Datasets:
christopher
/
oeis

Dataset card Data Studio Files
xet
Community
2
sequence_id
stringlengths
7
7
sequence_name
stringlengths
4
573
sequence
sequencelengths
1
348
keywords
sequencelengths
1
8
score
int64
1
2.31k
offset_a
int64
-14,827
666,262,453B
offset_b
int64
0
635M
⌀
cross_references
sequencelengths
1
128
⌀
former_ids
sequencelengths
1
3
⌀
author
stringlengths
7
231
⌀
timestamp
timestamp[us]date
1999-12-11 03:00:00
2025-04-28 00:58:08
filename
stringlengths
29
29
hash
stringlengths
32
32
A005201
Total number of fixed points in trees with n nodes.
[ "1", "0", "1", "1", "5", "10", "31", "72", "201", "509", "1374", "3587", "9647", "25686", "69348", "187052", "508480", "1384959", "3791466", "10407842", "28677319", "79231664", "219557624", "609922977", "1698526750", "4740469708", "13258136509", "37151664771", "104294992317", "293279485007" ]
[ "nonn", "easy", "nice" ]
35
1
5
[ "A000055", "A000081", "A005200", "A005201" ]
[ "M3803" ]
N. J. A. Sloane
2023-10-27T19:33:59
oeisdata/seq/A005/A005201.seq
70aed1cac8fc186b058b870cfd547a84
A005202
Total number of fixed points in planted trees with n nodes.
[ "0", "1", "0", "1", "1", "4", "6", "14", "28", "60", "125", "263", "558", "1181", "2513", "5339", "11392", "24290", "51926", "111017", "237757", "509404", "1092713", "2345256", "5038015", "10828720", "23291759", "50126055", "107939753", "232550011", "501270200", "1080996244", "2332221316", "5033764628", "10868950676", "23476998980", "50728408182", "109649040738", "237081174662", "512767906801", "1109354495908" ]
[ "nonn", "easy" ]
21
1
6
[ "A005200", "A005202" ]
[ "M3282" ]
N. J. A. Sloane
2020-03-22T10:01:28
oeisdata/seq/A005/A005202.seq
3a1504d9c8bae2338dd6a796b0bfbb29
A005203
Fibonacci numbers (or rabbit sequence) converted to decimal.
[ "0", "1", "2", "5", "22", "181", "5814", "1488565", "12194330294", "25573364166211253", "439347050970302571643057846", "15829145720289447797800874537321282579904181", "9797766637414564027586288536574448245991597197836000123235901011048118" ]
[ "nonn", "base", "changed" ]
71
0
3
[ "A000045", "A003714", "A005203", "A005205", "A048678", "A048679", "A048680", "A048707", "A048721", "A048722", "A063896", "A144287" ]
[ "M1539" ]
N. J. A. Sloane
2025-04-25T04:31:22
oeisdata/seq/A005/A005203.seq
098b376fd8b915de009ed640c296c414
A005204
Coding a recurrence.
[ "0", "0", "0", "1", "2", "4", "9", "38", "308", "4937", "316006", "161795380", "1325427757897", "694905868332618342", "186537373642942364470529332", "410200022670422956346283949740775609161", "472928427326946774459561651845917849178636866326243365478" ]
[ "nonn" ]
30
0
5
[ "A005203", "A005204" ]
[ "M1199" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A005/A005204.seq
126f6c4eab34a8e1b09337a1b01d3633
A005205
Coding Fibonacci numbers.
[ "1", "3", "10", "93", "2521", "612696", "4019900977", "6409020585966267", "67040619014505181883304178", "1118048584563024433220786501983631190591549", "195042693446883195450571898296824337898272003171567594807867055549521" ]
[ "nonn", "base" ]
36
1
2
[ "A005203", "A005205", "A036299", "A144287" ]
[ "M2877" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A005/A005205.seq
3b4de998b6507549f1dc274058e4fd53
A005206
Hofstadter G-sequence: a(0) = 0; a(n) = n - a(a(n-1)) for n > 0.
[ "0", "1", "1", "2", "3", "3", "4", "4", "5", "6", "6", "7", "8", "8", "9", "9", "10", "11", "11", "12", "12", "13", "14", "14", "15", "16", "16", "17", "17", "18", "19", "19", "20", "21", "21", "22", "22", "23", "24", "24", "25", "25", "26", "27", "27", "28", "29", "29", "30", "30", "31", "32", "32", "33", "33", "34", "35", "35", "36", "37", "37", "38", "38", "39", "40", "40", "41", "42", "42", "43", "43", "44", "45", "45", "46", "46", "47" ]
[ "nonn", "easy", "nice", "changed" ]
268
0
4
[ "A000201", "A005206", "A005614", "A019446", "A035513", "A060143", "A060144", "A072649", "A123070", "A213676", "A287870" ]
[ "M0436" ]
N. J. A. Sloane
2025-04-21T02:25:44
oeisdata/seq/A005/A005206.seq
6fcc579fc1a903157e728023279bf8e7
A005207
a(n) = (F(2*n-1) + F(n+1))/2 where F(n) is a Fibonacci number.
[ "1", "1", "2", "4", "9", "21", "51", "127", "322", "826", "2135", "5545", "14445", "37701", "98514", "257608", "673933", "1763581", "4615823", "12082291", "31628466", "82798926", "216761547", "567474769", "1485645049", "3889431721", "10182603746", "26658304492", "69792188337", "182718064101", "478361686155", "1252366480135" ]
[ "nonn", "easy" ]
94
0
3
[ "A000045", "A001006", "A001519", "A005207", "A131719" ]
[ "M1183" ]
N. J. A. Sloane
2023-11-24T14:55:34
oeisdata/seq/A005/A005207.seq
da7d5058532f93a4be3bfb1a5cbd7894
A005208
Operator-oriented complexity of n, i.e., the minimum number of occurrences of +, *, and ^ needed to build n from a supply of ones.
[ "0", "1", "2", "3", "4", "4", "5", "4", "4", "5", "6", "6", "7", "7", "7", "5", "6", "6", "7", "7", "8", "8", "9", "7", "6", "7", "5", "6", "7", "8", "9", "6", "7", "8", "9", "6", "7", "8", "9", "9", "10", "10", "11", "10", "9", "10", "11", "8", "7", "8", "9", "9", "10", "7", "8", "8", "9", "9", "10", "10", "11", "11", "10", "6", "7", "8", "9", "10", "11", "11", "12", "8", "9", "9", "9", "10", "11", "10", "11", "10" ]
[ "nonn" ]
33
1
3
[ "A005208", "A025280" ]
[ "M0448" ]
N. J. A. Sloane
2023-10-27T05:56:55
oeisdata/seq/A005/A005208.seq
99c0ba690bfb6f8edbf52cb4030c85d2
A005209
Multilevel sieve: at k-th step, accept k numbers, reject k, accept k, ...
[ "1", "3", "9", "25", "57", "145", "337", "793", "1921", "3849", "8835", "18889", "41473", "92305", "203211", "432699", "944313", "2027529", "4077769", "8745153", "18133305", "37898113", "80713737", "169730259", "358760457", "750591867", "1575313473", "3255787851", "6751959507", "14108682265", "29364255033", "61173205587" ]
[ "nonn" ]
47
1
2
null
[ "M2792" ]
N. J. A. Sloane
2022-08-07T12:58:31
oeisdata/seq/A005/A005209.seq
427fed46e8e8efe55e83e8ff823ba67f
A005210
a(n) = |a(n-1) + 2a(n-2) - n|.
[ "1", "1", "0", "2", "3", "1", "0", "6", "3", "5", "0", "2", "11", "1", "8", "6", "5", "1", "8", "10", "5", "3", "10", "8", "3", "7", "14", "0", "1", "29", "0", "26", "7", "25", "4", "18", "11", "9", "8", "14", "11", "3", "18", "20", "11", "5", "20", "18", "9", "5", "28", "14", "17", "9", "12", "26", "7", "1", "44", "14", "41", "7", "26", "24", "11", "7", "38", "16", "23", "15", "10", "32", "21", "11", "22", "32", "1", "13", "64", "10", "57", "5", "36", "38", "25", "15", "22", "36" ]
[ "nonn", "easy", "nice" ]
49
1
4
[ "A005210", "A005211", "A051202", "A051203", "A242014", "A256962" ]
[ "M0400" ]
N. J. A. Sloane
2023-10-29T21:07:16
oeisdata/seq/A005/A005210.seq
c28aa1cba4b4b13a7b2350a8e345644c
A005211
Record values in A005210.
[ "1", "2", "3", "6", "11", "14", "29", "44", "64", "65", "74", "92", "106", "127", "153", "165", "211", "240", "248", "288", "359", "369", "417", "441", "469", "518", "581", "612", "625", "666", "677", "707", "804", "830", "928", "944", "1001", "1060", "1269", "1300", "1361", "1445", "1496", "1548", "1655", "1727", "1742", "1868", "1928", "2043", "2303", "2323", "2579", "2604", "2617" ]
[ "nonn", "easy", "nice" ]
31
1
2
[ "A005210", "A005211", "A242014" ]
[ "M0780" ]
N. J. A. Sloane
2023-10-27T20:02:34
oeisdata/seq/A005/A005211.seq
72d763670e3ad67ee5bcdb84a0a76472
A005212
n! if n is odd otherwise 0 (from the Taylor series for sin x).
