]
[ "M0837" ]
N. J. A. Sloane
2017-12-01T18:58:16
oeisdata/seq/A006/A006840.seq
084dc5b80e447aa7839132af253d3e91
A006841
Permutation arrays of period n.
[ "1", "1", "1", "2", "4", "10", "28", "127", "686", "4975", "42529", "420948", "4622509", "55670332", "726738971", "10217376792", "153848448652", "2470073249960", "42120966152815", "760282326662191", "14481561464994821", "290289454462745374", "6108699653117045614" ]
[ "nonn", "nice" ]
27
1
4
[ "A006841", "A061417" ]
[ "M1225" ]
N. J. A. Sloane
2018-05-07T03:36:35
oeisdata/seq/A006/A006841.seq
bcecac5dfe1770d8e4efe0e783cc0a69
A006842
Triangle read by rows: row n gives numerators of Farey series of order n.
[ "0", "1", "0", "1", "1", "0", "1", "1", "2", "1", "0", "1", "1", "1", "2", "3", "1", "0", "1", "1", "1", "2", "1", "3", "2", "3", "4", "1", "0", "1", "1", "1", "1", "2", "1", "3", "2", "3", "4", "5", "1", "0", "1", "1", "1", "1", "2", "1", "2", "3", "1", "4", "3", "2", "5", "3", "4", "5", "6", "1", "0", "1", "1", "1", "1", "1", "2", "1", "3", "2", "3", "1", "4", "3", "5", "2", "5", "3", "4", "5", "6", "7", "1", "0", "1", "1", "1", "1", "1", "2", "1", "2", "1", "3", "2", "3", "4", "1", "5", "4", "3", "5", "2", "5" ]
[ "nonn", "nice", "frac", "tabf" ]
65
1
9
[ "A005728", "A006842", "A006843", "A007305", "A007306", "A049455", "A049456", "A177405", "A177407" ]
[ "M0041" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A006/A006842.seq
887de626903a8219711ac2bbd596821c
A006843
Triangle read by rows: row n gives denominators of Farey series of order n.
[ "1", "1", "1", "2", "1", "1", "3", "2", "3", "1", "1", "4", "3", "2", "3", "4", "1", "1", "5", "4", "3", "5", "2", "5", "3", "4", "5", "1", "1", "6", "5", "4", "3", "5", "2", "5", "3", "4", "5", "6", "1", "1", "7", "6", "5", "4", "7", "3", "5", "7", "2", "7", "5", "3", "7", "4", "5", "6", "7", "1", "1", "8", "7", "6", "5", "4", "7", "3", "8", "5", "7", "2", "7", "5", "8", "3", "7", "4", "5", "6", "7", "8", "1", "1", "9", "8", "7", "6", "5", "9", "4", "7", "3", "8", "5", "7", "9", "2", "9", "7", "5", "8", "3", "7" ]
[ "nonn", "nice", "frac", "tabf" ]
70
1
4
[ "A005728", "A006842", "A006843", "A007305", "A007306", "A049455", "A049456", "A177405", "A177407", "A240877" ]
[ "M0081" ]
N. J. A. Sloane
2025-02-24T09:27:54
oeisdata/seq/A006/A006843.seq
a2c4b03c481468b5d37f3f13ab32beef
A006844
a(1)=4, a(2)=5; thereafter a(n) is smallest number that is greater than a(n-1) and having a unique representation as a(j) + a(k) for j<k.
[ "4", "5", "9", "13", "14", "17", "19", "21", "24", "25", "27", "35", "37", "43", "45", "47", "57", "67", "69", "73", "77", "83", "93", "101", "105", "109", "113", "115", "123", "125", "133", "149", "153", "163", "173", "197", "201", "205", "209", "211", "213", "217", "219", "227", "229", "235", "237", "239" ]
[ "easy", "nonn", "nice" ]
39
1
1
null
[ "M3245" ]
N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A006/A006844.seq
574c2639e1d269e657142a83c5f130d3
A006845
State assignments for n-state machine.
[ "0", "1", "3", "3", "140", "420", "840", "840", "10810800", "75675600", "454053600", "2270268000", "9081072000", "27243216000", "54486432000", "54486432000", "52401161274029568000", "786017419110443520000", "11004243867546209280000", "143055170278100720640000" ]
[ "nonn" ]
24
1
3
[ "A006845", "A007041", "A133709" ]
[ "M2295" ]
N. J. A. Sloane
2020-04-03T07:52:47
oeisdata/seq/A006/A006845.seq
fa5f3ab2fab6f9865f06c39060a83187
A006846
Hammersley's polynomial p_n(1).
[ "1", "1", "2", "7", "41", "376", "5033", "92821", "2257166", "69981919", "2694447797", "126128146156", "7054258103921", "464584757637001", "35586641825705882", "3136942184333040727", "315295985573234822561", "35843594275585750890976", "4575961401477587844760793", "651880406652100451820206941" ]
[ "nonn" ]
45
0
3
[ "A006846", "A065547", "A085707", "A104027", "A104030" ]
[ "M1807" ]
N. J. A. Sloane
2024-05-02T15:04:27
oeisdata/seq/A006/A006846.seq
bdaef6cf8ed7e76b67f0f2117671b392
A006847
Number of extreme points of the set of n X n symmetric doubly-stochastic matrices.
