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int64
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2.35k
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int64
-14,827
666,262,453B
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1999-12-11 03:00:00
2025-07-19 00:40:46
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32
A354601
Maximal GCD of ten positive integers with sum n.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "3", "1", "2", "3", "2", "1", "3", "1", "2", "3", "4", "1", "3", "1", "4", "3", "2", "1", "4", "1", "5", "3", "4", "1", "3", "5", "4", "3", "2", "1", "6", "1", "2", "3", "4", "5", "6", "1", "4", "3", "7", "1", "6", "1", "2", "5", "4", "7", "6", "1", "8", "3", "2", "1", "7", "5", "2", "3", "8", "1", "9", "7", "4", "3", "2", "5", "8", "1", "7", "9", "10" ]
[ "nonn" ]
17
10
11
[ "A032742", "A354598", "A354599", "A354600", "A354601", "A355249", "A355319", "A355366", "A355368", "A355402" ]
null
Wesley Ivan Hurt, Jul 08 2022
2022-09-21T09:43:26
oeisdata/seq/A354/A354601.seq
9bd485f7a473122066755e46d420d311
A354602
a(n) is the number of trivial braids on 3 strands with 2*n crossings.
[ "1", "4", "28", "244", "2412", "25804", "290932", "3403404", "40914508" ]
[ "nonn", "more" ]
21
0
2
[ "A000984", "A047849", "A354602" ]
null
Alexei Vernitski, Jul 08 2022
2022-08-03T10:38:41
oeisdata/seq/A354/A354602.seq
6dacd569d7aa130c130c616a04eaba9e
A354603
Numbers k such that sum of distinct primes dividing k is equal to the sum of proper divisors of k+1.
[ "3", "7", "14", "31", "127", "206", "2974", "8191", "19358", "20490", "131071", "147454", "286122", "289650", "292332", "441276", "524287", "909498", "1207358", "1657968", "1782540", "2490042", "3368860", "9274806", "11367402", "14107852", "16776156", "18589386", "22910988", "24450316", "26867718", "28959606", "32674506", "33163372" ]
[ "nonn" ]
10
1
1
[ "A000668", "A001065", "A006145", "A008472", "A354603" ]
null
Metin Sariyar, Jul 08 2022
2022-09-07T11:10:45
oeisdata/seq/A354/A354603.seq
dbdb0a07fb3ca812c53fbd19ad9adbdb
A354604
Midpoints of record gaps between primes: a(n) = (A000101(n) + A002386(n))/2 for n > 1.
[ "4", "9", "26", "93", "120", "532", "897", "1140", "1344", "9569", "15705", "19635", "31433", "155964", "360701", "370317", "492170", "1349592", "1357267", "2010807", "4652430", "17051797", "20831428", "47326803", "122164858", "189695776", "191912907", "387096258", "436273150", "1294268635", "1453168287", "2300942709", "3842610941", "4302407536", "10726904850", "20678048489", "22367085156", "25056082315", "42652618575" ]
[ "nonn" ]
28
2
1
[ "A000040", "A000101", "A002386", "A024675", "A344385", "A354604" ]
null
Donghwi Park, Jul 08 2022
2025-04-21T08:35:33
oeisdata/seq/A354/A354604.seq
d5bebee93cf4fbf9166a159ddc6538ad
A354605
Number of vertices among all distinct circles that can be constructed from a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes using only a compass.
[ "101", "1145", "5001", "13753", "34497", "72185", "135157", "224321" ]
[ "nonn", "more" ]
57
1
1
[ "A331702", "A353782", "A354605", "A356358", "A359252", "A359569", "A359859", "A359932", "A361622", "A361623" ]
null
Scott R. Shannon, Mar 13 2023
2023-03-20T10:39:35
oeisdata/seq/A354/A354605.seq
95c679f0c692c47c284ed2cb622ceed3
A354606
a(1) = 1; for n > 1, a(n) is number of terms in the first n-1 terms of the sequence that have the same number of divisors as a(n-1).
[ "1", "1", "2", "1", "3", "2", "3", "4", "1", "4", "2", "5", "6", "1", "5", "7", "8", "2", "9", "3", "10", "3", "11", "12", "1", "6", "4", "4", "5", "13", "14", "5", "15", "6", "7", "16", "1", "7", "17", "18", "2", "19", "20", "3", "21", "8", "9", "6", "10", "11", "22", "12", "4", "7", "23", "24", "1", "8", "13", "25", "8", "14", "15", "16", "2", "26", "17", "27", "18", "5", "28", "6", "19", "29", "30", "2", "31", "32", "7", "33", "20", "8", "21", "22", "23", "34" ]
[ "nonn", "easy" ]
21
1
3
[ "A000005", "A124056", "A342585", "A354606", "A355606" ]
null
Scott R. Shannon, Jul 08 2022
2024-12-12T11:09:34
oeisdata/seq/A354/A354606.seq
40c08bb1ef4459cff5df1824873253a9
A354607
Triangular array read by rows: T(n,k) is the number of labeled tournaments on [n] that have exactly k irreducible (strongly connected) components, n >= 0, 0 <= k <= n.
[ "1", "0", "1", "0", "0", "2", "0", "2", "0", "6", "0", "24", "16", "0", "24", "0", "544", "240", "120", "0", "120", "0", "22320", "6608", "2160", "960", "0", "720", "0", "1677488", "315840", "70224", "20160", "8400", "0", "5040", "0", "236522496", "27001984", "3830400", "758016", "201600", "80640", "0", "40320", "0", "64026088576", "4268194560", "366729600", "46448640", "8628480", "2177280", "846720", "0", "362880" ]
[ "nonn", "tabl" ]
17
0
6
[ "A000142", "A006125", "A054946", "A354607" ]
null
Geoffrey Critzer, Jul 08 2022
2022-07-12T17:42:34
oeisdata/seq/A354/A354607.seq
045b0d52c69a50219e50189e6ec13bf3
A354608
Number of quadruples (p_1, ..., p_4) of positive integers such that p_{i-1} <= p_i <= n^(i-1).
[ "0", "1", "44", "541", "3236", "12885", "39656", "102249", "231736", "476121", "905620", "1618661", "2748604", "4471181", "7012656", "10658705", "15764016", "22762609", "32178876", "44639341", "60885140", "81785221", "108350264", "141747321", "183315176", "234580425", "297274276", "373350069", "465001516", "574681661" ]
[ "nonn", "easy" ]
15
0
3
[ "A354608", "A355576" ]
null
Alois P. Heinz, Jul 08 2022
2022-07-08T16:11:54
oeisdata/seq/A354/A354608.seq
1cadf6cf91618dff847101136b42a6c2
A354609
Carmichael numbers ending in 1.
[ "561", "2821", "6601", "8911", "15841", "29341", "41041", "75361", "101101", "115921", "162401", "172081", "188461", "252601", "314821", "340561", "399001", "410041", "488881", "512461", "530881", "552721", "656601", "658801", "838201", "852841", "1024651", "1152271", "1193221", "1461241", "1615681", "1857241", "1909001", "2100901", "2113921", "2433601", "2455921", "2704801", "3057601" ]
[ "nonn", "base" ]
32
1
1
[ "A002997", "A017281", "A352970", "A354609", "A355305", "A355307", "A355309" ]
null
Omar E. Pol, Jul 08 2022
2022-07-26T07:27:14
oeisdata/seq/A354/A354609.seq
7c58546168011b280c5ae1797d44b520
A354610
Expansion of e.g.f. exp(f(x) - 1) where f(x) = (1 - x)^x = e.g.f. for A007114.
[ "1", "0", "-2", "-3", "16", "90", "-84", "-2940", "-8672", "95256", "956160", "-811800", "-75724296", "-419150160", "4406562720", "78306555600", "89704074240", "-9655388184960", "-97621097227200", "657339885653760", "23680733504400000", "119677890314505600", "-3528587069869276800", "-64401874868363598720" ]
[ "sign" ]
10
0
3
[ "A007114", "A354610", "A354611" ]
null
Seiichi Manyama, Jul 08 2022
2022-07-09T11:05:16
oeisdata/seq/A354/A354610.seq
74173575446fe7ebf455b8de3b81d8d5
A354611
Expansion of e.g.f. 1/(2 - (1 - x)^x).