[ "0", "1", "0", "6", "0", "120", "0", "5040", "0", "362880", "0", "39916800", "0", "6227020800", "0", "1307674368000", "0", "355687428096000", "0", "121645100408832000", "0", "51090942171709440000", "0", "25852016738884976640000", "0" ]
[ "nonn" ]
41
0
4
null
null
Russ Cox
2017-06-23T21:26:51
oeisdata/seq/A005/A005212.seq
86c0c39c81bc7a50a88096d214b42968
A005213
Number of symmetric, reduced unit interval schemes with n+1 intervals (n>=1).
[ "1", "0", "1", "1", "3", "2", "7", "6", "19", "16", "51", "45", "141", "126", "393", "357", "1107", "1016", "3139", "2907", "8953", "8350", "25653", "24068", "73789", "69576", "212941", "201643", "616227", "585690", "1787607", "1704510", "5196627", "4969152", "15134931", "14508939", "44152809", "42422022", "128996853" ]
[ "nonn" ]
18
0
5
[ "A002426", "A005213", "A005717" ]
[ "M2254" ]
N. J. A. Sloane
2018-01-10T03:16:30
oeisdata/seq/A005/A005213.seq
a7ddc1375f8be6fd298d07270d3a75ec
A005214
Triangular numbers together with squares (excluding 0).
[ "1", "3", "4", "6", "9", "10", "15", "16", "21", "25", "28", "36", "45", "49", "55", "64", "66", "78", "81", "91", "100", "105", "120", "121", "136", "144", "153", "169", "171", "190", "196", "210", "225", "231", "253", "256", "276", "289", "300", "324", "325", "351", "361", "378", "400", "406", "435", "441", "465", "484", "496", "528", "529", "561", "576", "595", "625", "630", "666", "676" ]
[ "nonn", "easy" ]
65
1
2
[ "A000217", "A000290", "A001110", "A005214", "A010052", "A010054", "A054686", "A117704", "A157259", "A193711", "A193714", "A193715", "A193748", "A193749", "A241241", "A242401" ]
null
Russ Cox, Jun 14 1998
2025-04-04T04:18:51
oeisdata/seq/A005/A005214.seq
a3335e19574a464fb8f6e83af6b9d3ac
A005215
Number of labeled interval graphs with n nodes.
[ "1", "2", "8", "61", "822", "17914", "571475", "24566756", "1346167320", "90729050427", "7341861588316", "700870085606926", "77858914606919461", "9954018225212149326", "1450980922023874162612" ]
[ "nonn" ]
17
1
2
null
[ "M1893" ]
N. J. A. Sloane
2023-10-27T05:57:59
oeisdata/seq/A005/A005215.seq
bbd3e648146bf4ec1d07b0a5857f3377
A005216
Number of unlabeled identity interval graphs with n nodes.
[ "1", "0", "0", "0", "0", "4", "31", "199", "1313", "9158", "68336", "546697", "4682870", "42818887", "416581477", "4298371842", "46896673051", "539527125454", "6528590200432", "82900013695783", "1102289694637302", "15317689255215159", "222056321177147564", "3352587738814695770" ]
[ "nonn" ]
20
1
6
null
[ "M3636" ]
N. J. A. Sloane
2023-10-27T08:08:43
oeisdata/seq/A005/A005216.seq
23260363396267698b7d549f130041ff
A005217
Number of unlabeled unit interval graphs with n nodes.
[ "1", "2", "4", "9", "21", "55", "151", "447", "1389", "4502", "15046", "51505", "179463", "634086", "2265014", "8163125", "29637903", "108282989", "397761507", "1468063369", "5441174511", "20242989728", "75566702558", "282959337159", "1062523000005", "4000108867555", "15095081362907", "57088782570433" ]
[ "nonn" ]
24
1
2
null
[ "M1186" ]
N. J. A. Sloane
2023-10-27T05:59:30
oeisdata/seq/A005/A005217.seq
1bdd480cf7ace877351eedeeb501a061
A005218
Number of unlabeled reduced unit interval graphs on n nodes.
[ "0", "0", "1", "1", "3", "4", "11", "21", "55", "124", "327", "815", "2177", "5712", "15465", "41727", "114291", "313504", "866963", "2404251", "6701321", "18733340", "52557441", "147849031", "417080105", "1179355476", "3342487033", "9492629497", "27011665839", "77000574224" ]
[ "nonn" ]
24
1
5
null
[ "M2369" ]
N. J. A. Sloane
2023-10-27T08:08:36
oeisdata/seq/A005/A005218.seq
caf7f4b80623b51417bc9b208a0feda5
A005219
Number of unlabeled identity unit interval graphs.
[ "0", "0", "0", "0", "0", "2", "4", "15", "36", "108", "276", "771", "2044", "5622", "15204", "41835", "114708", "317382", "879008", "2447951", "6833084", "19146910", "53786076", "151537847", "427946916", "1211440440", "3436543336", "9768382171", "27817787344", "79356481542" ]
[ "nonn", "nice" ]
21
1
6
[ "A005219", "A007122" ]
[ "M1289" ]
N. J. A. Sloane
2022-01-31T01:32:48
oeisdata/seq/A005/A005219.seq
e217a7726a0c7ab1a13699a9943b2223
A005220
Number of Dyck paths of knight moves.
[ "1", "0", "1", "0", "3", "2", "12", "14", "54", "86", "274", "528", "1515", "3266", "8854", "20422", "53786", "129368", "336103", "830148", "2145020", "5390580", "13913325", "35378586", "91415954", "234397542", "606983495", "1566013450", "4065765499", "10540066710", "27437831060", "71404804002" ]
[ "nonn", "easy", "nice", "walk" ]
42
0
5
[ "A005220", "A285174" ]
[ "M2256" ]
N. J. A. Sloane
2022-06-30T19:41:39
oeisdata/seq/A005/A005220.seq
3eedf43b393c84c970cf4e373d63472a
A005221
Number of Dyck paths of knight moves.
[ "0", "0", "1", "1", "3", "4", "12", "22", "61", "128", "335", "756", "1936", "4580", "11652", "28402", "72209", "179460", "457274", "1151725", "2945129", "7489680", "19228598", "49256157", "126958030", "327072560", "846173899", "2190012371", "5685200054", "14770728584", "38463268482", "100259225816" ]
[ "nonn", "easy", "nice", "walk" ]
39
0
5
null
[ "M2371" ]
N. J. A. Sloane
2022-06-30T19:10:32
oeisdata/seq/A005/A005221.seq
1f0c3fcb1aae8a3c9910a9727bd172a0
A005222
Number of Dyck paths of knight moves.
[ "1", "0", "1", "0", "4", "4", "18", "26", "86", "158", "462", "976", "2665", "6082", "16040", "38338", "99536", "244880", "631923", "1583796", "4081939", "10358670", "26728731", "68425494", "176964795", "455967376", "1182454137", "3061954102", "7962768190", "20702327552", "53983118006", "140817757006" ]
[ "nonn", "easy", "nice", "walk" ]
28
0
5
null
[ "M3234" ]
N. J. A. Sloane
2021-12-26T21:05:46
oeisdata/seq/A005/A005222.seq
22984c2b953444a21d6644bc4ba6fda6
A005223
Number of Dyck paths of knight moves.
[ "0", "0", "1", "0", "2", "2", "7", "10", "29", "52", "142", "294", "772", "1732", "4451", "10482", "26715", "64908", "165194", "409720", "1044629", "2627712", "6721492", "17079076", "43853111", "112273270", "289390434", "745262022", "1928015211", "4988699442", "12949776427", "33638741110", "87590340673" ]
[ "nonn", "easy", "nice", "walk" ]
24
0
5
null
[ "M0369" ]
N. J. A. Sloane
2021-12-26T21:05:55
oeisdata/seq/A005/A005223.seq
c6176e25ac6e514a09725b704a601ec3
A005224
T is the first, fourth, eleventh, ... letter in this sentence, not counting spaces or commas (Aronson's sequence).
[ "1", "4", "11", "16", "24", "29", "33", "35", "39", "45", "47", "51", "56", "58", "62", "64", "69", "73", "78", "80", "84", "89", "94", "99", "104", "111", "116", "122", "126", "131", "136", "142", "147", "158", "164", "169", "174", "181", "183", "193", "199", "205", "208", "214", "220", "226", "231", "237", "243", "249", "254", "270", "288", "303", "307", "319", "323", "341" ]
[ "nonn", "word", "nice" ]
57
1
2
[ "A005224", "A049525", "A055508", "A079000", "A081023", "A081024", "A097395", "A284744" ]
[ "M3406" ]
N. J. A. Sloane
2025-02-16T12:41:28
oeisdata/seq/A005/A005224.seq
e70010c7d3c3b595407fbef405805037
A005225
Number of permutations of length n with equal cycles.