[ "1", "1", "2", "5", "14", "58", "238", "1516", "9020", "79892", "635984", "7127764", "70757968", "949723600", "11260506056", "175400319992", "2416123951952", "42776273847184", "671238787733920", "13302324582892048", "234257439470319776", "5135062189842955616", "100292619307729965152" ]
[ "nonn", "easy", "nice" ]
45
0
3
[ "A006847", "A053553" ]
[ "M1471" ]
N. J. A. Sloane
2015-08-03T08:34:43
oeisdata/seq/A006/A006847.seq
a3fcb7a85c7c3774206256d058eb497b
A006848
Number of extreme points of the set of n X n symmetric doubly-substochastic matrices.
[ "1", "2", "5", "18", "75", "414", "2643", "20550", "180057", "1803330", "19925541", "242749602", "3218286195", "46082917278", "710817377715", "11689297807734", "205359276208113", "3812653265319810", "75092750890627077", "1553136587207991090", "33876594618751675611", "772263699644709647262" ]
[ "nonn" ]
34
0
2
null
[ "M1515" ]
N. J. A. Sloane
2017-06-25T02:47:16
oeisdata/seq/A006/A006848.seq
b81328411d9c0c626d73e6161b3b8a45
A006849
Number of strongly self-dual planar maps with 2n edges.
[ "2", "9", "69", "567", "5112", "48114", "469179", "4691115", "47849940", "495893502", "5206886874", "55273052646", "592211326464", "6395881806180", "69555215111319", "761015877850035", "8371174661041500", "92523509359662150", "1027010953940099238" ]
[ "nonn", "nice" ]
35
1
1
[ "A000108", "A005159", "A005470", "A006849" ]
[ "M1947" ]
N. J. A. Sloane
2021-12-17T11:27:26
oeisdata/seq/A006/A006849.seq
cd20ae087919557d802a4405b8a267e5
A006850
Exponential self-convolution of numbers of rooted trees on n nodes.
[ "1", "2", "6", "20", "74", "290", "1196", "5102", "22418", "100762", "462184", "2155896", "10211440", "49013520", "238127606", "1169523872", "5801045062", "29033594556", "146509374164", "744892740620", "3813481756518", "19647505270704", "101820931159954", "530537879440540", "2778251007843926" ]
[ "nonn" ]
9
0
2
[ "A000081", "A006850" ]
null
N. J. A. Sloane.
2016-10-04T15:41:39
oeisdata/seq/A006/A006850.seq
91d5413fb82f09a385432c66e00829fd
A006851
Trails of length n on honeycomb lattice.
[ "1", "3", "6", "12", "24", "48", "96", "186", "360", "696", "1344", "2562", "4872", "9288", "17664", "33384", "63120", "119280", "225072", "423630", "797400", "1499256", "2817216", "5286480", "9918768", "18592080", "34840848", "65228874", "122105496", "228402168", "427176336", "798373662", "1491985800", "2786515176", "5203816992", "9712725234", "18127267800" ]
[ "nonn", "walk" ]
39
0
2
[ "A001668", "A006851" ]
[ "M2560" ]
N. J. A. Sloane
2023-11-29T11:41:47
oeisdata/seq/A006/A006851.seq
eb5f9305b788040bcd50bcea71ecc422
A006852
Step at which n is expelled in Kimberling's puzzle (A035486).
[ "1", "25", "2", "4", "3", "22", "6", "8", "10", "5", "32", "83", "44", "14", "7", "66", "169", "11", "49595", "9", "69", "16", "24", "12", "43", "47", "7598", "15", "133", "109", "13", "198", "19", "33", "18", "23", "58", "65", "60", "93167", "68", "17", "1523", "39", "75", "20", "99", "34", "117", "123" ]
[ "nonn", "nice" ]
31
1
2
[ "A006852", "A007063", "A175312" ]
[ "M5181" ]
N. J. A. Sloane
2016-01-24T23:55:14
oeisdata/seq/A006/A006852.seq
89d9f6ea251d6cb8f1718cfb83138bfc
A006853
Balanced colorings of n-cube.
[ "2", "2", "4", "18", "648", "3140062", "503483766022188", "171522187398423323340476473786538" ]
[ "nonn", "nice", "more" ]
19
0
1
null
[ "M1299" ]
N. J. A. Sloane
2017-08-16T05:28:01
oeisdata/seq/A006/A006853.seq
1b098072f3c1a83b2e9030fdf3595b89
A006854
Nonantipodal balanced colorings of n-cube.
[ "1", "1", "3", "33", "13699", "19738610121", "601031719117714604698691" ]
[ "nonn" ]
14
1
3
null
[ "M3136" ]
N. J. A. Sloane.
2017-08-16T05:28:26
oeisdata/seq/A006/A006854.seq
bdd634528a4ac36aa224846b04021747
A006855
Maximum number of edges in an n-node squarefree graph, or, in a graph containing no 4-cycle, or no C_4.
[ "0", "1", "3", "4", "6", "7", "9", "11", "13", "16", "18", "21", "24", "27", "30", "33", "36", "39", "42", "46", "50", "52", "56", "59", "63", "67", "71", "76", "80", "85", "90", "92", "96", "102", "106", "110", "113", "117", "122", "127" ]
[ "nonn", "more" ]
76
1
3
[ "A006855", "A335820" ]
[ "M2320" ]
N. J. A. Sloane
2024-08-15T10:58:21
oeisdata/seq/A006/A006855.seq
3e63be08a3c7f9977252e6382f8df53c
A006856
Maximal number of edges in n-node graph of girth at least 5.