[ "1", "0", "-2", "-3", "28", "150", "-714", "-10920", "13392", "1129464", "3694680", "-150143400", "-1515256104", "22631946480", "525582087408", "-2756199995640", "-192774443051520", "-525316900812480", "75951597634314048", "926307802605928320", "-30597152030347651200", "-833744424171043728000" ]
[ "sign" ]
11
0
3
[ "A007114", "A354610", "A354611" ]
null
Seiichi Manyama, Jul 08 2022
2022-07-09T11:05:20
oeisdata/seq/A354/A354611.seq
4745e0446dcf7ad0967ffb5a803e4972
A354612
Expansion of e.g.f. exp(f(x) - 1) where f(x) = (1 + x)^x = e.g.f. for A007113.
[ "1", "0", "2", "-3", "32", "-150", "1404", "-11340", "120448", "-1319976", "16600320", "-223664760", "3300331704", "-52223268240", "887583503520", "-16071609481200", "309263446333440", "-6296705309543040", "135262191966465600", "-3056359409652695040", "72462969268541596800" ]
[ "sign" ]
12
0
3
[ "A007113", "A202152", "A354612", "A354613" ]
null
Seiichi Manyama, Jul 08 2022
2022-07-09T11:05:24
oeisdata/seq/A354/A354612.seq
218eefd1fa1d1b507da3f020248ab46c
A354613
Expansion of e.g.f. 1/(2 - (1 + x)^x).
[ "1", "0", "2", "-3", "44", "-210", "2694", "-23520", "330672", "-4168584", "67622040", "-1095648840", "20621674776", "-403514963280", "8734659594192", "-199049377658040", "4894304369356800", "-126907901533425600", "3501394314254828352", "-101643840316833194880", "3112491474764866339200" ]
[ "sign" ]
11
0
3
[ "A007113", "A354612", "A354613" ]
null
Seiichi Manyama, Jul 08 2022
2022-07-09T11:05:27
oeisdata/seq/A354/A354613.seq
161892d59169837fe771e924817401c4
A354614
Number of distinct substrings of length A342263(n) that appear at least twice in the binary expansion of n.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "2", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "2", "1", "1", "2", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "2", "2", "1", "1", "1", "2", "1", "2", "2", "1", "1", "3", "1", "2", "1", "1", "1" ]
[ "nonn", "base" ]
9
0
10
[ "A342263", "A354614" ]
null
Peter Kagey, Jul 08 2022
2022-07-13T14:50:33
oeisdata/seq/A354/A354614.seq
cb0b0eb51f62c8bef766b53a712d45a0
A354615
Triangular array read by rows: T(n,k) is the number of labeled posets on [n] that are composed of exactly k irreducible posets, n >= 0, 0 <= k <= n.
[ "1", "0", "1", "0", "1", "2", "0", "7", "6", "6", "0", "97", "62", "36", "24", "0", "2251", "1110", "510", "240", "120", "0", "80821", "30902", "11340", "4440", "1800", "720", "0", "4305127", "1273566", "369726", "119280", "42000", "15120", "5040", "0", "332273257", "75831422", "17192196", "4476024", "1335600", "433440", "141120", "40320" ]
[ "nonn", "tabl" ]
15
0
6
[ "A000142", "A001035", "A046908", "A354615" ]
null
Geoffrey Critzer, Jul 08 2022
2022-07-10T08:26:00
oeisdata/seq/A354/A354615.seq
b22c90af2bedf020119f504864c712e9
A354616
Numbers such that every bit in its binary expansion is in a substring of length A342263(n) that appears more than once.
[ "3", "7", "9", "10", "12", "15", "19", "21", "25", "31", "34", "36", "37", "40", "41", "42", "45", "46", "54", "56", "58", "63", "69", "73", "77", "81", "85", "89", "91", "99", "109", "127", "132", "136", "137", "141", "142", "144", "145", "146", "148", "150", "151", "153", "154", "157", "165", "166", "167", "170", "173", "175", "177", "178", "181", "182", "184", "185", "187" ]
[ "base", "nonn" ]
12
1
1
[ "A342263", "A354614", "A354616" ]
null
Peter Kagey, Jul 08 2022
2022-07-21T03:07:24
oeisdata/seq/A354/A354616.seq
c97bc3559a43a352b16c9d2e8cf98036
A354617
Decimal expansion of 3*sqrt(5483/2)/50.
[ "3", "1", "4", "1", "5", "6", "0", "1", "2", "1", "9", "7", "7", "6", "1", "3", "8", "4", "8", "1", "2", "9", "8", "6", "5", "4", "0", "3", "8", "9", "4", "4", "4", "8", "7", "3", "2", "3", "3", "0", "4", "1", "6", "9", "4", "7", "4", "4", "1", "0", "6", "5", "6", "7", "7", "6", "2", "8", "8", "9", "4", "8", "9", "3", "9", "8", "7", "3", "8", "1", "3", "1", "0", "4", "0", "9", "1", "6", "0", "2", "5", "6", "2", "6", "2", "7", "7", "7", "7", "4" ]
[ "nonn", "cons", "easy" ]
17
1
1
[ "A010467", "A354617" ]
null
Stefano Spezia, Jul 08 2022
2025-01-13T15:40:48
oeisdata/seq/A354/A354617.seq
05db04e25cf3d8e6c0c0781dd7a32000
A354618
a(n) = (sum of the digits of 5^n) - (sum of the digits of 2^n).
[ "0", "3", "3", "0", "6", "6", "9", "12", "12", "18", "33", "24", "9", "3", "12", "18", "33", "42", "45", "30", "30", "36", "42", "33", "45", "48", "39", "54", "42", "42", "54", "57", "48", "27", "42", "33", "45", "48", "57", "63", "69", "87", "99", "93", "93", "54", "42", "60", "72", "93", "75", "72", "51", "42", "45", "75", "111", "135", "141", "114", "117", "120", "102", "81", "78", "78" ]
[ "nonn", "base" ]
24
0
2
[ "A001370", "A007953", "A066001", "A354618" ]
null
Bernard Schott, Jul 08 2022
2022-07-11T16:04:54
oeisdata/seq/A354/A354618.seq
ed31acb584a09154141b3c7ce077fdca
A354619
Decimal expansion of Pi + e + gamma, where gamma is Euler's constant (or the Euler-Mascheroni constant).
[ "6", "4", "3", "7", "0", "9", "0", "1", "4", "6", "9", "5", "0", "3", "7", "1", "3", "3", "4", "4", "2", "9", "4", "4", "2", "9", "4", "4", "7", "1", "4", "5", "6", "7", "8", "1", "2", "9", "9", "6", "5", "7", "5", "8", "2", "9", "0", "1", "4", "9", "8", "8", "9", "9", "4", "7", "4", "7", "6", "7", "9", "4", "5", "4", "9", "1", "6", "7", "6", "0", "7", "6", "3", "4", "1", "7", "4", "2", "1", "2", "6", "4", "1", "3", "6", "3", "6" ]
[ "nonn", "cons" ]
12
1
1
[ "A000796", "A001113", "A001620", "A203816", "A211015", "A354619" ]
null
Marco Ripà, Jul 08 2022
2022-07-10T16:44:47
oeisdata/seq/A354/A354619.seq
ea5f2b719b379b2bbb80a1e0aca75a56
A354620
Numbers k such that whenever the sum of three squares is divisible by k, at least two of the squares are congruent mod k.
[ "1", "2", "3", "4", "6", "8", "9", "11", "12", "16", "24", "32", "33", "36", "44", "48", "64", "96", "128", "132", "144", "176", "192", "256", "384", "512", "528", "576", "704", "768", "1024", "1536", "2048", "2112", "2304", "2816", "3072", "4096", "6144", "8192", "8448", "9216", "11264", "12288", "16384", "24576", "32768", "33792", "36864", "45056", "49152", "65536", "98304", "131072", "135168", "147456" ]
[ "nonn" ]
43
1
2
null
null
Robert Israel, Jul 10 2022
2023-05-12T08:38:11
oeisdata/seq/A354/A354620.seq
0e0029fe4cd26351648067c0c0846556
A354621
Number of n-tuples (p_1, p_2, ..., p_n) of positive integers such that p_{i-1} <= p_i <= prime(i).
[ "1", "2", "5", "19", "85", "586", "3583", "28568", "195449", "1666786", "18757980", "161386953", "1897428757", "20910643255", "186584844271", "1896239913403", "23753305611756", "322385257985845", "3291722491175736", "43011227141438328", "517673545204963277", "5056620552149902641", "65366993167319822971" ]
[ "nonn" ]
21
0
2
[ "A000040", "A000108", "A325057", "A354621" ]
null
Alois P. Heinz, Jul 08 2022
2023-01-04T17:08:52
oeisdata/seq/A354/A354621.seq
bbb7472f8d2e80bf0e0df25252e18a1d
A354622
Irregular triangle read by rows: Refined 3-Narayana triangle. Coefficients of partition polynomials of A134264, a refined Narayana triangle enumerating noncrossing partitions, with all h_k other than h_0, h_3, h_6, ..., h_(3n), ... replaced by zero.