[ "1", "2", "3", "10", "25", "176", "721", "6406", "42561", "436402", "3628801", "48073796", "479001601", "7116730336", "88966701825", "1474541093026", "20922789888001", "400160588853026", "6402373705728001", "133991603578884052", "2457732174030848001", "55735573291977790576", "1124000727777607680001" ]
[ "nonn", "easy", "nice" ]
58
1
2
[ "A005225", "A038041", "A055225", "A218868", "A236696", "A317329", "A364967" ]
[ "M0903" ]
N. J. A. Sloane
2023-12-17T16:05:33
oeisdata/seq/A005/A005225.seq
a913c09381073ae92844cde7b56ea932
A005226
Number of atomic species of degree n; also number of connected permutation groups of degree n.
[ "0", "1", "1", "2", "6", "6", "27", "20", "130", "124", "598", "641", "4850", "4772", "35625", "46074", "389839", "487408", "4617554" ]
[ "nonn", "more", "hard" ]
57
0
4
[ "A005226", "A005227", "A116655" ]
[ "M1563" ]
Simon Plouffe
2020-03-17T04:37:38
oeisdata/seq/A005/A005226.seq
54955d339cd1546e1cb7cba7af1beee7
A005227
Number of atomic species of degree n which are not nontrivial substitutions.
[ "0", "1", "1", "2", "4", "6", "19", "20", "111", "116", "567", "641", "4718", "4772", "35489", "46012", "389277", "487408", "4616580" ]
[ "nonn", "hard", "more" ]
37
0
4
[ "A005226", "A005227" ]
[ "M1029" ]
N. J. A. Sloane
2023-10-27T06:02:29
oeisdata/seq/A005/A005227.seq
9ddddc7fcd00a750255f5dec405351c3
A005228
Sequence and first differences (A030124) together list all positive numbers exactly once.
[ "1", "3", "7", "12", "18", "26", "35", "45", "56", "69", "83", "98", "114", "131", "150", "170", "191", "213", "236", "260", "285", "312", "340", "369", "399", "430", "462", "495", "529", "565", "602", "640", "679", "719", "760", "802", "845", "889", "935", "982", "1030", "1079", "1129", "1180", "1232", "1285", "1339", "1394", "1451", "1509", "1568", "1628", "1689" ]
[ "nonn", "easy", "nice" ]
149
1
2
[ "A001651", "A005132", "A005228", "A006509", "A022935", "A022936", "A022937", "A022938", "A022939", "A022940", "A022941", "A022942", "A022944", "A022946", "A022952", "A022953", "A022954", "A022955", "A022956", "A022957", "A030124", "A037257", "A037258", "A037259", "A056731", "A056738", "A061577", "A075326", "A081145", "A093903", "A095115", "A099004", "A100707", "A121229", "A129198", "A129199", "A140778", "A225376", "A225377", "A225378", "A225385", "A225386", "A225387", "A225687", "A225850", "A232739", "A232740", "A232746", "A232747", "A232750", "A232751", "A232752" ]
[ "M2629" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005228.seq
cb3c2b93d882e5678bf1abeaf4a9a99f
A005229
a(1) = a(2) = 1; for n > 2, a(n) = a(a(n-2)) + a(n - a(n-2)).
[ "1", "1", "2", "3", "3", "4", "5", "6", "6", "7", "7", "8", "9", "10", "10", "11", "12", "12", "13", "14", "15", "16", "16", "17", "17", "18", "19", "19", "20", "20", "21", "22", "23", "24", "24", "25", "26", "26", "27", "28", "29", "29", "30", "30", "30", "31", "32", "33", "34", "35", "36", "36", "37", "37", "38", "39", "39", "40", "41", "42", "43", "43", "44", "45", "45", "45", "46" ]
[ "nonn", "nice", "easy" ]
57
1
3
[ "A004001", "A005229", "A051105", "A087758", "A116591", "A147880", "A169638" ]
[ "M0441" ]
N. J. A. Sloane, Simon Plouffe
2025-02-16T08:32:28
oeisdata/seq/A005/A005229.seq
82f4f6451a4d6d9bb2cff62fba69c7c6
A005230
Stern's sequence: a(1) = 1, a(n+1) is the sum of the m preceding terms, where m*(m-1)/2 < n <= m*(m+1)/2 or equivalently m = ceiling((sqrt(8*n+1)-1)/2) = A002024(n).
[ "1", "1", "2", "3", "6", "11", "20", "40", "77", "148", "285", "570", "1120", "2200", "4323", "8498", "16996", "33707", "66844", "132568", "262936", "521549", "1043098", "2077698", "4138400", "8243093", "16419342", "32706116", "65149296", "130298592", "260075635", "519108172", "1036138646", "2068138892", "4128034691" ]
[ "core", "easy", "nonn", "nice" ]
70
1
3
[ "A002487", "A005230" ]
[ "M0785" ]
N. J. A. Sloane, Simon Plouffe
2024-04-12T01:41:26
oeisdata/seq/A005/A005230.seq
4d58ade61555bc19240a755a1675e7a5
A005231
Odd abundant numbers (odd numbers m whose sum of divisors exceeds 2m).
[ "945", "1575", "2205", "2835", "3465", "4095", "4725", "5355", "5775", "5985", "6435", "6615", "6825", "7245", "7425", "7875", "8085", "8415", "8505", "8925", "9135", "9555", "9765", "10395", "11025", "11655", "12285", "12705", "12915", "13545", "14175", "14805", "15015", "15435", "16065", "16695", "17325", "17955" ]
[ "nonn" ]
114
1
1
[ "A000203", "A005101", "A005231", "A005835", "A006038", "A039725", "A064001", "A064989", "A112640", "A115414", "A122036", "A136446", "A173490", "A337386" ]
null
N. J. A. Sloane
2024-10-04T10:02:35
oeisdata/seq/A005/A005231.seq
f38753e4d2f9c315eb389dafcc59556a
A005232
Expansion of (1-x+x^2)/((1-x)^2*(1-x^2)*(1-x^4)).
[ "1", "1", "3", "4", "8", "10", "16", "20", "29", "35", "47", "56", "72", "84", "104", "120", "145", "165", "195", "220", "256", "286", "328", "364", "413", "455", "511", "560", "624", "680", "752", "816", "897", "969", "1059", "1140", "1240", "1330", "1440", "1540", "1661", "1771", "1903", "2024", "2168", "2300", "2456", "2600", "2769", "2925", "3107", "3276" ]
[ "nonn", "easy", "nice" ]
180
0
3
[ "A005232", "A006381", "A006382", "A008805", "A052307", "A343875" ]
[ "M2346" ]
N. J. A. Sloane
2025-03-07T11:57:41
oeisdata/seq/A005/A005232.seq
1a3de677605b082afac3ff03b77fb5e8
A005233
A finite sequence associated with the Lie algebra A_5.
[ "1", "2", "3", "4", "5", "8", "10", "11", "20", "35" ]
[ "nonn", "fini", "full" ]
7
0
2
null
null
N. J. A. Sloane
2023-10-27T06:03:00
oeisdata/seq/A005/A005233.seq
3ad96b1324d037ee1ea7be05abf29637
A005234
Primes p such that 1 + product of primes up to p is prime.
[ "2", "3", "5", "7", "11", "31", "379", "1019", "1021", "2657", "3229", "4547", "4787", "11549", "13649", "18523", "23801", "24029", "42209", "145823", "366439", "392113", "4328927", "5256037", "6369619", "7351117" ]
[ "nonn", "hard", "more", "nice" ]
115
1
1
[ "A002110", "A005234", "A006794", "A006862", "A014545", "A018239", "A057704" ]
[ "M0669" ]
N. J. A. Sloane
2025-03-28T04:54:23
oeisdata/seq/A005/A005234.seq
a492ba102e43341e3462c9db1fcdfeaa
A005235
Fortunate numbers: least m > 1 such that m + prime(n)# is prime, where p# denotes the product of all primes <= p.
[ "3", "5", "7", "13", "23", "17", "19", "23", "37", "61", "67", "61", "71", "47", "107", "59", "61", "109", "89", "103", "79", "151", "197", "101", "103", "233", "223", "127", "223", "191", "163", "229", "643", "239", "157", "167", "439", "239", "199", "191", "199", "383", "233", "751", "313", "773", "607", "313", "383", "293", "443", "331", "283", "277", "271", "401", "307", "331" ]
[ "nonn", "nice" ]
199
1
1
[ "A002110", "A005235", "A005408", "A006862", "A010051", "A035345", "A035346", "A038711", "A038771", "A046066", "A055211", "A129912" ]
[ "M2418" ]
N. J. A. Sloane
2025-02-24T09:27:13
oeisdata/seq/A005/A005235.seq
bb8d2d0e8a4b81992b7614861097995b
A005236
Barriers for omega(n): numbers n such that, for all m < n, m + omega(m) <= n.
[ "2", "3", "4", "5", "6", "8", "9", "10", "12", "14", "17", "18", "20", "24", "26", "28", "30", "33", "38", "42", "48", "50", "54", "60", "65", "74", "82", "84", "90", "98", "102", "108", "110", "114", "126", "129", "138", "150", "164", "168", "174", "180", "194", "198", "228", "234", "244", "252", "258", "264", "270", "290", "294", "318", "348", "354", "360", "384", "390", "402" ]
[ "nonn", "nice" ]
42
1
1
[ "A001221", "A005236", "A229109" ]
[ "M0501" ]
N. J. A. Sloane
2023-09-07T04:45:11
oeisdata/seq/A005/A005236.seq
5fa3a8f7f411f3483571558d18944af7
A005237
Numbers k such that k and k+1 have the same number of divisors.