[ "0", "1", "2", "3", "5", "6", "8", "10", "12", "15", "16", "18", "21", "23", "26", "28", "31", "34", "38", "41", "44", "47", "50", "54", "57", "61", "65", "68", "72", "76", "80", "85", "87", "90", "95", "99", "104", "109", "114", "120", "124", "129", "134", "139", "145", "150", "156", "162", "168", "175", "176", "178", "181" ]
[ "nonn", "more" ]
60
1
3
[ "A006856", "A159847" ]
[ "M0624" ]
N. J. A. Sloane
2023-01-06T10:55:03
oeisdata/seq/A006/A006856.seq
529e2690e59c778cd8d29afea831e946
A006857
a(n) = binomial(n+5,5) * binomial(n+5,4)/(n+5).
[ "1", "15", "105", "490", "1764", "5292", "13860", "32670", "70785", "143143", "273273", "496860", "866320", "1456560", "2372112", "3755844", "5799465", "8756055", "12954865", "18818646", "26883780", "37823500", "52474500", "71867250", "97260345", "130179231", "172459665", "226296280", "294296640", "379541184" ]
[ "nonn", "easy" ]
80
0
2
[ "A000012", "A000217", "A001263", "A002378", "A002415", "A006542", "A006857", "A108679", "A114242", "A134288", "A134289", "A134290", "A134291", "A140925", "A140935", "A169937" ]
[ "M4977" ]
Simon Plouffe
2025-03-12T08:06:51
oeisdata/seq/A006/A006857.seq
a90b555134a1d241deec45df67ee136d
A006858
Expansion of g.f. x*(1 + x)*(1 + 6*x + x^2)/(1 - x)^7.
[ "0", "1", "14", "84", "330", "1001", "2548", "5712", "11628", "21945", "38962", "65780", "106470", "166257", "251720", "371008", "534072", "752913", "1041846", "1417780", "1900514", "2513049", "3281916", "4237520", "5414500", "6852105", "8594586", "10691604", "13198654", "16177505", "19696656", "23831808", "28666352", "34291873" ]
[ "nonn", "easy" ]
71
0
3
[ "A000108", "A006332", "A006858", "A085461" ]
[ "M4935" ]
Simon Plouffe and N. J. A. Sloane
2025-01-07T12:55:16
oeisdata/seq/A006/A006858.seq
dd547db344646010f6c1442ea6ee1ab3
A006859
From paths in the plane.
[ "1", "30", "330", "2145", "10010", "37128", "116280", "319770", "793155", "1808950", "3848130", "7719075", "14725620", "26898080", "47303520", "80454132", "132835365", "213578430", "335304970", "515175045", "776173134", "1148670600", "1672307000", "2398236750", "3391791975", "4735616886", "6533333730", "8913805255" ]
[ "nonn", "easy" ]
23
0
2
null
[ "M5210" ]
Simon Plouffe
2025-01-07T12:57:18
oeisdata/seq/A006/A006859.seq
7c09f02def3f4974ec406676c6409799
A006860
Erroneous version of A223911: Tiered orders on n nodes.
[ "1", "3", "13", "111", "1381", "25623", "678133", "26269735", "1447451707", "114973020921", "13034306495563" ]
[ "dead" ]
55
1
2
null
[ "M2959" ]
Simon Plouffe
2016-06-16T23:27:16
oeisdata/seq/A006/A006860.seq
0e79f9dfa5a1718206a7d3ceef3e6fc2
A006861
Number of directed site animals on hexagonal lattice.
[ "1", "2", "3", "6", "11", "21", "40", "77", "149", "289", "563", "1099", "2152", "4222", "8299", "16339", "32217", "63612", "125753", "248870", "493015", "977576", "1940042", "3853117", "7658211", "15231219", "30312012", "60360046", "120260317" ]
[ "nonn" ]
12
1
2
null
[ "M0786" ]
Simon Plouffe and N. J. A. Sloane.
2013-05-19T19:08:16
oeisdata/seq/A006/A006861.seq
cab173ae65df1646bbdfad60a8d0b47f
A006862
Euclid numbers: 1 + product of the first n primes.
[ "2", "3", "7", "31", "211", "2311", "30031", "510511", "9699691", "223092871", "6469693231", "200560490131", "7420738134811", "304250263527211", "13082761331670031", "614889782588491411", "32589158477190044731", "1922760350154212639071", "117288381359406970983271", "7858321551080267055879091" ]
[ "nonn", "nice", "easy" ]
111
0
1
[ "A005867", "A006862", "A007916", "A014545", "A018239", "A034386", "A048103", "A057588", "A377871" ]
[ "M2698" ]
Simon Plouffe and N. J. A. Sloane
2025-03-13T12:18:53
oeisdata/seq/A006/A006862.seq
713ce16a81d1c10c6e1341d8263d70cc
A006863
Denominator of B_{2n}/(-4n), where B_m are the Bernoulli numbers.
[ "1", "24", "240", "504", "480", "264", "65520", "24", "16320", "28728", "13200", "552", "131040", "24", "6960", "171864", "32640", "24", "138181680", "24", "1082400", "151704", "5520", "1128", "4455360", "264", "12720", "86184", "13920", "1416", "6814407600", "24" ]
[ "nonn", "easy", "frac", "nice" ]
66
0
2
[ "A000367", "A001067", "A002322", "A002445", "A006863", "A079612" ]
[ "M5150" ]
N. J. A. Sloane, Jeffrey Shallit, Simon Plouffe
2025-02-16T08:32:31
oeisdata/seq/A006/A006863.seq
9b2ef8acae6a3229d108b092f69c51e3
A006864
Number of Hamiltonian cycles in P_4 X P_n.