[ "1", "1", "3", "1", "9", "12", "1", "12", "6", "66", "55", "1", "15", "15", "105", "105", "455", "273", "1", "18", "18", "9", "153", "306", "51", "816", "1224", "3060", "1428", "1", "21", "21", "21", "210", "420", "210", "210", "1330", "3990", "1330", "5985", "11970", "20349", "7752", "1", "24", "24", "24", "12", "276", "552", "552", "276", "276", "2024", "6072", "3036", "6072", "506", "10626", "42504", "21252", "42504", "106260", "134596", "43263" ]
[ "nonn", "tabf" ]
74
1
3
[ "A000041", "A001764", "A002293", "A003408", "A004321", "A108767", "A125181", "A127537", "A134264", "A173020", "A179848", "A235534", "A338135", "A354622" ]
null
Tom Copeland, Jul 08 2022
2024-02-20T01:16:24
oeisdata/seq/A354/A354622.seq
e9c6798f34e825bfe35834e860dfb205
A354623
Expansion of e.g.f. ( Product_{k>0} 1/(1-x^k) )^x.
[ "1", "0", "2", "9", "44", "390", "2754", "32760", "310064", "4244184", "54887400", "818615160", "12909921672", "225872515440", "4045885572624", "79360837887240", "1649832369335040", "35666417240193600", "822291935260976064", "19830352438530840960", "501144432316767688320", "13229590606682042436480" ]
[ "nonn" ]
39
0
3
[ "A000203", "A053529", "A066166", "A354623", "A355064", "A356335", "A356554", "A356565" ]
null
Seiichi Manyama, Aug 12 2022
2022-08-17T02:36:54
oeisdata/seq/A354/A354623.seq
0bf2743189e87f304f3f19554762b5f2
A354624
Expansion of e.g.f. (1 - x)^(-x^4).
[ "1", "0", "0", "0", "0", "120", "360", "1680", "10080", "72576", "2419200", "25660800", "279417600", "3286483200", "41894012160", "794511244800", "13755488947200", "238514695372800", "4269265386946560", "79696849513881600", "1658065431859200000" ]
[ "nonn" ]
12
0
6
[ "A353228", "A353229", "A354624", "A354625", "A355609" ]
null
Seiichi Manyama, Jul 09 2022
2022-07-21T02:04:28
oeisdata/seq/A354/A354624.seq
c28ddb7de110dc5325c1af3e9872d428
A354625
Expansion of e.g.f. (1 + x)^(x^4).
[ "1", "0", "0", "0", "0", "120", "-360", "1680", "-10080", "72576", "1209600", "-14256000", "159667200", "-1902700800", "24458353920", "-120860812800", "-193037644800", "23690780467200", "-646842994237440", "14916006359654400", "-230812655044608000", "3182953434006528000", "-37667817509059584000" ]
[ "sign" ]
13
0
6
[ "A007121", "A354624", "A354625", "A355607" ]
null
Seiichi Manyama, Jul 09 2022
2022-07-09T11:05:36
oeisdata/seq/A354/A354625.seq
0d3534e6549126e5cef72ed6205190a2
A354626
Numbers that can't be written as the sum of a Fibonacci number and the square of a Fibonacci number.
[ "15", "16", "18", "19", "20", "23", "24", "29", "31", "32", "36", "37", "39", "40", "41", "42", "44", "45", "47", "48", "49", "50", "51", "52", "53", "54", "57", "58", "60", "61", "62", "63", "68", "70", "71", "73", "74", "75", "76", "78", "79", "81", "82", "83", "84", "86", "87", "88", "91", "92", "94", "95", "96", "97", "99", "100", "101", "102", "103", "104", "105", "106", "107", "108", "109", "110", "111", "112", "113", "115" ]
[ "nonn" ]
25
1
1
[ "A000045", "A007598", "A059727", "A354626" ]
null
Angad Singh, Jul 09 2022
2022-07-25T15:52:06
oeisdata/seq/A354/A354626.seq
ebd99578794a5a76b335b4bc72c9d602
A354627
Decimal expansion of the negated digamma function at 1/7.
[ "7", "3", "6", "3", "9", "8", "0", "2", "4", "2", "2", "2", "4", "3", "4", "3", "1", "9", "8", "5", "4", "9", "5", "1", "5", "3", "0", "3", "0", "1", "6", "8", "8", "1", "0", "4", "7", "8", "1", "9", "9", "1", "6", "2", "3", "5", "5", "9", "0", "3", "2", "4", "1", "5", "2", "1", "8", "4", "0", "3", "8", "2", "3", "9", "2", "5", "7", "6", "7", "8", "7", "5", "7", "4", "6", "3", "3", "7", "6", "9", "6", "6", "2", "5", "2", "8", "0", "8", "1", "9", "4", "2", "4", "0", "4", "2", "5", "3", "9", "9", "6" ]
[ "nonn", "cons" ]
9
1
1
[ "A354627", "A354628", "A354629", "A354630", "A354631", "A354632" ]
null
R. J. Mathar, Jun 01 2022
2023-06-14T07:43:08
oeisdata/seq/A354/A354627.seq
2114b1f7855c6ac3f9655dcdec870323
A354628
Decimal expansion of the negated digamma function at 2/7.
[ "3", "6", "8", "5", "5", "1", "7", "9", "8", "0", "2", "8", "5", "8", "1", "5", "3", "3", "3", "6", "2", "3", "0", "3", "1", "4", "3", "9", "1", "5", "9", "9", "3", "8", "1", "3", "6", "3", "8", "1", "7", "6", "9", "5", "8", "8", "5", "1", "5", "1", "7", "2", "6", "5", "9", "8", "4", "3", "9", "7", "1", "6", "1", "6", "2", "3", "1", "5", "1", "9", "5", "8", "6", "3", "8", "7", "8", "7", "7", "6", "6", "5", "6", "0", "9", "4", "5", "0", "3", "7", "1", "4", "3", "8", "8", "2" ]
[ "nonn", "cons" ]
7
1
1
[ "A354627", "A354628", "A354629", "A354630", "A354631", "A354632" ]
null
R. J. Mathar, Jun 01 2022
2023-06-14T07:46:51
oeisdata/seq/A354/A354628.seq
600141841e06699f1cd7b6e8cc09a4c3
A354629
Decimal expansion of the negated digamma function at 3/7.
[ "2", "3", "6", "5", "8", "1", "8", "7", "5", "7", "2", "9", "4", "9", "8", "2", "5", "9", "7", "2", "1", "3", "4", "7", "3", "4", "1", "2", "2", "7", "2", "1", "1", "6", "1", "8", "5", "9", "6", "0", "5", "6", "0", "4", "6", "2", "9", "8", "9", "7", "0", "4", "2", "6", "9", "6", "0", "7", "4", "5", "2", "9", "5", "3", "3", "1", "4", "5", "2", "4", "4", "0", "3", "2", "5", "9", "7", "7", "5", "7", "3", "2", "6", "9", "3", "1", "3", "2", "9", "2", "7", "2" ]
[ "nonn", "cons" ]
7
1
1
[ "A354627", "A354628", "A354629", "A354630", "A354631", "A354632" ]
null
R. J. Mathar, Jun 01 2022
2023-06-14T07:46:39
oeisdata/seq/A354/A354629.seq
a75dfd45f2ba2d95cc379d20d8392bef
A354630
Decimal expansion of the negated digamma function at 4/7.
[ "1", "6", "4", "8", "7", "7", "0", "7", "3", "4", "9", "2", "1", "0", "7", "7", "4", "3", "8", "2", "6", "1", "9", "1", "2", "6", "7", "2", "9", "4", "4", "2", "8", "7", "7", "6", "7", "6", "2", "7", "7", "6", "0", "1", "3", "8", "8", "2", "8", "4", "1", "3", "2", "9", "5", "3", "0", "0", "3", "6", "5", "7", "2", "4", "4", "5", "1", "5", "4", "0", "4", "7", "4", "3", "8", "3", "2", "3", "2", "3", "3", "2", "3", "9", "2", "7", "0", "2", "3", "6", "8", "8", "3" ]
[ "nonn", "cons" ]
7
1
2
[ "A354627", "A354628", "A354629", "A354630", "A354631", "A354632" ]
null
R. J. Mathar, Jun 01 2022
2023-06-14T07:46:31
oeisdata/seq/A354/A354630.seq
d3e67a994f340850dd509eebcc4b27e3
A354631
Decimal expansion of the negated digamma function at 5/7.