[ "2", "14", "21", "26", "33", "34", "38", "44", "57", "75", "85", "86", "93", "94", "98", "104", "116", "118", "122", "133", "135", "141", "142", "145", "147", "158", "171", "177", "189", "201", "202", "205", "213", "214", "217", "218", "230", "231", "242", "243", "244", "253", "285", "296", "298", "301", "302", "326", "332", "334", "344", "374", "375", "381", "387" ]
[ "nonn" ]
88
1
1
[ "A000005", "A005237", "A005238", "A006558", "A006601", "A019273", "A039665", "A049051", "A073915", "A083795" ]
[ "M2068" ]
N. J. A. Sloane
2024-02-08T01:35:53
oeisdata/seq/A005/A005237.seq
4fe8c2c66e7585c0348e027aaaab5b84
A005238
Numbers k such that k, k+1 and k+2 have the same number of divisors.
[ "33", "85", "93", "141", "201", "213", "217", "230", "242", "243", "301", "374", "393", "445", "603", "633", "663", "697", "902", "921", "1041", "1105", "1137", "1261", "1274", "1309", "1334", "1345", "1401", "1641", "1761", "1832", "1837", "1885", "1893", "1924", "1941", "1981", "2013", "2054", "2101", "2133", "2181", "2217", "2264", "2305" ]
[ "nonn", "easy", "nice" ]
51
1
1
[ "A000005", "A005237", "A005238", "A006558", "A006601", "A019273", "A039665", "A049051", "A051950" ]
[ "M5236" ]
N. J. A. Sloane
2024-02-19T01:48:39
oeisdata/seq/A005/A005238.seq
bd064b587de0da7ac8928f32940e4e78
A005239
Irregular triangle of Section I numbers. Row n contains numbers k with 2^n < k < 2^(n+1) and phi^n(k) = 2, where phi^n means n iterations of Euler's totient function.
[ "3", "5", "7", "11", "13", "15", "17", "23", "25", "29", "31", "41", "47", "51", "53", "55", "59", "61", "83", "85", "89", "97", "101", "103", "107", "113", "115", "119", "121", "123", "125", "137", "167", "179", "187", "193", "205", "221", "227", "233", "235", "239", "241", "249", "251", "253", "255", "257", "289", "353", "359", "389", "391", "401", "409" ]
[ "nonn", "tabf" ]
36
1
1
[ "A000010", "A005239", "A058812", "A092878", "A135832" ]
[ "M2409" ]
N. J. A. Sloane
2023-10-27T10:02:08
oeisdata/seq/A005/A005239.seq
79b4b7c023221e88ef764cf65ccbc867
A005240
P-positions in Epstein's Put or Take a Square game.
[ "0", "5", "20", "29", "45", "80", "101", "116", "135", "145", "165", "173", "236", "257", "397", "404", "445", "477", "540", "565", "580", "585", "629", "666", "836", "845", "885", "909", "944", "949", "954", "975", "1125", "1177" ]
[ "nonn" ]
32
1
2
[ "A005240", "A005241", "A048760" ]
[ "M3893" ]
N. J. A. Sloane
2023-10-27T10:02:00
oeisdata/seq/A005/A005240.seq
8df9955c75897d535b71510e471ff5ff
A005241
N-positions in Epstein's Put or Take a Square game.
[ "1", "4", "9", "11", "14", "16", "21", "25", "30", "36", "41", "44", "49", "52", "54", "64", "69", "71", "81", "84", "86", "92", "100", "105", "120", "121", "126", "136", "141", "144", "149", "164", "169", "174", "189", "196", "201", "208", "216", "225", "230", "245", "252" ]
[ "nonn" ]
12
1
2
[ "A005240", "A005241" ]
[ "M3350" ]
N. J. A. Sloane.
2017-06-28T17:16:27
oeisdata/seq/A005/A005241.seq
7e0e2a57f96f5a2147a6dc33f372f009
A005242
A self-generating sequence.
[ "1", "2", "4", "5", "8", "10", "12", "14", "15", "16", "19", "20", "21", "24", "25", "27", "28", "32", "33", "34", "37", "38", "40", "42", "43", "44", "46", "47", "48", "51", "53", "54", "56", "57", "58", "59", "61", "62", "63", "64", "66", "68", "69", "72", "73", "74", "77", "79", "81", "83", "84", "86", "88", "89", "91", "92", "94", "96", "97", "98", "100" ]
[ "nonn" ]
28
1
2
[ "A002048", "A005242", "A033627" ]
[ "M0971" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005242.seq
5d8c493be6724c091a2a600d30d815d2
A005243
A self-generating sequence: start with 1 and 2, take all sums of any number of successive previous elements and adjoin them to the sequence. Repeat!
[ "1", "2", "3", "5", "6", "8", "10", "11", "14", "16", "17", "18", "19", "21", "22", "24", "25", "29", "30", "32", "33", "34", "35", "37", "40", "41", "43", "45", "46", "47", "49", "51", "54", "57", "58", "59", "60", "62", "65", "67", "68", "69", "70", "71", "72", "73", "75", "76", "77", "78", "80", "81", "82", "84", "86", "87", "88", "90", "91", "92", "93", "94", "95", "96", "97", "99", "100" ]
[ "nonn", "nice", "easy" ]
45
1
2
[ "A005243", "A048973", "A118065", "A118166" ]
[ "M0623" ]
D. R. Hofstadter, Jul 15 1977
2025-02-16T08:32:28
oeisdata/seq/A005/A005243.seq
e472c5f903ef29d4ac115117d8ec0853
A005244
A self-generating sequence: start with 2 and 3, take all products of any 2 previous elements, subtract 1 and adjoin them to the sequence.
[ "2", "3", "5", "9", "14", "17", "26", "27", "33", "41", "44", "50", "51", "53", "65", "69", "77", "80", "81", "84", "87", "98", "99", "101", "105", "122", "125", "129", "131", "134", "137", "149", "152", "153", "158", "159", "161", "164", "167", "173", "194", "195", "197", "201", "204", "206", "209", "219", "230", "233", "237", "239", "242", "243", "249" ]
[ "nonn", "nice", "easy" ]
41
1
1
[ "A005244", "A139127", "A139128", "A171413" ]
[ "M0704" ]
D. R. Hofstadter
2025-02-16T08:32:28
oeisdata/seq/A005/A005244.seq
ffff834df858e78bd31298fd1202d160
A005245
The (Mahler-Popken) complexity of n: minimal number of 1's required to build n using + and *.
[ "1", "2", "3", "4", "5", "5", "6", "6", "6", "7", "8", "7", "8", "8", "8", "8", "9", "8", "9", "9", "9", "10", "11", "9", "10", "10", "9", "10", "11", "10", "11", "10", "11", "11", "11", "10", "11", "11", "11", "11", "12", "11", "12", "12", "11", "12", "13", "11", "12", "12", "12", "12", "13", "11", "12", "12", "12", "13", "14", "12", "13", "13", "12", "12", "13", "13", "14", "13", "14", "13", "14", "12", "13", "13", "13", "13", "14", "13", "14" ]
[ "nonn", "nice", "look" ]
219
1
2
[ "A000792", "A003037", "A003313", "A005245", "A005421", "A005520", "A025280", "A061373", "A064097", "A076091", "A076142", "A091333", "A091334", "A161906", "A161908", "A244743", "A348089", "A348262" ]
[ "M0457" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005245.seq
5e3e1647c9e0bc74580398f76b8e4e1e
A005246
a(n) = (1 + a(n-1)*a(n-2))/a(n-3), a(0) = a(1) = a(2) = 1.
[ "1", "1", "1", "2", "3", "7", "11", "26", "41", "97", "153", "362", "571", "1351", "2131", "5042", "7953", "18817", "29681", "70226", "110771", "262087", "413403", "978122", "1542841", "3650401", "5757961", "13623482", "21489003", "50843527", "80198051", "189750626", "299303201", "708158977", "1117014753" ]
[ "easy", "nonn", "nice" ]
118
0
4
[ "A001075", "A001353", "A001835", "A005246", "A101265", "A211956" ]
[ "M0829" ]
N. J. A. Sloane
2023-07-27T12:37:47
oeisdata/seq/A005/A005246.seq
79670ceb8be4261bc77e26d4df6da795
A005247
a(n) = 3*a(n-2) - a(n-4), a(0)=2, a(1)=1, a(2)=3, a(3)=2. Alternates Lucas (A000032) and Fibonacci (A000045) sequences for even and odd n.
[ "2", "1", "3", "2", "7", "5", "18", "13", "47", "34", "123", "89", "322", "233", "843", "610", "2207", "1597", "5778", "4181", "15127", "10946", "39603", "28657", "103682", "75025", "271443", "196418", "710647", "514229", "1860498", "1346269", "4870847", "3524578", "12752043", "9227465", "33385282", "24157817" ]
[ "nonn", "nice", "easy" ]
64
0
1
[ "A000032", "A000045", "A005013", "A005246", "A005247", "A005248" ]
[ "M0149" ]
N. J. A. Sloane
2022-03-16T02:58:06
oeisdata/seq/A005/A005247.seq
f19c04a6cf9d1e34287d7c2737e6080b
A005248
Bisection of Lucas numbers: a(n) = L(2*n) = A000032(2*n).