[ "0", "1", "2", "6", "14", "37", "92", "236", "596", "1517", "3846", "9770", "24794", "62953", "159800", "405688", "1029864", "2614457", "6637066", "16849006", "42773094", "108584525", "275654292", "699780452", "1776473532", "4509783909", "11448608270", "29063617746", "73781357746", "187302518353", "475489124976" ]
[ "easy", "nonn" ]
59
1
3
[ "A006864", "A321172" ]
[ "M1603" ]
kwong(AT)cs.fredonia.edu (Harris Kwong), N. J. A. Sloane, Simon Plouffe and Frans J. Faase
2024-12-13T15:22:29
oeisdata/seq/A006/A006864.seq
5892f3f60e7a55024ed6b035cda547c2
A006865
Number of Hamiltonian cycles in P_5 X P_{2n}: a(n) = 11*a(n-1) + 2*a(n-3).
[ "1", "14", "154", "1696", "18684", "205832", "2267544", "24980352", "275195536", "3031685984", "33398506528", "367933962880", "4053336963648", "44653503613184", "491924407670784", "5419275158305920", "59701333748591488", "657698520049847936", "7245522270864939136", "79820147647011513472" ]
[ "nonn", "easy" ]
26
1
2
null
[ "M4946" ]
N. J. A. Sloane, kwong(AT)cs.fredonia.edu (Harris Kwong), Frans J. Faase
2024-02-07T09:37:08
oeisdata/seq/A006/A006865.seq
5d78be6fd6bf99017316f78974c30d12
A006866
Number of irreducible polyhedral graphs with n nodes.
[ "1", "1", "2", "3", "9", "19", "71", "249", "1058", "4705", "22380" ]
[ "nonn" ]
8
4
3
null
[ "M0897" ]
N. J. A. Sloane.
2012-03-30T16:45:04
oeisdata/seq/A006/A006866.seq
7303aa9feffbecce480c2ff130b867a6
A006867
Number of irreducible polyhedral graphs with n faces.
[ "1", "2", "5", "20", "107", "826", "7703", "81231", "914973", "10772406" ]
[ "nonn", "more" ]
11
4
2
[ "A000944", "A006866", "A006867" ]
[ "M1527" ]
N. J. A. Sloane
2024-02-28T09:39:18
oeisdata/seq/A006/A006867.seq
db5f81bb7691e5c4c2ac8bdeb49eb6aa
A006868
Number of minimal 3-polyhedra with n edges.
[ "1", "0", "1", "1", "1", "2", "3", "6", "9", "15", "45", "59", "188", "399", "827", "2472", "5073", "14153", "35489", "85726" ]
[ "nonn" ]
8
6
6
null
[ "M0758" ]
N. J. A. Sloane.
2012-03-30T16:45:04
oeisdata/seq/A006/A006868.seq
e10e290f6a390dcf555ca854dc74f55b
A006869
Number of distinct vertex-degree sequences of n-faced polyhedral graphs.
[ "1", "2", "7", "18", "52", "133", "330", "762", "1681" ]
[ "nonn", "more" ]
19
4
2
[ "A000944", "A006869" ]
[ "M1748" ]
N. J. A. Sloane
2022-06-15T13:10:28
oeisdata/seq/A006/A006869.seq
7bab62d084f06f992bbb963a51538667
A006870
Number of quasi-orders with n elements.
[ "1", "1", "3", "8", "26", "94", "435", "2564", "19983", "205729" ]
[ "nonn", "nice", "more" ]
18
0
3
null
[ "M2755" ]
N. J. A. Sloane
2017-11-08T15:55:14
oeisdata/seq/A006/A006870.seq
6c5c8ebbd50792c21f2a8d299ee4b58d
A006871
Exponentiation of g.f. for rooted trees.
[ "1", "2", "6", "22", "95", "470", "2618", "16159", "109177", "799959", "6309111", "53230208", "477941835", "4546562149", "45646689381", "482052312792", "5338922526947", "61851205026759", "747755335385701", "9413952961001366", "123184994320876476", "1672494478592315483", "23523730530581660635" ]
[ "nonn" ]
21
0
2
[ "A000081", "A006871" ]
null
N. J. A. Sloane.
2015-03-18T20:50:33
oeisdata/seq/A006/A006871.seq
6cf0f8fd4e622d7ef8154d69eeeab988
A006872
Numbers k such that phi(k) = phi(sigma(k)).
[ "1", "3", "15", "26", "39", "45", "74", "104", "111", "117", "122", "146", "175", "183", "195", "219", "296", "314", "333", "357", "386", "471", "488", "549", "554", "555", "579", "584", "585", "608", "626", "646", "657", "794", "831", "842", "914", "915", "939", "962", "1071", "1082", "1095", "1191", "1226", "1256", "1263", "1292", "1322", "1346" ]
[ "nonn" ]
57
1
2
[ "A000010", "A000203", "A006872", "A033631", "A033632", "A062401", "A067880", "A137815", "A260020", "A260021", "A353634", "A353635", "A353636", "A353637", "A353679", "A353683", "A353684", "A353685", "A353686" ]
[ "M2984" ]
Jeffrey Shallit, N. J. A. Sloane
2024-02-19T01:49:08
oeisdata/seq/A006/A006872.seq
ccb64a4f8c131cda385a17fb0d6cb8fb
A006873
Number of alternating 4-signed permutations.
[ "1", "1", "7", "47", "497", "6241", "95767", "1704527", "34741217", "796079041", "20273087527", "567864586607", "17352768515537", "574448847467041", "20479521468959287", "782259922208550287", "31872138933891307457", "1379749466246228538241", "63243057486503656319047", "3059895336952604166395567" ]
[ "nonn" ]
57
0
3
[ "A006873", "A007286", "A007289", "A225109" ]
[ "M4430" ]
N. J. A. Sloane and Simon Plouffe
2024-12-29T14:16:48
oeisdata/seq/A006/A006873.seq
54b2f96b719b49132458f503b267983a
A006874
Number of mu-atoms of period n on continent of Mandelbrot set.