[ "1", "1", "8", "0", "1", "8", "1", "4", "4", "0", "3", "3", "9", "4", "9", "8", "7", "5", "4", "8", "4", "4", "6", "7", "7", "7", "2", "0", "4", "4", "6", "1", "6", "1", "3", "2", "8", "3", "1", "9", "6", "2", "3", "2", "2", "2", "0", "2", "8", "7", "0", "3", "4", "7", "5", "8", "2", "1", "7", "0", "9", "2", "7", "4", "5", "6", "4", "4", "9", "1", "1", "9", "7", "3", "3", "6", "6", "6", "8", "2", "3", "5", "4", "9", "8", "4", "9", "0", "5", "1", "2" ]
[ "nonn", "cons" ]
7
1
3
[ "A354627", "A354628", "A354629", "A354630", "A354631", "A354632" ]
null
R. J. Mathar, Jun 01 2022
2023-06-14T07:46:21
oeisdata/seq/A354/A354631.seq
151082ee831b23d899b3c1a8cca20015
A354632
Decimal expansion of the negated digamma function at 6/7.
[ "8", "4", "0", "3", "9", "5", "8", "7", "7", "7", "3", "0", "6", "7", "2", "9", "7", "6", "8", "8", "3", "9", "3", "1", "1", "9", "6", "7", "5", "7", "2", "8", "8", "2", "2", "7", "6", "0", "2", "9", "1", "9", "4", "7", "4", "7", "6", "0", "2", "5", "2", "0", "5", "9", "2", "9", "2", "7", "9", "6", "6", "5", "1", "0", "5", "2", "5", "1", "0", "9", "8", "1", "0", "9", "9", "5", "4", "1", "9", "6", "7", "6", "8", "8", "7", "0", "7", "4", "9", "5", "8", "9" ]
[ "cons", "nonn" ]
7
0
1
[ "A354627", "A354628", "A354629", "A354630", "A354631", "A354632" ]
null
R. J. Mathar, Jun 01 2022
2023-06-14T07:45:20
oeisdata/seq/A354/A354632.seq
1b45c6d96e4a54edaed5c13d70b717c0
A354633
Decimal expansion of the negated digamma function at 3/8.
[ "2", "7", "5", "3", "9", "9", "9", "0", "4", "9", "1", "4", "5", "1", "3", "9", "5", "7", "5", "7", "6", "4", "0", "1", "9", "2", "1", "8", "8", "0", "4", "5", "6", "8", "1", "0", "5", "2", "5", "1", "4", "9", "5", "3", "9", "3", "6", "8", "8", "1", "0", "2", "3", "1", "0", "5", "4", "6", "2", "8", "3", "2", "2", "7", "9", "9", "0", "4", "1", "1", "3", "9", "8", "9", "6", "9", "0", "4", "7", "6", "2", "8", "3", "9", "8", "7", "0", "8", "2", "7", "9" ]
[ "nonn", "cons" ]
8
1
1
[ "A001620", "A091648", "A354633" ]
null
R. J. Mathar, Jun 01 2022
2022-06-03T03:21:33
oeisdata/seq/A354/A354633.seq
f3f1a466af2c6bc71d37697e5344391f
A354634
Decimal expansion of the negated digamma function at 5/8.
[ "1", "4", "5", "2", "7", "0", "8", "7", "6", "4", "5", "7", "6", "5", "6", "6", "5", "6", "7", "2", "1", "0", "7", "8", "1", "6", "1", "2", "0", "2", "3", "3", "7", "7", "2", "9", "0", "8", "3", "4", "0", "4", "3", "1", "0", "3", "6", "8", "7", "5", "1", "7", "9", "0", "8", "4", "3", "5", "8", "3", "2", "2", "1", "3", "3", "4", "1", "7", "9", "3", "0", "1", "2", "1", "5", "5", "7", "8", "2", "7", "1", "6", "4", "5", "1", "4", "1", "6", "1", "7", "0" ]
[ "nonn", "cons" ]
8
1
2
[ "A001620", "A091648", "A354634" ]
null
R. J. Mathar, Jun 01 2022
2022-06-03T03:21:13
oeisdata/seq/A354/A354634.seq
63b93457b4f94818c8ec162f570673df
A354635
Decimal expansion of the negated digamma function at 7/8.
[ "8", "0", "4", "0", "1", "7", "0", "7", "1", "5", "4", "7", "6", "9", "5", "3", "8", "2", "3", "2", "4", "2", "1", "8", "5", "4", "9", "7", "4", "6", "1", "4", "6", "4", "1", "7", "2", "3", "9", "6", "5", "4", "9", "5", "3", "6", "9", "8", "6", "8", "1", "0", "9", "9", "0", "5", "5", "7", "4", "6", "7", "2", "5", "4", "1", "8", "6", "5", "6", "6", "2", "4", "0", "5", "7", "6", "3", "0", "4", "3", "9", "6", "9", "4", "0", "5", "7", "6", "3", "7", "6" ]
[ "nonn", "cons" ]
9
0
1
[ "A001620", "A091648", "A354635" ]
null
R. J. Mathar, Jun 01 2022
2024-06-10T00:19:26
oeisdata/seq/A354/A354635.seq
5a4895dfb78f649f052f194c42742183
A354636
Decimal expansion of the negated digamma function at 1/9.
[ "9", "4", "0", "7", "9", "4", "3", "2", "7", "7", "1", "3", "1", "8", "3", "1", "9", "1", "3", "2", "0", "3", "7", "5", "4", "0", "2", "9", "3", "3", "2", "6", "9", "8", "8", "7", "5", "2", "4", "2", "2", "2", "4", "0", "0", "4", "5", "8", "4", "3", "6", "5", "5", "5", "3", "0", "7", "7", "6", "0", "7", "2", "7", "7", "8", "1", "3", "6", "1", "5", "2", "1", "2", "3", "3", "8", "0", "7", "1", "8", "1", "9", "2", "1", "7", "2", "1", "0", "8", "4", "8", "8" ]
[ "nonn", "cons" ]
7
1
1
[ "A354636", "A354637", "A354638", "A354639", "A354640", "A354641" ]
null
R. J. Mathar, Jun 01 2022
2023-06-14T07:45:11
oeisdata/seq/A354/A354636.seq
c23695595eb4ef1650e0bf75b6487cde
A354637
Decimal expansion of the negated digamma function at 2/9.
[ "4", "7", "6", "1", "2", "3", "5", "0", "7", "2", "7", "5", "5", "2", "3", "0", "7", "7", "0", "8", "4", "0", "2", "5", "9", "4", "1", "1", "5", "2", "7", "1", "5", "0", "1", "7", "3", "1", "3", "8", "5", "4", "8", "5", "3", "0", "7", "3", "6", "2", "2", "6", "8", "1", "7", "1", "5", "6", "8", "4", "2", "8", "4", "5", "4", "4", "5", "6", "2", "2", "3", "8", "3", "5", "7", "3", "7", "7", "6", "2", "7", "6", "0", "6", "2", "6", "4", "1", "6", "7", "7", "4" ]
[ "nonn", "cons" ]
7
1
1
[ "A354636", "A354637", "A354638", "A354639", "A354640", "A354641" ]
null
R. J. Mathar, Jun 01 2022
2023-06-14T07:45:03
oeisdata/seq/A354/A354637.seq
2b56406d8d370c9d3c2550e35b167102
A354638
Decimal expansion of the negated digamma function at 4/9.
[ "2", "2", "6", "6", "7", "6", "4", "1", "8", "7", "5", "6", "2", "8", "9", "8", "7", "8", "6", "5", "6", "4", "6", "3", "7", "5", "4", "9", "1", "3", "7", "7", "6", "1", "6", "0", "1", "8", "0", "8", "8", "3", "1", "4", "9", "5", "7", "1", "3", "6", "3", "7", "8", "4", "4", "8", "0", "5", "8", "8", "3", "5", "8", "2", "3", "3", "9", "8", "2", "1", "2", "0", "9", "0", "7", "7", "0", "7", "0", "8", "7", "5", "5", "7", "6", "6", "0", "6", "7", "1", "2" ]
[ "nonn", "cons" ]
7
1
1
[ "A354636", "A354637", "A354638", "A354639", "A354640", "A354641" ]
null
R. J. Mathar, Jun 01 2022
2023-06-14T07:44:55
oeisdata/seq/A354/A354638.seq
455eaac58c06ec0dbfe24cfe329bf64f
A354639
Decimal expansion of the negated digamma function at 5/9.