[ "2", "3", "7", "18", "47", "123", "322", "843", "2207", "5778", "15127", "39603", "103682", "271443", "710647", "1860498", "4870847", "12752043", "33385282", "87403803", "228826127", "599074578", "1568397607", "4106118243", "10749957122", "28143753123", "73681302247", "192900153618", "505019158607", "1322157322203" ]
[ "nonn", "easy" ]
366
0
1
[ "A000032", "A001519", "A001906", "A001946", "A002878", "A004146", "A005248", "A005592", "A014448", "A056854", "A065034", "A065705", "A087215", "A087265", "A087281", "A087287", "A089772", "A089775", "A103997", "A153415", "A201157", "A228842" ]
[ "M0848", "N1067" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005248.seq
d3230e27a5a59253abba968fd8b412ce
A005249
Determinant of inverse Hilbert matrix.
[ "1", "1", "12", "2160", "6048000", "266716800000", "186313420339200000", "2067909047925770649600000", "365356847125734485878112256000000", "1028781784378569697887052962909388800000000", "46206893947914691316295628839036278726983680000000000" ]
[ "nonn", "easy", "nice" ]
83
0
3
[ "A000178", "A000515", "A005249", "A056040", "A060739", "A067689", "A069945", "A074962", "A163085" ]
[ "M4882" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005249.seq
28d2305926237536007d251620f978fa
A005250
Record gaps between primes.
[ "1", "2", "4", "6", "8", "14", "18", "20", "22", "34", "36", "44", "52", "72", "86", "96", "112", "114", "118", "132", "148", "154", "180", "210", "220", "222", "234", "248", "250", "282", "288", "292", "320", "336", "354", "382", "384", "394", "456", "464", "468", "474", "486", "490", "500", "514", "516", "532", "534", "540", "582", "588", "602", "652" ]
[ "nonn", "nice" ]
253
1
2
[ "A000040", "A000101", "A001223", "A002386", "A005250", "A005669", "A008996", "A058320", "A107578" ]
[ "M0994" ]
N. J. A. Sloane, R. K. Guy, May 20 1991
2025-02-16T08:32:28
oeisdata/seq/A005/A005250.seq
2510cce09682c32730e60eaff57fd2fa
A005251
a(0) = 0, a(1) = a(2) = a(3) = 1; thereafter, a(n) = a(n-1) + a(n-2) + a(n-4).
[ "0", "1", "1", "1", "2", "4", "7", "12", "21", "37", "65", "114", "200", "351", "616", "1081", "1897", "3329", "5842", "10252", "17991", "31572", "55405", "97229", "170625", "299426", "525456", "922111", "1618192", "2839729", "4983377", "8745217", "15346786", "26931732", "47261895", "82938844", "145547525", "255418101", "448227521" ]
[ "nonn", "nice", "easy" ]
305
0
5
[ "A000931", "A001608", "A003242", "A004148", "A005251", "A005314", "A006498", "A011973", "A049853", "A049864", "A078065", "A097230", "A114901", "A118891", "A173022", "A176971", "A178470", "A261041", "A303696", "A329871" ]
[ "M1059" ]
N. J. A. Sloane and R. K. Guy
2025-04-04T04:32:04
oeisdata/seq/A005/A005251.seq
894119babbec284fa1a830cc8e45058f
A005252
a(n) = Sum_{k=0..floor(n/4)} binomial(n-2k,2k).
[ "1", "1", "1", "1", "2", "4", "7", "11", "17", "27", "44", "72", "117", "189", "305", "493", "798", "1292", "2091", "3383", "5473", "8855", "14328", "23184", "37513", "60697", "98209", "158905", "257114", "416020", "673135", "1089155", "1762289", "2851443", "4613732", "7465176", "12078909", "19544085", "31622993" ]
[ "nonn", "easy", "nice" ]
176
0
5
[ "A005251", "A005252", "A005676", "A007318", "A010892", "A024490", "A106511", "A111734", "A173021" ]
[ "M1048" ]
N. J. A. Sloane
2025-01-19T17:11:54
oeisdata/seq/A005/A005252.seq
300e9735a4a3afa3fa8fada96b984da8
A005253
Number of binary words of length n in which the ones occur only in blocks of length at least 4.
[ "1", "1", "1", "1", "2", "4", "7", "11", "16", "23", "34", "52", "81", "126", "194", "296", "450", "685", "1046", "1601", "2452", "3753", "5739", "8771", "13404", "20489", "31327", "47904", "73252", "112004", "171245", "261813", "400285", "612009", "935737", "1430710", "2187496", "3344567", "5113647", "7818464", "11953991", "18277014", "27944604" ]
[ "nonn", "easy" ]
65
0
5
null
[ "M1044" ]
N. J. A. Sloane
2025-01-21T23:56:25
oeisdata/seq/A005/A005253.seq
194826298eb4b9586cb2fc68e5f2c56a
A005254
Number of weighted voting procedures.
[ "1", "3", "9", "21", "51", "117", "271", "607", "1363", "3013", "6643", "14491", "31495", "67965", "146115", "312483", "666015", "1413915", "2992815", "6315135", "13292007", "27906585", "58464339", "122229123", "255072423", "531369483", "1105217223", "2295383319", "4760727375" ]
[ "nonn", "nice", "easy" ]
48
1
2
[ "A005254", "A037254" ]
[ "M2779", "M2780" ]
N. J. A. Sloane
2022-01-31T01:33:23
oeisdata/seq/A005/A005254.seq
19bec4f197717d8765093bf179c33404
A005255
Atkinson-Negro-Santoro sequence: a(n+1) = 2*a(n) - a(n-floor(n/2+1)).
[ "0", "1", "2", "4", "7", "13", "24", "46", "88", "172", "337", "667", "1321", "2629", "5234", "10444", "20842", "41638", "83188", "166288", "332404", "664636", "1328935", "2657533", "5314399", "10628131", "21254941", "42508561", "85014493", "170026357", "340047480", "680089726", "1360169008", "2720327572" ]
[ "nonn", "easy", "nice" ]
38
0
3
[ "A002083", "A005255", "A005318", "A062178" ]
[ "M1076" ]
N. J. A. Sloane, Simon Plouffe
2022-09-03T23:02:56
oeisdata/seq/A005/A005255.seq
49b53ad2b4c9db4b4e9ef207a2e38847
A005256
Number of weighted voting procedures.
[ "1", "3", "6", "12", "23", "45", "87", "171", "336", "666", "1320", "2628", "5233", "10443", "20841", "41637", "83187", "166287", "332403", "664635", "1328934", "2657532", "5314398", "10628130", "21254940", "42508560", "85014492", "170026356", "340047479", "680089725", "1360169007", "2720327571" ]
[ "nonn", "easy", "nice" ]
36
1
2
null
[ "M2556" ]
N. J. A. Sloane
2022-01-31T03:06:00
oeisdata/seq/A005/A005256.seq
d5661a0c3bd16e054b3ca76febb54ec2
A005257
Number of weighted voting procedures.
[ "2", "3", "5", "9", "17", "33", "64", "126", "249", "495", "984", "1962", "3913", "7815", "15608", "31194", "62346", "124650", "249216", "498348", "996531", "1992897", "3985464", "7970598", "15940542", "31880430", "63759552", "127517796", "255032987", "510063369", "1020121528", "2040237846", "4080465294", "8160920190" ]
[ "nonn", "easy", "nice" ]
42
1
1
null
[ "M0716" ]
N. J. A. Sloane
2023-11-10T08:51:32
oeisdata/seq/A005/A005257.seq
2d2543b2e99b8334e4a7f332e840e14a
A005258
Apéry numbers: a(n) = Sum_{k=0..n} binomial(n,k)^2 * binomial(n+k,k).
[ "1", "3", "19", "147", "1251", "11253", "104959", "1004307", "9793891", "96918753", "970336269", "9807518757", "99912156111", "1024622952993", "10567623342519", "109527728400147", "1140076177397091", "11911997404064793", "124879633548031009", "1313106114867738897", "13844511065506477501" ]
[ "nonn", "easy", "nice" ]
282
0
2
[ "A000172", "A000984", "A001008", "A002736", "A002805", "A002893", "A002895", "A005258", "A005259", "A005260", "A005429", "A005430", "A006077", "A007318", "A036917", "A063007", "A081085", "A093388", "A108625", "A125143", "A133370", "A143003", "A143007", "A143413", "A143414", "A143415", "A143583", "A183204", "A214262", "A218690", "A218692", "A219692", "A226535", "A227216", "A227454", "A229111", "A260667", "A260793", "A260832", "A262177", "A264541", "A264542", "A279619", "A290575", "A290576", "A291275", "A291284" ]
[ "M3057" ]
N. J. A. Sloane
2025-04-02T05:14:43
oeisdata/seq/A005/A005258.seq
69b81687c52c7957d26141e5d9433c63
A005259
Apery (Apéry) numbers: Sum_{k=0..n} (binomial(n,k)*binomial(n+k,k))^2.