[ "1", "1", "2", "3", "4", "6", "6", "9", "10", "12", "10", "22", "12", "18", "24", "27", "16", "38", "18", "44", "36", "30", "22", "78", "36", "36", "50", "66", "28", "104", "30", "81", "60", "48", "72", "158", "36", "54", "72", "156", "40", "156", "42", "110", "152", "66", "46", "270", "78", "140", "96", "132", "52", "230", "120", "234", "108", "84", "58", "456", "60", "90", "228", "243", "144", "260" ]
[ "nonn" ]
57
1
3
[ "A000010", "A006874", "A006875", "A006876" ]
[ "M0535" ]
Robert Munafo, Apr 28 1994
2023-11-15T11:52:07
oeisdata/seq/A006/A006874.seq
c1f6f987c02df0810073235b3a76907e
A006875
Non-seed mu-atoms of period n in Mandelbrot set.
[ "0", "1", "2", "3", "4", "7", "6", "12", "12", "23", "10", "51", "12", "75", "50", "144", "16", "324", "18", "561", "156", "1043", "22", "2340", "80", "4119", "540", "8307", "28", "17521", "30", "32928", "2096", "65567", "366", "135432", "36", "262179", "8250", "525348", "40", "1065093", "42", "2098263", "33876", "4194347", "46", "8456160", "420", "16779280" ]
[ "nonn" ]
37
1
3
[ "A000740", "A006874", "A006875", "A006876", "A118454" ]
[ "M0579" ]
Robert Munafo
2022-01-25T00:44:04
oeisdata/seq/A006/A006875.seq
d1421c0a78502b2be70406940f4aa071
A006876
Mu-molecules in Mandelbrot set whose seeds have period n.
[ "1", "0", "1", "3", "11", "20", "57", "108", "240", "472", "1013", "1959", "4083", "8052", "16315", "32496", "65519", "130464", "262125", "523209", "1048353", "2095084", "4194281", "8384100", "16777120", "33546216", "67108068", "134201223", "268435427", "536836484", "1073741793", "2147417952", "4294964173", "8589803488", "17179868739" ]
[ "nonn" ]
26
1
4
[ "A000740", "A006874", "A006875", "A006876", "A118454" ]
[ "M2883" ]
Robert Munafo
2024-11-04T04:26:03
oeisdata/seq/A006/A006876.seq
bc6ab45a64736f5a240078a7c4a430f4
A006877
In the '3x+1' problem, these values for the starting value set new records for number of steps to reach 1.
[ "1", "2", "3", "6", "7", "9", "18", "25", "27", "54", "73", "97", "129", "171", "231", "313", "327", "649", "703", "871", "1161", "2223", "2463", "2919", "3711", "6171", "10971", "13255", "17647", "23529", "26623", "34239", "35655", "52527", "77031", "106239", "142587", "156159", "216367", "230631", "410011", "511935", "626331", "837799" ]
[ "nonn", "nice" ]
116
1
2
[ "A006877", "A006878", "A006884", "A006885", "A033492", "A380138" ]
[ "M0748" ]
N. J. A. Sloane and Robert Munafo
2025-02-07T09:44:29
oeisdata/seq/A006/A006877.seq
d0f52ad2bb7a86ba03c746f166ba471b
A006878
Record number of steps to reach 1 in '3x+1' problem, corresponding to starting values in A006877.
[ "0", "1", "7", "8", "16", "19", "20", "23", "111", "112", "115", "118", "121", "124", "127", "130", "143", "144", "170", "178", "181", "182", "208", "216", "237", "261", "267", "275", "278", "281", "307", "310", "323", "339", "350", "353", "374", "382", "385", "442", "448", "469", "508", "524", "527", "530", "556", "559", "562", "583", "596", "612", "664", "685", "688", "691", "704" ]
[ "nonn", "nice" ]
42
1
3
[ "A006877", "A006878", "A006884", "A006885", "A033492", "A033958", "A033959" ]
[ "M4335" ]
N. J. A. Sloane, Robert Munafo
2024-08-06T09:55:39
oeisdata/seq/A006/A006878.seq
737b1bc42465d4c9615a4a32f5bee0e9
A006879
Number of primes with n digits.
[ "0", "4", "21", "143", "1061", "8363", "68906", "586081", "5096876", "45086079", "404204977", "3663002302", "33489857205", "308457624821", "2858876213963", "26639628671867", "249393770611256", "2344318816620308", "22116397130086627", "209317712988603747", "1986761935284574233", "18906449883457813088", "180340017203297174362" ]
[ "nonn", "base", "hard" ]
84
0
2
[ "A006879", "A006880", "A309329" ]
[ "M3577" ]
N. J. A. Sloane, Simon Plouffe
2024-04-16T16:13:37
oeisdata/seq/A006/A006879.seq
649be1e674e3112352adf2002c429ddf
A006880
Number of primes < 10^n.
[ "0", "4", "25", "168", "1229", "9592", "78498", "664579", "5761455", "50847534", "455052511", "4118054813", "37607912018", "346065536839", "3204941750802", "29844570422669", "279238341033925", "2623557157654233", "24739954287740860", "234057667276344607", "2220819602560918840", "21127269486018731928", "201467286689315906290" ]
[ "nonn", "hard", "nice" ]
229
0
2
[ "A000720", "A006879", "A006880", "A006988", "A007053", "A011557", "A025201", "A040014" ]
[ "M3608" ]
N. J. A. Sloane and Simon Plouffe
2025-03-15T14:37:18
oeisdata/seq/A006/A006880.seq
e1858e182de64724c4f3daadbbdab3d6
A006881
Squarefree semiprimes: Numbers that are the product of two distinct primes.