[ "1", "7", "1", "2", "8", "1", "6", "6", "4", "0", "3", "3", "9", "5", "1", "6", "0", "3", "0", "0", "1", "9", "6", "3", "4", "4", "8", "0", "2", "2", "0", "8", "5", "8", "1", "4", "8", "3", "5", "7", "4", "1", "9", "5", "1", "2", "8", "0", "8", "2", "6", "1", "3", "1", "1", "7", "7", "3", "1", "0", "2", "7", "1", "5", "8", "2", "9", "6", "6", "3", "0", "7", "1", "2", "0", "9", "2", "6", "7", "1", "2", "8", "8", "5", "3", "4", "3", "8", "7", "5", "3", "6" ]
[ "nonn", "cons" ]
7
1
2
[ "A354636", "A354637", "A354638", "A354639", "A354640", "A354641" ]
null
R. J. Mathar, Jun 01 2022
2023-06-14T07:44:47
oeisdata/seq/A354/A354639.seq
242ef0595a4bf0a5c8392c990e58a145
A354640
Decimal expansion of the negated digamma function at 7/9.
[ "1", "0", "1", "7", "2", "3", "0", "7", "4", "1", "3", "7", "2", "0", "1", "7", "3", "4", "3", "4", "0", "6", "6", "0", "1", "3", "5", "5", "1", "5", "8", "9", "2", "3", "1", "9", "9", "3", "5", "7", "7", "0", "1", "0", "6", "3", "3", "3", "1", "4", "9", "9", "1", "4", "9", "8", "9", "8", "8", "4", "5", "7", "4", "9", "8", "6", "4", "5", "5", "8", "7", "2", "9", "7", "4", "6", "9", "4", "9", "3", "9", "5", "0", "9", "5", "3", "2", "9", "2", "7", "1", "8" ]
[ "nonn", "cons" ]
7
1
4
[ "A354636", "A354637", "A354638", "A354639", "A354640", "A354641" ]
null
R. J. Mathar, Jun 01 2022
2023-06-14T07:44:38
oeisdata/seq/A354/A354640.seq
8afd6ace505dcf75df73c1c00517e7d3
A354641
Decimal expansion of the negated digamma function at 8/9.
[ "7", "7", "6", "4", "8", "8", "4", "0", "0", "2", "6", "9", "3", "4", "7", "6", "9", "0", "5", "3", "2", "8", "6", "4", "2", "6", "8", "9", "5", "4", "9", "0", "8", "1", "5", "8", "0", "6", "0", "5", "8", "9", "7", "7", "5", "8", "0", "6", "7", "9", "2", "6", "9", "2", "1", "4", "2", "7", "3", "6", "2", "4", "2", "5", "7", "8", "3", "4", "0", "1", "5", "2", "9", "9", "9", "9", "8", "7", "0", "3", "3", "9", "2", "0", "6", "9", "1", "4", "3", "7", "4" ]
[ "nonn", "cons" ]
7
0
1
[ "A354636", "A354637", "A354638", "A354639", "A354640", "A354641" ]
null
R. J. Mathar, Jun 01 2022
2023-06-14T07:44:28
oeisdata/seq/A354/A354641.seq
eb8a03d28ac2d0651dc691e9acd2bd45
A354642
Decimal expansion of the negated digamma function at 3/10.
[ "3", "5", "0", "2", "5", "2", "4", "2", "2", "2", "2", "0", "0", "1", "3", "2", "9", "8", "8", "9", "6", "4", "4", "9", "4", "5", "0", "7", "3", "7", "1", "9", "8", "1", "5", "9", "9", "5", "3", "7", "9", "0", "8", "2", "8", "8", "4", "0", "4", "5", "0", "2", "0", "9", "5", "6", "6", "4", "9", "1", "9", "7", "5", "1", "2", "6", "4", "1", "6", "3", "7", "1", "9", "0", "3", "5", "9", "1", "0", "3", "5", "9", "0", "5", "2", "0", "3", "4", "9", "3", "0", "1" ]
[ "nonn", "cons" ]
12
1
1
[ "A306716", "A354642", "A354643", "A354644" ]
null
R. J. Mathar, Jun 01 2022
2023-06-14T07:44:17
oeisdata/seq/A354/A354642.seq
1642790a5e61dd0f2d3be580abd9cb2d
A354643
Decimal expansion of the negated digamma function at 7/10.
[ "1", "2", "2", "0", "0", "2", "3", "5", "5", "3", "6", "9", "7", "9", "3", "4", "6", "1", "4", "7", "4", "8", "6", "0", "7", "2", "4", "4", "5", "6", "1", "4", "5", "7", "9", "4", "2", "9", "7", "8", "1", "3", "4", "1", "8", "7", "5", "3", "5", "4", "8", "8", "0", "1", "2", "5", "3", "3", "4", "0", "8", "7", "0", "5", "2", "2", "0", "3", "8", "4", "5", "7", "5", "7", "0", "8", "8", "5", "2", "5", "4", "6", "6", "0", "9", "4", "7", "0", "2", "1", "4" ]
[ "nonn", "cons" ]
10
1
2
[ "A306716", "A354642", "A354643", "A354644" ]
null
R. J. Mathar, Jun 01 2022
2023-06-14T07:43:34
oeisdata/seq/A354/A354643.seq
74fcb7bd5e6976bbf9a5da1de9f1947f
A354644
Decimal expansion of the negated digamma function at 9/10.
[ "7", "5", "4", "9", "2", "6", "9", "4", "9", "9", "4", "7", "0", "5", "1", "3", "9", "1", "8", "8", "6", "3", "8", "4", "0", "2", "7", "1", "8", "2", "4", "9", "5", "5", "1", "9", "5", "9", "2", "9", "6", "0", "1", "5", "1", "6", "0", "0", "1", "4", "6", "0", "0", "9", "2", "2", "7", "0", "2", "7", "9", "3", "2", "2", "6", "4", "0", "9", "8", "6", "1", "5", "7", "8", "0", "2", "1", "6", "0", "5", "5", "8", "5", "2", "3", "1", "9", "2", "8", "0", "1", "1", "9" ]
[ "nonn", "cons" ]
10
0
1
[ "A306716", "A354642", "A354643", "A354644" ]
null
R. J. Mathar, Jun 01 2022
2023-06-14T07:43:19
oeisdata/seq/A354/A354644.seq
348f0c4be14f4dc8fef336c891e1fb2f
A354645
G.f. A(x) satisfies: -x = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n-1)/2) * A(x)^n.
[ "1", "1", "3", "9", "23", "62", "179", "571", "1888", "6309", "21114", "71387", "245162", "854703", "3010602", "10673814", "38036229", "136250135", "490696565", "1776089734", "6456234450", "23554296293", "86210280655", "316481218498", "1165089759958", "4300364442451", "15910717070706", "58996259565000" ]
[ "nonn" ]
12
0
3
[ "A354645", "A369086" ]
null
Paul D. Hanna, Jun 07 2022
2024-01-23T08:41:10
oeisdata/seq/A354/A354645.seq
02d129540a537a7694aa89807a6dc72c
A354646
G.f. A(x) satisfies: 1 = Sum_{n=-oo..+oo} (x + x^n)^n * (-2*A(x))^(n*(n-1)/2).
[ "1", "-1", "-4", "44", "316", "-22695", "-769536", "156937802", "30299780744", "-18827264809946", "-17187430890378027", "37887447329364481223", "148620374587239353630657", "-1249806569497062808351943525", "-20168103472406206381500342351035", "666759209181977763318463790517458280" ]
[ "sign" ]
7
0
3
[ "A260116", "A354646" ]
null
Paul D. Hanna, Jun 07 2022
2022-06-10T11:31:54
oeisdata/seq/A354/A354646.seq
1550fd76986071244b34e2ce7f2ee6b0
A354647
G.f. A(x) satisfies: -x^2 = Sum_{n=-oo..oo} (-1)^n * x^(n*(n+1)/2) * A(x)^(n*(n-1)/2).