[ "1", "5", "73", "1445", "33001", "819005", "21460825", "584307365", "16367912425", "468690849005", "13657436403073", "403676083788125", "12073365010564729", "364713572395983725", "11111571997143198073", "341034504521827105445", "10534522198396293262825", "327259338516161442321485" ]
[ "nonn", "easy", "nice" ]
323
0
2
[ "A000172", "A000578", "A000984", "A002117", "A002736", "A002893", "A002895", "A005258", "A005259", "A005260", "A005429", "A005430", "A006077", "A006221", "A006353", "A036917", "A059415", "A059416", "A063007", "A081085", "A092826", "A093388", "A125143", "A133370", "A143003", "A143007", "A143413", "A143414", "A143415", "A143583", "A183204", "A214262", "A219692", "A226535", "A227216", "A227454", "A229111", "A260667", "A260793", "A260832", "A262177", "A264541", "A264542", "A268545", "A268555", "A279619", "A290575", "A290576", "A291275", "A291284" ]
[ "M4020" ]
Simon Plouffe, N. J. A. Sloane, May 20 1991
2025-03-12T13:17:23
oeisdata/seq/A005/A005259.seq
2f069b38fddc8024a54000118190a3bf
A005260
a(n) = Sum_{k = 0..n} binomial(n,k)^4.
[ "1", "2", "18", "164", "1810", "21252", "263844", "3395016", "44916498", "607041380", "8345319268", "116335834056", "1640651321764", "23365271704712", "335556407724360", "4854133484555664", "70666388112940818", "1034529673001901732", "15220552520052960516", "224929755893153896200", "3337324864503769353060" ]
[ "nonn", "easy", "changed" ]
195
0
2
[ "A000079", "A000172", "A000984", "A002893", "A002895", "A005258", "A005259", "A005260", "A005261", "A006077", "A036917", "A063007", "A069865", "A081085", "A093388", "A096192", "A125143", "A143003", "A143007", "A143413", "A143414", "A143415", "A143583", "A182421", "A182422", "A182446", "A182447", "A183204", "A202750", "A214262", "A219692", "A226535", "A227216", "A227454", "A229111", "A260667", "A260832", "A262177", "A264541", "A264542", "A268545", "A268555", "A279619", "A290575", "A290576", "A309010", "A328725", "A342294", "A342295" ]
[ "M2110" ]
N. J. A. Sloane
2025-04-19T17:50:37
oeisdata/seq/A005/A005260.seq
0ee29b749b22bd314e66feef658c1c81
A005261
a(n) = Sum_{k = 0..n} C(n,k)^5.
[ "1", "2", "34", "488", "9826", "206252", "4734304", "113245568", "2816649826", "72001228052", "1883210876284", "50168588906768", "1357245464138656", "37198352117916992", "1030920212982957184", "28847760730478655488", "814066783370083977826" ]
[ "nonn", "easy" ]
83
0
2
[ "A000079", "A000172", "A000984", "A005260", "A005261", "A069865", "A182421", "A182422", "A182446", "A182447", "A309010", "A342294", "A342295" ]
[ "M2156" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005261.seq
4d10aa6c50a6299a735deff00692208c
A005262
a(n) = floor((7*2^(n+1)-9*n-10)/3).
[ "1", "3", "9", "25", "59", "131", "277", "573", "1167", "2359", "4745", "9521", "19075", "38187", "76413", "152869", "305783", "611615", "1223281", "2446617", "4893291", "9786643", "19573349", "39146765", "78293599", "156587271", "313174617", "626349313", "1252698707", "2505397499", "5010795085", "10021590261" ]
[ "nonn", "easy" ]
60
0
2
null
[ "M2793" ]
N. J. A. Sloane
2022-09-08T08:44:33
oeisdata/seq/A005/A005262.seq
f0c4d63e6e85aeed4b821a01ed60143d
A005263
Number of labeled Greg trees.
[ "1", "1", "1", "4", "32", "396", "6692", "143816", "3756104", "115553024", "4093236352", "164098040448", "7345463787136", "363154251536896", "19653476190481408", "1155636468524067328", "73364615077878838784", "5001199614295920565248", "364363128390631094137856" ]
[ "nonn", "nice", "easy" ]
51
0
4
[ "A005263", "A005264", "A005640", "A048159", "A048160", "A052300", "A052303" ]
[ "M3647" ]
N. J. A. Sloane
2019-07-16T02:17:19
oeisdata/seq/A005/A005263.seq
7b5f24e86b4b9f992bbe2290a3b68f2d
A005264
Number of labeled rooted Greg trees with n nodes.
[ "1", "3", "22", "262", "4336", "91984", "2381408", "72800928", "2566606784", "102515201984", "4575271116032", "225649908491264", "12187240730230528", "715392567595403520", "45349581052869924352", "3087516727770990992896", "224691760916830871873536" ]
[ "nonn", "nice", "easy" ]
106
1
2
[ "A005172", "A005263", "A005264", "A048159", "A048160", "A052300", "A052301", "A052302", "A052303", "A157142" ]
[ "M3096" ]
N. J. A. Sloane
2023-10-11T11:45:10
oeisdata/seq/A005/A005264.seq
8c46b257b34af4cd8756e9072390ba64
A005265
a(1)=3, b(n) = Product_{k=1..n} a(k), a(n+1) is the smallest prime factor of b(n)-1.
[ "3", "2", "5", "29", "11", "7", "13", "37", "32222189", "131", "136013303998782209", "31", "197", "19", "157", "17", "8609", "1831129", "35977", "508326079288931", "487", "10253", "1390043", "18122659735201507243", "25319167", "9512386441", "85577", "1031", "3650460767", "107", "41", "811", "15787", "89", "68168743", "4583", "239", "1283", "443", "902404933", "64775657", "2753", "23", "149287", "149749", "7895159", "79", "43", "1409", "184274081", "47", "569", "63843643" ]
[ "nonn", "nice", "hard" ]
42
1
1
[ "A000945", "A000946", "A005265", "A005266", "A084598", "A084599" ]
[ "M2246" ]
N. J. A. Sloane
2022-01-31T03:05:52
oeisdata/seq/A005/A005265.seq
3705cde13c2484c03659d727a1bbe8c3
A005266
a(1)=3, b(n) = Product_{k=1..n} a(k), a(n+1) is the largest prime factor of (b(n)-1).
[ "3", "2", "5", "29", "79", "68729", "3739", "6221191", "157170297801581", "70724343608203457341903", "46316297682014731387158877659877", "78592684042614093322289223662773", "181891012640244955605725966274974474087", "547275580337664165337990140111772164867508038795347198579326533639132704344301831464707648235639448747816483406685904347568344407941" ]
[ "nonn", "nice", "hard" ]
38
1
1
[ "A000945", "A000946", "A005265", "A005266", "A084599" ]
[ "M2247" ]
N. J. A. Sloane
2022-01-31T03:06:40
oeisdata/seq/A005/A005266.seq
1c936ef078a2025fb4cea931e173fcf5
A005267
a(n) = -1 + a(0)*a(1)*...*a(n-1) with a(0) = 3.
[ "3", "2", "5", "29", "869", "756029", "571580604869", "326704387862983487112029", "106735757048926752040856495274871386126283608869", "11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068029" ]
[ "easy", "nonn" ]
44
0
1
[ "A000058", "A000289", "A005267", "A117805" ]
[ "M2248" ]
N. J. A. Sloane
2024-08-25T11:23:48
oeisdata/seq/A005/A005267.seq
7ae27ba2a9b7521513d31ba381469186
A005268
Number of elementary sequences of length n.
[ "1", "1", "2", "4", "10", "31", "120", "578", "3422", "24504", "208833", "2086777", "24123293", "318800755", "4766262421", "79874304340", "1488227986802" ]
[ "nonn", "more" ]
27
1
3
[ "A003513", "A005268", "A005269", "A005272", "A008926", "A234595" ]
[ "M1233" ]
N. J. A. Sloane
2021-12-26T21:14:36
oeisdata/seq/A005/A005268.seq
820cbffedc62a1de5e85da8791259058
A005269
a(n) = number of length-n sequences s with s[1]=1, s[2]=1, s[k-1] <=s[k] <= s[k-2]+s[k-1] (s is called a sub-Fibonacci sequence of length n).
[ "1", "2", "4", "10", "31", "127", "711", "5621", "64049", "1067599", "26287664", "963023487", "52766766100", "4342736509018", "538755914902622", "101067429677072459", "28751803102222498512", "12436935036300286507123", "8200693250120852291693833", "8262592110164298068793701546" ]
[ "nonn" ]
31
2
2
[ "A003513", "A005268", "A005269", "A005272", "A008926", "A234595" ]
[ "M1234" ]
N. J. A. Sloane.
2020-03-03T10:26:57
oeisdata/seq/A005/A005269.seq
49ce879a44fb05d19581c41f25efeb51
A005270
Number of sequences s of length n with s[1]=1, s[2]=1, s[j-1]<s[j]<=s[j-2]+s[j-1] for j>=3.
[ "1", "1", "1", "2", "6", "27", "177", "1680", "23009", "455368", "13067353", "546378617", "33472296082", "3021920660821", "404374532614122", "80646410554881100", "24095492607316134304", "10837141045948365696938", "7369252748590790186483284", "7606603491185739308318700818" ]
[ "nonn" ]
23
2
4
[ "A005269", "A005270", "A125051", "A125052" ]
[ "M1684" ]
N. J. A. Sloane.
2020-03-03T09:59:42
oeisdata/seq/A005/A005270.seq
ddbe139c1d8d81e88f4638a30b0b6ed1
A005271
Number of perfect matchings in n-cube.