[ "6", "10", "14", "15", "21", "22", "26", "33", "34", "35", "38", "39", "46", "51", "55", "57", "58", "62", "65", "69", "74", "77", "82", "85", "86", "87", "91", "93", "94", "95", "106", "111", "115", "118", "119", "122", "123", "129", "133", "134", "141", "142", "143", "145", "146", "155", "158", "159", "161", "166", "177", "178", "183", "185", "187", "194", "201", "202", "203", "205" ]
[ "nonn", "easy", "nice" ]
248
1
1
[ "A000040", "A001221", "A001222", "A001358", "A005117", "A006881", "A007304", "A007422", "A016105", "A030229", "A036351", "A039833", "A046386", "A046387", "A051709", "A067885", "A213952", "A237114", "A259758", "A363923" ]
[ "M4082" ]
N. J. A. Sloane, Robert Munafo, Simon Plouffe
2025-02-16T08:32:31
oeisdata/seq/A006/A006881.seq
21040429385a032c81833995f1250019
A006882
Double factorials n!!: a(n) = n*a(n-2) for n > 1, a(0) = a(1) = 1.
[ "1", "1", "2", "3", "8", "15", "48", "105", "384", "945", "3840", "10395", "46080", "135135", "645120", "2027025", "10321920", "34459425", "185794560", "654729075", "3715891200", "13749310575", "81749606400", "316234143225", "1961990553600", "7905853580625", "51011754393600", "213458046676875", "1428329123020800" ]
[ "nonn", "easy", "core", "nice" ]
149
0
3
[ "A000085", "A000165", "A001147", "A001813", "A006882", "A052319", "A135401", "A143280", "A202212", "A297708" ]
[ "M0876" ]
Robert Munafo
2025-03-19T08:24:05
oeisdata/seq/A006/A006882.seq
efa0c20f0b68662fb1b7a873bce6dbac
A006883
Long period primes: the decimal expansion of 1/p has period p-1.
[ "2", "7", "17", "19", "23", "29", "47", "59", "61", "97", "109", "113", "131", "149", "167", "179", "181", "193", "223", "229", "233", "257", "263", "269", "313", "337", "367", "379", "383", "389", "419", "433", "461", "487", "491", "499", "503", "509", "541", "571", "577", "593", "619", "647", "659", "701", "709", "727", "743", "811", "821", "823", "857", "863" ]
[ "nonn", "nice", "easy", "base" ]
76
1
1
[ "A001122", "A001913", "A005596", "A006559", "A006883", "A067556" ]
[ "M1745" ]
Robert Munafo
2025-02-16T08:32:31
oeisdata/seq/A006/A006883.seq
8a4ec01715f7e5ee5fba18399c7ec075
A006884
In the '3x+1' problem, these values for the starting value set new records for highest point of trajectory before reaching 1.
[ "1", "2", "3", "7", "15", "27", "255", "447", "639", "703", "1819", "4255", "4591", "9663", "20895", "26623", "31911", "60975", "77671", "113383", "138367", "159487", "270271", "665215", "704511", "1042431", "1212415", "1441407", "1875711", "1988859", "2643183", "2684647", "3041127", "3873535", "4637979", "5656191" ]
[ "nonn", "nice" ]
107
1
2
[ "A006877", "A006878", "A006884", "A006885", "A033492", "A060409", "A060410", "A060411", "A060412", "A060415", "A132348" ]
[ "M0843" ]
N. J. A. Sloane, Robert Munafo
2025-02-07T09:44:34
oeisdata/seq/A006/A006884.seq
25300fa7371a3559f7b7fa9c4aa7388e
A006885
Record highest point of trajectory before reaching 1 in '3x+1' problem, corresponding to starting values in A006884.
[ "1", "2", "16", "52", "160", "9232", "13120", "39364", "41524", "250504", "1276936", "6810136", "8153620", "27114424", "50143264", "106358020", "121012864", "593279152", "1570824736", "2482111348", "2798323360", "17202377752", "24648077896", "52483285312", "56991483520", "90239155648", "139646736808" ]
[ "nonn", "nice" ]
53
1
2
[ "A006877", "A006878", "A006884", "A006885", "A033492" ]
[ "M2086" ]
Robert Munafo
2025-01-13T06:34:29
oeisdata/seq/A006/A006885.seq
a6bb943637104632cbf73a328d8dc455
A006886
Kaprekar numbers: positive numbers n such that n = q+r and n^2 = q*10^m+r, for some m >= 1, q >= 0 and 0 <= r < 10^m, with n != 10^a, a >= 1.
[ "1", "9", "45", "55", "99", "297", "703", "999", "2223", "2728", "4879", "4950", "5050", "5292", "7272", "7777", "9999", "17344", "22222", "38962", "77778", "82656", "95121", "99999", "142857", "148149", "181819", "187110", "208495", "318682", "329967", "351352", "356643", "390313", "461539", "466830", "499500", "500500", "533170" ]
[ "nonn", "nice", "base", "easy" ]
146
1
2
[ "A003052", "A006886", "A037042", "A045913", "A053394", "A053395", "A053396", "A053397", "A053816", "A193992", "A194232", "A248353" ]
[ "M4625" ]
Robert Munafo
2025-03-29T18:28:22
oeisdata/seq/A006/A006886.seq
e54af2b9b9b2697173f34fc544b89e0d
A006887
Kaprekar triples: q such that q = x + y + z and q^3 = x*10^2n + y*10^n + z, where z < 10^n and n is the number of digits in q. q is not a power of 10 (except q=1).