[ "1", "0", "1", "3", "9", "25", "78", "256", "881", "3064", "10831", "38766", "140550", "514625", "1900301", "7067013", "26448613", "99539716", "376489459", "1430330451", "5455742957", "20885223619", "80213926069", "309002022843", "1193616950854", "4622372591972", "17942238661229", "69795082381496", "272046051362013" ]
[ "nonn" ]
9
0
4
[ "A268650", "A354647", "A354648", "A354649" ]
null
Paul D. Hanna, Jun 21 2022
2022-06-25T10:04:47
oeisdata/seq/A354/A354647.seq
38667e45946f9eacc709ebf53a2d4345
A354648
G.f. A(x) satisfies: -x^3 = Sum_{n=-oo..oo} (-1)^n * x^(n*(n+1)/2) * A(x)^(n*(n-1)/2).
[ "1", "0", "0", "1", "3", "9", "22", "54", "135", "368", "1060", "3135", "9295", "27472", "81309", "242255", "728429", "2208483", "6736523", "20634196", "63410076", "195467757", "604457802", "1875053982", "5833449236", "18195767301", "56888745654", "178238369769", "559538565187", "1759796017533", "5544359742297" ]
[ "nonn" ]
6
0
5
[ "A000716", "A268650", "A354647", "A354648", "A354649" ]
null
Paul D. Hanna, Jun 21 2022
2022-06-30T10:38:38
oeisdata/seq/A354/A354648.seq
90ef30d891269d70666ca1e0c3383b4c
A354649
G.f. A(x,y) satisfies: y = f(x,A(x,y)), where f(x,y) = Sum_{n=-oo..oo} x^(n*(n+1)/2) * y^(n*(n-1)/2) is Ramanujan's theta function.
[ "-1", "1", "0", "-3", "3", "-1", "0", "9", "-27", "30", "-15", "3", "0", "-22", "147", "-340", "390", "-246", "83", "-12", "0", "51", "-630", "2530", "-5070", "5928", "-4284", "1908", "-486", "55", "0", "-108", "2295", "-14595", "45450", "-83559", "98910", "-78282", "41580", "-14355", "2937", "-273", "0", "221", "-7476", "70737", "-319605", "849450", "-1472261", "1757688", "-1484451", "891890", "-375442", "105930", "-18109", "1428", "0", "-429", "22302", "-301070", "1886010", "-6878907", "16386636", "-27205308", "32683680", "-28981855", "19081854", "-9258678", "3231514", "-771225", "113220", "-7752" ]
[ "sign", "tabf" ]
11
0
4
[ "A000716", "A001764", "A268299", "A268650", "A354649", "A354650", "A354652", "A354653", "A354654", "A354655", "A354656", "A354657", "A354658", "A354659", "A354660", "A354661", "A354662", "A354663", "A354664" ]
null
Paul D. Hanna, Jun 02 2022
2023-03-28T13:15:21
oeisdata/seq/A354/A354649.seq
40f7fc6a2794c0ccfaee7da243fbe4a8
A354650
G.f. A(x,y) satisfies: -y = f(-x,-A(x,y)), where f(x,y) = Sum_{n=-oo..oo} x^(n*(n+1)/2) * y^(n*(n-1)/2) is Ramanujan's theta function.
[ "1", "1", "0", "3", "3", "1", "0", "9", "27", "30", "15", "3", "0", "22", "147", "340", "390", "246", "83", "12", "0", "51", "630", "2530", "5070", "5928", "4284", "1908", "486", "55", "0", "108", "2295", "14595", "45450", "83559", "98910", "78282", "41580", "14355", "2937", "273", "0", "221", "7476", "70737", "319605", "849450", "1472261", "1757688", "1484451", "891890", "375442", "105930", "18109", "1428", "0", "429", "22302", "301070", "1886010", "6878907", "16386636", "27205308", "32683680", "28981855", "19081854", "9258678", "3231514", "771225", "113220", "7752" ]
[ "nonn", "tabf" ]
10
0
4
[ "A000716", "A001764", "A268299", "A268650", "A354649", "A354650", "A354652", "A354653", "A354654", "A354655", "A354656", "A354657", "A354658", "A354659", "A354660", "A354661", "A354662", "A354663", "A354664" ]
null
Paul D. Hanna, Jun 02 2022
2023-03-28T13:18:16
oeisdata/seq/A354/A354650.seq
6e1397dbc56e891c041de8ac1cff9620
A354651
G.f. A(x) satisfies: 1/(1 - x) = Sum_{n>=1} (-1)^(n-1) * A(x)^(n^2).
[ "1", "1", "1", "2", "5", "11", "25", "64", "168", "434", "1136", "3046", "8246", "22400", "61290", "169036", "468628", "1304390", "3646104", "10232796", "28814306", "81376616", "230462906", "654363034", "1862260359", "5311064061", "15176758091", "43448083792", "124593820615", "357853635931", "1029326055479", "2964817204082" ]
[ "nonn" ]
17
1
4
[ "A006456", "A354651", "A355151" ]
null
Paul D. Hanna, Jun 18 2022
2025-02-16T08:34:03
oeisdata/seq/A354/A354651.seq
6f2abe73a97f785ea22fe9baf09b9d62
A354652
G.f. A(x) satisfies: -2 = Sum_{n=-oo..oo} (-1)^n * x^(n*(n+1)/2) * A(x)^(n*(n-1)/2).
[ "3", "26", "702", "24312", "964654", "41438412", "1876038114", "88154317378", "4258925591364", "210228411365958", "10556622328639744", "537564689914558410", "27693960347082015456", "1440798064785384773930", "75590961232091579641890", "3994794446280096850372038", "212460780898577846286309772" ]
[ "nonn" ]
16
0
1
[ "A268299", "A354649", "A354650", "A354652", "A354653", "A354654", "A354661", "A354662", "A354663", "A354664" ]
null
Paul D. Hanna, Jun 02 2022
2024-01-19T08:17:37
oeisdata/seq/A354/A354652.seq
fb0bc0d9a5a4e2c9f324f0c855960c20
A354653
G.f. A(x) satisfies: -3 = Sum_{n=-oo..oo} (-1)^n * x^(n*(n+1)/2) * A(x)^(n*(n-1)/2).
[ "4", "63", "3024", "188688", "13492350", "1044853344", "85281392688", "7224776707896", "629288553814092", "56002675660109424", "5070000855941708292", "465454828626459320736", "43230859988456631732954", "4054827527508982869148392", "383529048423080768494135488", "36541031890621600233033859488" ]
[ "nonn" ]
9
0
1
[ "A268299", "A354649", "A354650", "A354652", "A354653", "A354654", "A354661", "A354662", "A354663", "A354664" ]
null
Paul D. Hanna, Jun 02 2022
2022-07-22T17:43:28
oeisdata/seq/A354/A354653.seq
3608564c3bdb58da1932222c2d63125d
A354654
G.f. A(x) satisfies: -4 = Sum_{n=-oo..oo} (-1)^n * x^(n*(n+1)/2) * A(x)^(n*(n-1)/2).
[ "5", "124", "9300", "912520", "102616748", "12498655200", "1604505393140", "213790010204692", "29287693334340840", "4099332312599011100", "583685111605968443456", "84277588096627459702860", "12310921909740521584887824", "1816058097888803062860159620", "270156262107594683175523302780" ]
[ "nonn" ]
7
0
1
[ "A268299", "A354649", "A354650", "A354652", "A354653", "A354654", "A354661", "A354662", "A354663", "A354664" ]
null
Paul D. Hanna, Jun 02 2022
2022-06-07T18:58:45
oeisdata/seq/A354/A354654.seq
629688b42bc1d38aadcac2708dbc3b6d
A354655
Column 2 of triangle A354650: a(n) = A354650(n,2), for n >= 1.
[ "3", "27", "147", "630", "2295", "7476", "22302", "62100", "163260", "409080", "983367", "2280306", "5122026", "11184075", "23806575", "49521456", "100872135", "201558231", "395675475", "764130780", "1453424259", "2725614243", "5044092372", "9219499800", "16655554125", "29759775435", "52623867051" ]
[ "nonn" ]
7
1
1
[ "A354649", "A354650", "A354655", "A354656" ]
null
Paul D. Hanna, Jun 02 2022
2022-06-04T08:01:17
oeisdata/seq/A354/A354655.seq
de1b8e5414eeb3a3d4f8480ff6e5bc9c
A354656
Column 3 of triangle A354650: a(n) = A354650(n,3), for n >= 1.