[ "1", "2", "9", "272", "589185", "16332454526976", "391689748492473664721077609089" ]
[ "nonn", "hard", "more", "nice" ]
67
1
2
[ "A005271", "A045310", "A112311", "A220904" ]
[ "M1955" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005271.seq
7c13a6cf0f85fe38e142e2708892dc5a
A005272
Number of Van Lier sequences of length n.
[ "1", "2", "6", "26", "164", "1529", "21439", "461481", "15616226", "851607867", "76555549499", "11550559504086" ]
[ "nonn", "nice", "more" ]
41
2
2
[ "A003513", "A005268", "A005269", "A005272", "A008926", "A234595" ]
[ "M1682" ]
N. J. A. Sloane
2023-05-16T08:12:15
oeisdata/seq/A005/A005272.seq
eb88d61ec2d7c2883666a34e01793d47
A005273
(5,4)-graphs.
[ "1", "2", "3", "16", "423", "5337932", "198815685282" ]
[ "nonn" ]
11
3
2
null
[ "M0918" ]
N. J. A. Sloane.
2017-06-29T19:28:04
oeisdata/seq/A005/A005273.seq
eac58e35a95ecd444cb3c0090982bf2c
A005274
(6,5)-graphs.
[ "1", "2", "4", "54", "5337932", "3253511965960720" ]
[ "nonn" ]
11
4
2
null
[ "M1303" ]
N. J. A. Sloane.
2017-06-29T19:28:13
oeisdata/seq/A005/A005274.seq
3cc07f904dd8c4613ad8473a916a1a78
A005275
(7,6)-graphs.
[ "1", "2", "4", "243", "198815685282" ]
[ "nonn" ]
11
5
2
null
[ "M1309" ]
N. J. A. Sloane.
2017-06-29T19:28:21
oeisdata/seq/A005/A005275.seq
8d107ce711182d817e775f4cf42c7262
A005276
Betrothed (or quasi-amicable) numbers.
[ "48", "75", "140", "195", "1050", "1575", "1648", "1925", "2024", "2295", "5775", "6128", "8892", "9504", "16587", "20735", "62744", "75495", "186615", "196664", "199760", "206504", "219975", "266000", "309135", "312620", "507759", "526575", "544784", "549219", "573560", "587460", "817479", "1000824", "1057595", "1081184" ]
[ "nonn", "nice" ]
56
1
1
[ "A003502", "A003503", "A005276", "A048050", "A057533", "A328370" ]
[ "M5291" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005276.seq
0d654da547315ae248f933a898776ba7
A005277
Nontotients: even numbers k such that phi(m) = k has no solution.
[ "14", "26", "34", "38", "50", "62", "68", "74", "76", "86", "90", "94", "98", "114", "118", "122", "124", "134", "142", "146", "152", "154", "158", "170", "174", "182", "186", "188", "194", "202", "206", "214", "218", "230", "234", "236", "242", "244", "246", "248", "254", "258", "266", "274", "278", "284", "286", "290", "298", "302", "304", "308", "314", "318" ]
[ "nonn" ]
168
1
1
[ "A000010", "A002202", "A005277", "A005384", "A006093", "A007617", "A014197", "A057192", "A076336", "A079695", "A106571" ]
[ "M4927" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005277.seq
d00b0e0f4f14881ebbc0950ce3ead905
A005278
Noncototients: numbers k such that x - phi(x) = k has no solution.
[ "10", "26", "34", "50", "52", "58", "86", "100", "116", "122", "130", "134", "146", "154", "170", "172", "186", "202", "206", "218", "222", "232", "244", "260", "266", "268", "274", "290", "292", "298", "310", "326", "340", "344", "346", "362", "366", "372", "386", "394", "404", "412", "436", "466", "470", "474", "482", "490", "518", "520" ]
[ "nonn", "nice" ]
68
1
1
[ "A005278", "A006093", "A051953", "A063740", "A126887", "A263958" ]
[ "M4688" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005278.seq
a16b71f6a96a53130bfaffd9dbc49afe
A005279
Numbers having divisors d,e with d < e < 2*d.
[ "6", "12", "15", "18", "20", "24", "28", "30", "35", "36", "40", "42", "45", "48", "54", "56", "60", "63", "66", "70", "72", "75", "77", "78", "80", "84", "88", "90", "91", "96", "99", "100", "102", "104", "105", "108", "110", "112", "114", "117", "120", "126", "130", "132", "135", "138", "140", "143", "144", "150", "153", "154", "156", "160", "162", "165", "168", "170", "174", "175", "176" ]
[ "nonn" ]
115
1
1
[ "A002808", "A005279", "A010814", "A020886", "A024619", "A046793", "A089341", "A174903", "A174905", "A237271", "A237593", "A239657" ]
[ "M4093" ]
N. J. A. Sloane, Robert G. Wilson v
2025-03-20T17:15:26
oeisdata/seq/A005/A005279.seq
a8b49e91f8834dba2c312ca707a46a28
A005280
Davenport-Schinzel numbers of degree 5 on n symbols.
[ "1", "5", "10", "16", "22", "29" ]
[ "nonn", "more" ]
13
1
2
[ "A002004", "A005280", "A005281", "A259874" ]
[ "M3796" ]
N. J. A. Sloane
2021-08-09T08:39:39
oeisdata/seq/A005/A005280.seq
faeb19e86124f1910191652e3c2bdb29
A005281
Davenport-Schinzel numbers of degree 6 on n symbols.
[ "1", "6", "14", "23", "34", "46" ]
[ "nonn", "hard", "more" ]
18
1
2
[ "A002004", "A005280", "A005281", "A259874" ]
[ "M4104" ]
N. J. A. Sloane
2022-12-01T05:02:14
oeisdata/seq/A005/A005281.seq
0d0c0c8b43bb5e28644352624066f518
A005282
Mian-Chowla sequence (a B_2 sequence): a(1) = 1; for n>1, a(n) = smallest number > a(n-1) such that the pairwise sums of elements are all distinct.
[ "1", "2", "4", "8", "13", "21", "31", "45", "66", "81", "97", "123", "148", "182", "204", "252", "290", "361", "401", "475", "565", "593", "662", "775", "822", "916", "970", "1016", "1159", "1312", "1395", "1523", "1572", "1821", "1896", "2029", "2254", "2379", "2510", "2780", "2925", "3155", "3354", "3591", "3797", "3998", "4297", "4433", "4779", "4851" ]
[ "nonn", "nice" ]
105
1
2
[ "A003022", "A005282", "A011185", "A046185", "A051788", "A080200", "A227590", "A259964", "A347570" ]
[ "M1094" ]
N. J. A. Sloane and Simon Plouffe
2025-02-16T08:32:28
oeisdata/seq/A005/A005282.seq
245881e233e51e08e94e8301c4f6d06f
A005283
Number of permutations of (1,...,n) having n-5 inversions (n>=5).
[ "1", "5", "20", "76", "285", "1068", "4015", "15159", "57486", "218895", "836604", "3208036", "12337630", "47572239", "183856635", "712033264", "2762629983", "10736569602", "41788665040", "162869776650", "635562468075", "2482933033659", "9710010151831", "38008957336974", "148912655255315", "583885852950802" ]
[ "nonn" ]
29
5
2
[ "A000707", "A001892", "A001893", "A001894", "A005283", "A005284", "A005285", "A008302", "A048651" ]
[ "M3905" ]
N. J. A. Sloane
2017-06-29T19:28:33
oeisdata/seq/A005/A005283.seq
d0eeb73eebc85eaec83f98d644283a32
A005284
Number of permutations of (1,...,n) having n-6 inversions (n>=6).
[ "1", "6", "27", "111", "440", "1717", "6655", "25728", "99412", "384320", "1487262", "5762643", "22357907", "86859412", "337879565", "1315952428", "5131231668", "20029728894", "78265410550", "306109412100", "1198306570554", "4694809541046", "18407850118383" ]
[ "nonn" ]
30
6
2
[ "A000707", "A001892", "A001893", "A001894", "A005283", "A005284", "A005285", "A008302", "A048651" ]
[ "M4178" ]
N. J. A. Sloane
2017-06-29T19:28:39
oeisdata/seq/A005/A005284.seq
2eb0eb5de1e59cbb4a1c60c01acf620e
A005285
Number of permutations of (1,...,n) having n-7 inversions (n>=7).
[ "1", "7", "35", "155", "649", "2640", "10569", "41926", "165425", "650658", "2554607", "10020277", "39287173", "154022930", "603919164", "2368601685", "9293159292", "36476745510", "143239635450", "562744102479", "2211876507387", "8697839966552", "34218338900591" ]
[ "nonn" ]
28
7
2
[ "A000707", "A001892", "A001893", "A001894", "A005283", "A005284", "A005285", "A008302", "A048651" ]
[ "M4414" ]
N. J. A. Sloane
2017-06-29T19:28:46
oeisdata/seq/A005/A005285.seq
9f397a228ec5498f9d39d33423761547
A005286
a(n) = (n + 3)*(n^2 + 6*n + 2)/6.