[ "1", "8", "45", "297", "2322", "2728", "4445", "4544", "4949", "5049", "5455", "5554", "7172", "27100", "44443", "55556", "60434", "77778", "143857", "208494", "226071", "279720", "313390", "324675", "329967", "346060", "368928", "395604", "422577", "427868", "461539", "472823", "478115", "488214", "494208" ]
[ "nonn", "base" ]
58
1
2
[ "A006887", "A291461" ]
[ "M4478" ]
Robert Munafo
2025-03-11T08:33:56
oeisdata/seq/A006/A006887.seq
ae7fd0297fe18dfcf045be58b2891426
A006888
a(n) = a(n-1) + a(n-2)*a(n-3) for n > 2 with a(0) = a(1) = a(2) = 1.
[ "1", "1", "1", "2", "3", "5", "11", "26", "81", "367", "2473", "32200", "939791", "80570391", "30341840591", "75749670168872", "2444729709746709953", "2298386861814452020993305", "185187471463742319884263934176321", "5618934645754484318302453706799174724040986" ]
[ "nonn", "easy" ]
53
0
4
null
[ "M0733" ]
Robert Munafo
2024-12-29T16:10:34
oeisdata/seq/A006/A006888.seq
e1cc7689bea3aa68d8581a18b8fd5d70
A006889
Exponent of least power of 2 having n consecutive 0's in its decimal representation.
[ "0", "10", "53", "242", "377", "1491", "1492", "6801", "14007", "100823", "559940", "1148303", "4036338", "4036339", "53619497", "119476156", "146226201", "918583174", "4627233991", "11089076233" ]
[ "nonn", "hard", "base", "more" ]
69
0
2
[ "A006889", "A031146", "A063565", "A131535", "A131536", "A259089", "A259091", "A259092" ]
[ "M4710" ]
P. D. Mitchelmore (dh115(AT)city.ac.uk)
2019-11-07T13:23:29
oeisdata/seq/A006/A006889.seq
97c27c12f0fd59d90c4be62cca86710d
A006890
Decimal expansion of Feigenbaum bifurcation velocity.
[ "4", "6", "6", "9", "2", "0", "1", "6", "0", "9", "1", "0", "2", "9", "9", "0", "6", "7", "1", "8", "5", "3", "2", "0", "3", "8", "2", "0", "4", "6", "6", "2", "0", "1", "6", "1", "7", "2", "5", "8", "1", "8", "5", "5", "7", "7", "4", "7", "5", "7", "6", "8", "6", "3", "2", "7", "4", "5", "6", "5", "1", "3", "4", "3", "0", "0", "4", "1", "3", "4", "3", "3", "0", "2", "1", "1", "3", "1", "4", "7", "3", "7", "1", "3", "8", "6", "8", "9", "7", "4", "4", "0", "2", "3", "9", "4", "8", "0", "1", "3", "8", "1", "7", "1", "6" ]
[ "cons", "nonn", "nice" ]
80
1
1
[ "A006890", "A006891", "A069261", "A069544", "A102817", "A108952", "A159766", "A218453" ]
[ "M3264" ]
N. J. A. Sloane, Colin Mallows, Jeffrey Shallit
2025-03-16T10:44:10
oeisdata/seq/A006/A006890.seq
cd6ffd45e82d4fdd18f1d6d316da715c
A006891
Decimal expansion of Feigenbaum reduction parameter.
[ "2", "5", "0", "2", "9", "0", "7", "8", "7", "5", "0", "9", "5", "8", "9", "2", "8", "2", "2", "2", "8", "3", "9", "0", "2", "8", "7", "3", "2", "1", "8", "2", "1", "5", "7", "8", "6", "3", "8", "1", "2", "7", "1", "3", "7", "6", "7", "2", "7", "1", "4", "9", "9", "7", "7", "3", "3", "6", "1", "9", "2", "0", "5", "6", "7", "7", "9", "2", "3", "5", "4", "6", "3", "1", "7", "9", "5", "9", "0", "2", "0", "6", "7", "0", "3", "2", "9", "9", "6", "4", "9", "7", "4", "6", "4", "3", "3", "8", "3", "4", "1", "2", "9", "5", "9" ]
[ "cons", "nonn", "nice" ]
48
1
1
[ "A006890", "A006891", "A159767" ]
[ "M1311" ]
N. J. A. Sloane, Colin Mallows, Jeffrey Shallit
2025-03-07T11:36:07
oeisdata/seq/A006/A006891.seq
1ddf0a15e58346181d35c6219176f269
A006892
Representation as a sum of squares requires n squares with greedy algorithm.
[ "1", "2", "3", "7", "23", "167", "7223", "13053767", "42600227803223", "453694852221687377444001767", "51459754733114686962148583993443846186613037940783223" ]
[ "nonn" ]
74
1
2
[ "A004215", "A006892", "A053610" ]
[ "M0860" ]
Jeffrey Shallit
2023-07-13T02:50:12
oeisdata/seq/A006/A006892.seq
37b8ea8068d05258fef1c4089d9c4f2b
A006893
Smallest number whose representation requires n triangular numbers with greedy algorithm; also number of 1-2 rooted trees of height n.
[ "1", "2", "5", "20", "230", "26795", "359026205", "64449908476890320", "2076895351339769460477611370186680", "2156747150208372213435450937462082366919951682912789656986079991220" ]
[ "nonn", "easy" ]
60
1
2
[ "A006893", "A007501", "A057945" ]
[ "M1533" ]
Jeffrey Shallit
2024-08-03T01:49:27
oeisdata/seq/A006/A006893.seq
3643f5a02572adb615f736caf45294cd
A006894
Number of planted 3-trees of height < n.