[ "1", "30", "340", "2530", "14595", "70737", "301070", "1157820", "4100785", "13563010", "42321840", "125586440", "356621070", "973989030", "2569116330", "6567458520", "16317741975", "39504992395", "93390535840", "215983566780", "489454806785", "1088433416785", "2378160809610", "5111208572940", "10816601842950" ]
[ "nonn" ]
10
1
2
[ "A354649", "A354650", "A354655", "A354656", "A354657" ]
null
Paul D. Hanna, Jun 02 2022
2023-09-30T18:02:34
oeisdata/seq/A354/A354656.seq
29ce59f2795dc969d52bf66dd37e2a74
A354657
a(n) = A354655(n)/3, for n >= 1.
[ "1", "9", "49", "210", "765", "2492", "7434", "20700", "54420", "136360", "327789", "760102", "1707342", "3728025", "7935525", "16507152", "33624045", "67186077", "131891825", "254710260", "484474753", "908538081", "1681364124", "3073166600", "5551851375", "9919925145", "17541289017", "30714092066", "53279031420" ]
[ "nonn" ]
6
1
2
[ "A354649", "A354650", "A354655", "A354657" ]
null
Paul D. Hanna, Jun 02 2022
2022-06-04T08:01:24
oeisdata/seq/A354/A354657.seq
96cb1de577cf0ac77d30578ac0beff80
A354658
A diagonal of triangle A354650: a(n) = A354650(n,n), for n >= 0.
[ "1", "3", "27", "340", "5070", "83559", "1472261", "27205308", "520974180", "10257025240", "206469879462", "4232227325352", "88073315164471", "1856404180514940", "39560345751767970", "851083806077023888", "18462636758298743712", "403459312929849694791", "8874351725505564788350" ]
[ "nonn" ]
8
0
2
[ "A354649", "A354650", "A354658", "A354659", "A354660" ]
null
Paul D. Hanna, Jun 02 2022
2022-06-08T02:31:08
oeisdata/seq/A354/A354658.seq
78b67676365989174094ddf60ca9c9d7
A354659
A diagonal of triangle A354650: a(n) = A354650(n,n+1), for n >= 0.
[ "1", "3", "30", "390", "5928", "98910", "1757688", "32683680", "628884300", "12428334215", "250940544738", "5156722096422", "107538413657010", "2270751678647100", "48464836803383400", "1044050265679857144", "22675350105240015204", "496034970650911331550", "10920742396832034391590" ]
[ "nonn" ]
8
0
2
[ "A354649", "A354650", "A354658", "A354659", "A354660" ]
null
Paul D. Hanna, Jun 02 2022
2023-03-19T07:39:05
oeisdata/seq/A354/A354659.seq
03a77c8db8ef446d7bd84362d0511eff
A354660
a(n) = A354650(n,2*n), for n >= 0.
[ "1", "3", "15", "83", "486", "2937", "18109", "113220", "715122", "4552229", "29156985", "187683795", "1213110600", "7868238588", "51184173036", "333809308696", "2181842704602", "14288748463485", "93737673347185", "615889045662345", "4052198020223430", "26694405836621985", "176052003674681925" ]
[ "nonn" ]
8
0
2
[ "A354649", "A354650", "A354658", "A354659", "A354660" ]
null
Paul D. Hanna, Jun 02 2022
2023-03-19T07:44:39
oeisdata/seq/A354/A354660.seq
80fb80abfbfdae61fc22efcd05880662
A354661
G.f. A(x) satisfies: 1 = Sum_{n=-oo..oo} (-x)^(n*(n+1)/2) * A(x)^(n*(n-1)/2), with A(0) = 0.
[ "1", "0", "0", "2", "0", "0", "8", "0", "0", "44", "0", "6", "280", "0", "96", "1934", "0", "1124", "14088", "18", "11792", "106536", "648", "117626", "828360", "13416", "1142288", "6580780", "216000", "10921088", "53184864", "3019614", "103408416", "435930008", "38629656", "973041448", "3615741192", "465419760", "9118011128", "30298375236" ]
[ "nonn" ]
11
1
4
[ "A268299", "A354649", "A354650", "A354652", "A354653", "A354654", "A354661", "A354662", "A354663", "A354664" ]
null
Paul D. Hanna, Jun 02 2022
2023-03-19T08:06:23
oeisdata/seq/A354/A354661.seq
66cc5c188818ed8c387a16f203645b11
A354662
G.f. A(x) satisfies: 2 = Sum_{n=-oo..+oo} (-x)^(n*(n+1)/2) * A(x)^(n*(n-1)/2).
[ "1", "2", "6", "32", "190", "1236", "8482", "60434", "442788", "3315046", "25249888", "195040914", "1524256336", "12030033178", "95748941322", "767655502862", "6193902044684", "50257335231264", "409825115116030", "3356850545246400", "27606085924603602", "227850606781308660", "1886792409865105988" ]
[ "nonn" ]
13
0
2
[ "A268299", "A354649", "A354650", "A354652", "A354653", "A354654", "A354661", "A354662", "A354663", "A354664" ]
null
Paul D. Hanna, Jun 02 2022
2024-01-17T23:32:02
oeisdata/seq/A354/A354662.seq
f4bd0be8b8c570d5d2bc5604dbcde6e2
A354663
G.f. A(x) satisfies: 3 = Sum_{n=-oo..oo} (-x)^(n*(n+1)/2) * A(x)^(n*(n-1)/2).
[ "2", "9", "108", "1848", "36306", "771768", "17280096", "401451192", "9587095686", "233892105912", "5804193409056", "146051807458320", "3717875447707254", "95571022734750600", "2477365983601721280", "64684289495622383472", "1699638032224106092368", "44909438746576707103608" ]
[ "nonn" ]
9
0
1
[ "A268299", "A354649", "A354650", "A354652", "A354653", "A354654", "A354661", "A354662", "A354663", "A354664" ]
null
Paul D. Hanna, Jun 02 2022
2022-07-22T17:44:19
oeisdata/seq/A354/A354663.seq
bf761d1bb08b318a1a95fe7672622387
A354664
G.f. A(x) satisfies: 4 = Sum_{n=-oo..oo} (-x)^(n*(n+1)/2) * A(x)^(n*(n-1)/2).
[ "3", "28", "756", "28200", "1205228", "55731456", "2714642292", "137199520340", "7127794098792", "378292284479388", "20421818573265728", "1117886561607128940", "61904487399635790288", "3461693986652051482948", "195203095905903229325340", "11087371481682320212435332", "633751222047605882649272600" ]
[ "nonn" ]
16
0
1
[ "A268299", "A354649", "A354650", "A354652", "A354653", "A354654", "A354661", "A354662", "A354663", "A354664" ]
null
Paul D. Hanna, Jun 02 2022
2024-01-19T08:01:04
oeisdata/seq/A354/A354664.seq
1b7436b29b19ce551588466387c37048
A354665
Triangle read by rows, T(n,k) = T(n-1,k) + T(n-1,k-1) - T(n-2,k-1) + T(n-2,k-2) + T(n-3,k-1) - T(n-3,k-3) + delta(n,0)*delta(k,0) - delta(n,1)*delta(k,1), T(n<k,k) = T(n,k<0) = 0.
[ "1", "1", "0", "1", "0", "1", "1", "1", "2", "0", "1", "2", "4", "0", "1", "1", "3", "6", "3", "3", "0", "1", "4", "9", "8", "9", "0", "1", "1", "5", "13", "17", "18", "6", "4", "0", "1", "6", "18", "30", "36", "20", "16", "0", "1", "1", "7", "24", "48", "66", "55", "40", "10", "5", "0", "1", "8", "31", "72", "114", "120", "100", "40", "25", "0", "1", "1", "9", "39", "103", "186" ]
[ "easy", "nonn", "tabl" ]
25
0
9
[ "A007318", "A011782", "A059259", "A123521", "A157897", "A224809", "A335964", "A350110", "A350111", "A350112", "A354665", "A354666", "A354667", "A354668" ]
null
Michael A. Allen, Jun 04 2022
2022-12-27T03:26:23
oeisdata/seq/A354/A354665.seq
90a6f1dd73eba2167ce4ddda3bc15aca
A354666
Triangle read by rows, T(n,k) = T(n-1,k) + T(n-2,k-1) + 2*T(n-2,k-2) - T(n-3,k-1) - T(n-3,k-2) + T(n-4,k-1) + T(n-4,k-2) - T(n-4,k-3) - T(n-4,k-4) + delta(n,0)*delta(k,0) - delta(n,2)*(delta(k,1) + delta(k,2)), T(n<k,k) = T(n,k<0) = 0.