[ "1", "6", "15", "29", "49", "76", "111", "155", "209", "274", "351", "441", "545", "664", "799", "951", "1121", "1310", "1519", "1749", "2001", "2276", "2575", "2899", "3249", "3626", "4031", "4465", "4929", "5424", "5951", "6511", "7105", "7734", "8399", "9101", "9841", "10620", "11439", "12299", "13201", "14146", "15135", "16169", "17249" ]
[ "nonn", "easy", "nice" ]
81
0
2
[ "A005286", "A008302", "A193106", "A193107", "A241765" ]
[ "M4109" ]
N. J. A. Sloane
2022-04-13T13:25:17
oeisdata/seq/A005/A005286.seq
5babc58097e24168c794d422ed151ea8
A005287
Number of permutations of [n] with four inversions.
[ "5", "20", "49", "98", "174", "285", "440", "649", "923", "1274", "1715", "2260", "2924", "3723", "4674", "5795", "7105", "8624", "10373", "12374", "14650", "17225", "20124", "23373", "26999", "31030", "35495", "40424", "45848", "51799", "58310", "65415", "73149", "81548", "90649", "100490", "111110", "122549", "134848", "148049" ]
[ "nonn", "easy" ]
60
4
1
[ "A005286", "A005287", "A005288", "A008302" ]
[ "M3894" ]
N. J. A. Sloane, Robert G. Wilson v
2022-09-08T08:44:33
oeisdata/seq/A005/A005287.seq
1b5be13ab1917ac640269d1cf101c5b1
A005288
a(n) = C(n,5) + C(n,4) - C(n,3) + 1, n >= 7.
[ "3", "22", "71", "169", "343", "628", "1068", "1717", "2640", "3914", "5629", "7889", "10813", "14536", "19210", "25005", "32110", "40734", "51107", "63481", "78131", "95356", "115480", "138853", "165852", "196882", "232377", "272801", "318649", "370448", "428758", "494173", "567322" ]
[ "easy", "nonn" ]
44
6
1
[ "A005288", "A008302" ]
[ "M3090" ]
N. J. A. Sloane
2022-04-13T13:25:17
oeisdata/seq/A005/A005288.seq
3c4ccaa6ad107b45c35e815c60e86538
A005289
Number of graphs on n nodes with 3 cliques.
[ "0", "0", "1", "4", "12", "31", "67", "132", "239", "407", "657", "1019", "1523", "2211", "3126", "4323", "5859", "7806", "10236", "13239", "16906", "21346", "26670", "33010", "40498", "49290", "59543", "71438", "85158", "100913", "118913", "139398", "162609", "188817", "218295", "251349", "288285" ]
[ "nonn", "nice", "easy" ]
45
1
4
null
[ "M3440" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005289.seq
1c531c09851cfc36ed75e9d434017ad7
A005290
Representation degeneracies for boson strings.
[ "1", "-1", "0", "0", "1", "0", "2", "0", "3", "1", "5", "2", "10", "5", "16", "13", "28", "24", "50", "46", "84", "87", "141", "153", "241", "266", "396", "459", "653", "766", "1070", "1267", "1725", "2075", "2762", "3342", "4397", "5330", "6918", "8432", "10814", "13188", "16784", "20468", "25836", "31529", "39505", "48169", "60033", "73092", "90597", "110203", "135920", "165058", "202754", "245774", "300707" ]
[ "sign", "easy" ]
21
0
7
null
[ "M0026" ]
N. J. A. Sloane.
2016-05-01T01:31:20
oeisdata/seq/A005/A005290.seq
559d2bf83c2ae63fc3cb22375e2ad828
A005291
Representation degeneracies for boson strings.
[ "1", "0", "1", "0", "2", "1", "4", "3", "8", "7", "15", "15", "28", "30", "51", "58", "92", "108", "163", "196", "285", "348", "490", "605", "833", "1034", "1396", "1740", "2313", "2887", "3789", "4730", "6141", "7661", "9853", "12276", "15664", "19477", "24678", "30621", "38558", "47728", "59767", "73795", "91949", "113239", "140452" ]
[ "nonn" ]
25
1
5
null
[ "M0168" ]
N. J. A. Sloane.
2016-04-30T17:22:56
oeisdata/seq/A005/A005291.seq
9b8d135330937be583cef07f591f4ab2
A005292
Representation degeneracies for boson strings.
[ "1", "0", "2", "1", "3", "3", "7", "6", "14", "15", "26", "31", "51", "60", "95", "116", "171", "215", "308", "385", "541", "683", "932", "1183", "1591", "2012", "2673", "3381", "4429", "5599", "7266", "9150", "11781", "14802", "18898", "23683", "30044", "37516", "47321", "58913", "73889", "91716", "114480", "141629", "176010" ]
[ "nonn" ]
13
2
3
null
[ "M0153" ]
N. J. A. Sloane.
2016-04-30T17:22:36
oeisdata/seq/A005/A005292.seq
7b2c0ac26e1294fc65a4a08fb7468226
A005293
Representation degeneracies for boson strings.
[ "1", "0", "2", "2", "4", "4", "10", "10", "19", "23", "38", "47", "75", "92", "140", "179", "257", "329", "466", "595", "821", "1055", "1426", "1828", "2442", "3117", "4112", "5244", "6836", "8685", "11236", "14215", "18240", "23006", "29307", "36824", "46636", "58368", "73504", "91689", "114859", "142764", "178039", "220521", "273813" ]
[ "nonn" ]
12
3
3
null
[ "M0314" ]
N. J. A. Sloane.
2016-04-30T17:22:12
oeisdata/seq/A005/A005293.seq
24357b45ffffffb8a6de4d8e29e14f75
A005294
Representation degeneracies for boson strings.
[ "1", "0", "2", "2", "5", "5", "11", "13", "24", "29", "48", "61", "96", "122", "182", "236", "339", "440", "617", "800", "1099", "1422", "1920", "2479", "3302", "4244", "5587", "7157", "9327", "11894", "15370", "19516", "25030", "31648", "40312", "50763", "64273", "80604", "101496", "126796", "158857", "197708", "246563", "305758" ]
[ "nonn" ]
13
4
3
null
[ "M0348" ]
N. J. A. Sloane.
2016-05-01T01:31:56
oeisdata/seq/A005/A005294.seq
5a898abbadd12d86faf1a2cea0ebcdb8
A005295
Representation degeneracies for Neveu-Schwarz strings.
[ "1", "0", "1", "0", "3", "1", "8", "6", "19", "21", "48", "57", "117", "150", "268", "366", "609", "840", "1338", "1866", "2856", "4004", "5961", "8332", "12163", "16938", "24278", "33666", "47577", "65571", "91584", "125469", "173394" ]
[ "nonn" ]
8
0
5
null
[ "M2229" ]
N. J. A. Sloane.
2015-08-23T12:26:15
oeisdata/seq/A005/A005295.seq
ded7aa7a3cd6607e33c462de0e9541d8
A005296
Representation degeneracies for Neveu-Schwarz strings.
[ "1", "0", "3", "3", "9", "11", "26", "36", "71", "102", "183", "268", "450", "661", "1059", "1554" ]
[ "nonn" ]
8
0
3
null
[ "M2287" ]
N. J. A. Sloane.
2015-08-23T12:25:51
oeisdata/seq/A005/A005296.seq
f2ae4ee510c86f789ad2825efa992761
A005297
Representation degeneracies for Neveu-Schwarz strings.
[ "2", "1", "5", "7", "17", "25", "52", "77", "143", "218", "371", "564", "920", "1380", "2168" ]
[ "nonn" ]
9
1
1
null
[ "M0177" ]
N. J. A. Sloane.
2015-08-23T12:25:23
oeisdata/seq/A005/A005297.seq
c87948fc21a2fbcfbbc3a13ff25ff174
A005298
Representation degeneracies for Neveu-Schwarz strings.
[ "2", "2", "7", "11", "25", "38", "78", "122", "219", "344", "579", "894", "1446", "2198" ]
[ "nonn" ]
13
2
1
null
[ "M0370" ]
N. J. A. Sloane.
2015-08-23T12:24:59
oeisdata/seq/A005/A005298.seq
9008ecf312579cb6b62fea0864b57a20
A005299
Representation degeneracies for Neveu-Schwarz strings.
[ "1", "1", "0", "2", "1", "6", "4", "16", "15", "38", "46", "93", "118", "220", "294", "496", "687", "1101", "1533", "2371", "3315", "4969", "6960", "10194", "14213", "20469", "28407", "40277", "55610", "77871", "106847", "148046", "201906" ]
[ "nonn" ]
9
0
4
null
[ "M0179" ]
N. J. A. Sloane.
2015-08-23T11:42:39
oeisdata/seq/A005/A005299.seq
1600d1d0296209b3bb8b155494183bba
A005300
Representation degeneracies for Neveu-Schwarz strings.
[ "1", "0", "2", "2", "7", "8", "20", "27", "56", "79", "145", "212", "361", "530", "858", "1260" ]
[ "nonn" ]
9
0
3
null
[ "M0367" ]
N. J. A. Sloane.
2015-08-23T11:43:05
oeisdata/seq/A005/A005300.seq
566167a462ff1664cde09b3342eff459