[ "1", "2", "4", "11", "67", "2279", "2598061", "3374961778892", "5695183504492614029263279", "16217557574922386301420536972254869595782763547561", "131504586847961235687181874578063117114329409897615188504091716162522225834932122128288032336298142" ]
[ "nonn", "easy", "core", "nice" ]
67
1
2
[ "A006894", "A036602" ]
[ "M1254" ]
Jeffrey Shallit and N. J. A. Sloane
2024-10-08T18:39:21
oeisdata/seq/A006/A006894.seq
69630680c2ec08189223656e5f33a6d8
A006895
Parenthesized one way gives the powers of 2: (1), (2), (1+3), ..., another way the powers of 3: (1), (2+1), (3+6), ....
[ "1", "2", "1", "3", "6", "2", "16", "9", "23", "58", "6", "128", "109", "147", "512", "70", "954", "1233", "815", "4096", "1650", "6542", "13141", "3243", "32768", "23038", "42498", "131072", "3577", "258567", "272874", "251414", "1048576", "294333", "1802819", "2980150", "1214154", "8388608", "4746145", "12031071", "31015650", "2538782" ]
[ "nonn", "nice" ]
12
0
2
[ "A000079", "A000244", "A006895", "A006899", "A085239", "A108906" ]
[ "M0158" ]
N. J. A. Sloane, K. S. Brown [ kevin2003(AT)delphi.com ]
2013-10-09T16:32:36
oeisdata/seq/A006/A006895.seq
826ed4fb1fd2b3a55d9ad02369ebe0ee
A006896
a(n) is the number of hierarchical linear models on n labeled factors allowing 2-way interactions (but no higher order interactions); or the number of simple labeled graphs with nodes chosen from an n-set.
[ "1", "2", "5", "18", "113", "1450", "40069", "2350602", "286192513", "71213783666", "35883905263781", "36419649682706466", "74221659280476136241", "303193505953871645562970", "2480118046704094643352358501", "40601989176407026666590990422106", "1329877330167226219547875498464516481" ]
[ "easy", "nonn", "nice" ]
75
0
2
[ "A004140", "A006896", "A006897" ]
[ "M1520" ]
N. J. A. Sloane, Colin Mallows, Simon Plouffe
2021-06-09T22:40:02
oeisdata/seq/A006/A006896.seq
f724cc063d3b15357643c7ee02fbe0e6
A006897
a(n) is the number of hierarchical linear models on n unlabeled factors allowing 2-way interactions (but no higher order interactions); or the number of unlabeled simple graphs with <= n nodes.
[ "1", "2", "4", "8", "19", "53", "209", "1253", "13599", "288267", "12293435", "1031291299", "166122463891", "50668153831843", "29104823811067331", "31455590793615376099", "64032471295321173271027", "245999896624828253856990803", "1787823725042236528801735181651", "24639597076850046760911809226614419" ]
[ "easy", "nonn", "nice" ]
52
0
2
[ "A000088", "A006896", "A006897" ]
[ "M1153" ]
Colin Mallows
2024-09-29T11:56:02
oeisdata/seq/A006/A006897.seq
df9a49686a5d53e9773839fe3e3e61a3
A006898
a(n) = Sum_{k=0..n} C(n,k)*2^(k*(k+1)/2).
[ "1", "3", "13", "95", "1337", "38619", "2310533", "283841911", "70927591153", "35812691480115", "36383765777442685", "74185239630793429775", "303119284294591169426729", "2479814853198140771706795531", "40599509058360322571947638063605" ]
[ "nonn" ]
48
0
2
[ "A006896", "A006897", "A006898", "A135748" ]
[ "M2958" ]
Colin Mallows
2023-04-01T11:04:50
oeisdata/seq/A006/A006898.seq
3972585cd9ea2780f31bd6597aaa06af
A006899
Numbers of the form 2^i or 3^j.
[ "1", "2", "3", "4", "8", "9", "16", "27", "32", "64", "81", "128", "243", "256", "512", "729", "1024", "2048", "2187", "4096", "6561", "8192", "16384", "19683", "32768", "59049", "65536", "131072", "177147", "262144", "524288", "531441", "1048576", "1594323", "2097152", "4194304", "4782969", "8388608", "14348907", "16777216", "33554432" ]
[ "nonn", "easy", "nice" ]
88
1
2
[ "A000079", "A000244", "A003586", "A005100", "A006530", "A006895", "A006899", "A053669", "A085238", "A085239", "A108906", "A170803", "A186927", "A186928", "A227928", "A235365", "A235366", "A236210" ]
[ "M0588" ]
Simon Plouffe and N. J. A. Sloane
2025-02-16T08:32:31
oeisdata/seq/A006/A006899.seq
bc30e5d65e49287da1f25841d14fbea4
A006900
Log of g.f. for rooted trees.
[ "1", "0", "1", "-1", "3", "-14", "47", "-227", "1343", "-7772", "53145", "-408102", "3284325", "-29130869", "279951911", "-2849836062", "31093638892", "-361102774004", "4425942618296", "-57338046436904", "782321680405477", "-11197403028728939", "167963239073106477" ]
[ "sign" ]
6
0
5
[ "A000081", "A006900" ]
null
N. J. A. Sloane.
2012-03-30T16:45:05
oeisdata/seq/A006/A006900.seq
65691582b4bb20ea864c0fb4403fdd73