[ "1", "1", "0", "1", "0", "1", "1", "0", "2", "0", "1", "1", "4", "0", "1", "1", "2", "6", "0", "3", "0", "1", "3", "9", "4", "9", "0", "1", "1", "4", "12", "10", "18", "0", "4", "0", "1", "5", "16", "21", "36", "10", "16", "0", "1", "1", "6", "21", "36", "60", "30", "40", "0", "5", "0", "1", "7", "27", "57", "100", "81", "100", "20", "25", "0", "1", "1", "8", "34", "84", "158", "168" ]
[ "easy", "nonn", "tabl" ]
12
0
9
[ "A007318", "A059259", "A099163", "A123521", "A157897", "A224808", "A335964", "A350110", "A350111", "A350112", "A354665", "A354666", "A354667", "A354668" ]
null
Michael A. Allen, Jun 04 2022
2022-12-27T03:26:32
oeisdata/seq/A354/A354666.seq
54d9f196e226b44393d3b3c5ad48fbec
A354667
Triangle read by rows: T(n,k) is the number of tilings of an (n+4*k) X 1 board using k (1,1;5)-combs and n-k squares.
[ "1", "1", "0", "1", "0", "1", "1", "0", "2", "0", "1", "0", "4", "0", "1", "1", "1", "6", "0", "3", "0", "1", "2", "9", "0", "9", "0", "1", "1", "3", "12", "5", "18", "0", "4", "0", "1", "4", "16", "12", "36", "0", "16", "0", "1", "1", "5", "20", "25", "60", "15", "40", "0", "5", "0", "1", "6", "25", "42", "100", "42", "100", "0", "25", "0", "1", "1", "7", "31", "66", "150", "112", "200" ]
[ "easy", "nonn", "tabl" ]
12
0
9
[ "A005578", "A007318", "A059259", "A123521", "A157897", "A224811", "A335964", "A350110", "A350111", "A350112", "A354665", "A354666", "A354667", "A354668" ]
null
Michael A. Allen, Jun 05 2022
2022-12-27T03:26:39
oeisdata/seq/A354/A354667.seq
fc26bbaa8263f8c02a154e906918ae54
A354668
Triangle read by rows: T(n,k) is the number of tilings of an (n+2*k) X 1 board using k (1,2;3)-combs and n-k squares.
[ "1", "1", "0", "1", "0", "0", "1", "0", "0", "1", "1", "0", "1", "2", "0", "1", "1", "3", "4", "0", "0", "1", "2", "5", "8", "0", "0", "1", "1", "3", "8", "12", "0", "3", "3", "0", "1", "4", "12", "18", "9", "12", "9", "0", "0", "1", "5", "16", "27", "25", "29", "27", "0", "0", "1", "1", "6", "21", "42", "51", "66", "54", "0", "6", "4", "0", "1", "7", "27", "62", "95", "135", "108", "36" ]
[ "easy", "nonn", "tabl" ]
15
0
14
[ "A007318", "A059259", "A123521", "A157897", "A224810", "A335964", "A350110", "A350111", "A350112", "A354665", "A354666", "A354667", "A354668" ]
null
Michael A. Allen, Jul 30 2022
2022-12-27T08:59:39
oeisdata/seq/A354/A354668.seq
fce7a41fe212f8f969e529b5b8299970
A354669
Number of minors in the n-gear graph.
[ "145", "799", "4264", "21403", "100551", "449637" ]
[ "nonn", "more" ]
9
3
1
null
null
Eric W. Weisstein, Jun 02 2022
2025-02-16T08:34:03
oeisdata/seq/A354/A354669.seq
68c5db2d6b2fb4222db798fb47f0995f
A354670
Number of graph minors in the n-book graph.
[ "13", "60", "262", "957", "2934", "7786", "18434", "39869", "80166", "151830", "273540", "472363", "786516", "1268760", "1990516", "3046799", "4562072", "6697128", "9657114", "13700817", "19151338", "26408286", "35961630", "48407353", "64465058", "84997682", "111033480", "143790447", "184703352", "235453564" ]
[ "nonn", "easy" ]
24
1
1
null
null
Eric W. Weisstein, Jun 02 2022
2025-02-16T08:34:03
oeisdata/seq/A354/A354670.seq
e8bbafff188154ac5bed58ce7b9cc004
A354671
Number of minors in the n-sunlet graph.
[ "3", "11", "43", "133", "371", "1021", "2779", "7681", "21439", "60550", "172161", "492298", "1410952", "4049513", "11622014", "33336964", "95521759", "273357891", "781150889", "2228929238", "6350415132", "18065990265", "51319949402", "145577550238", "412387443328", "1166650464497", "3296258649759", "9301823400571", "26218111901032", "73814367066252" ]
[ "nonn" ]
15
1
1
[ "A352102", "A354671" ]
null
Eric W. Weisstein, Jun 02 2022
2025-06-20T20:24:06
oeisdata/seq/A354/A354671.seq
b1b745812a9706be08a8a28ab4dccbcc
A354672
Numbers x with property that x is not the smallest possible value in the Pellian equation x^2 - D*y^2 = 1 with D = squarefree part of (x^2 - 1).
[ "7", "17", "26", "31", "49", "71", "97", "99", "127", "161", "199", "241", "244", "287", "337", "362", "391", "449", "485", "511", "577", "647", "721", "799", "846", "881", "967", "1057", "1151", "1249", "1351", "1457", "1567", "1681", "1799", "1921", "2024", "2047", "2177", "2311", "2449", "2591", "2737", "2887", "2889", "3041", "3199", "3361", "3363" ]
[ "nonn" ]
45
1
1
null
null
Herbert Kociemba, Jun 02 2022
2025-02-16T08:34:03
oeisdata/seq/A354/A354672.seq
8561101b4277dc1fe56f41410f517552
A354673
Smallest number of unit cells that must be removed from an n X n square board in order to avoid any cycles.
[ "0", "1", "2", "4", "6", "10", "13", "18", "22", "28", "34", "42", "49", "58", "66", "76", "86", "98", "109", "122", "134", "148", "162", "178", "193", "210", "226", "244", "262", "282", "301", "322", "342", "364", "386", "410", "433", "458", "482", "508", "534", "562", "589", "618", "646", "676", "706", "738", "769", "802", "834", "868", "902", "938", "973", "1010", "1046" ]
[ "nonn", "easy" ]
26
1
3
[ "A000170", "A085577", "A104519", "A239072", "A239231", "A354673" ]
null
Giedrius Alkauskas, Jun 02 2022
2022-06-17T16:05:30
oeisdata/seq/A354/A354673.seq
293051ecbbe7cd1972eafcb7ad9e1cd2
A354674
a(n) = Sum_{k=0..n} k! * k^(k+n) * |Stirling1(n,k)|.
[ "1", "1", "33", "4568", "1653010", "1236180194", "1657339714418", "3620923498508952", "12037504737979759944", "57827877567223173191712", "385581993722741959459382352", "3454851578510897594456017095504", "40509304222426523176427339597382336" ]
[ "nonn" ]
8
0
3
[ "A320096", "A350721", "A350722", "A351333", "A351769", "A354674" ]
null
Seiichi Manyama, Jun 02 2022
2022-06-02T15:38:26
oeisdata/seq/A354/A354674.seq
e64121e30dd4dc2c15c297184a8cbc99
A354675
a(n) is the number of near-Wieferich primes with |A| <= 10 less than 10^n, where A(k) = A258367(k).
[ "3", "15", "21", "29", "34", "35", "36", "36", "41" ]
[ "nonn", "hard", "more" ]
16
1
1
[ "A001220", "A006880", "A195988", "A246568", "A258367", "A353141", "A354675", "A354676", "A354677", "A354678" ]
null
Felix Fröhlich, Jun 02 2022
2022-06-26T03:08:26
oeisdata/seq/A354/A354675.seq
878fbe165c7175f8afdb3b72a4b608e1
A354676
a(n) = number of near-Wieferich primes with |A| <= 100 less than 10^n.
[ "3", "24", "105", "154", "213", "243", "268", "288", "307" ]
[ "nonn", "hard", "more" ]
5
1
1
[ "A006880", "A195988", "A246568", "A258367", "A353141", "A354675", "A354676", "A354677", "A354678" ]
null
Felix Fröhlich, Jun 02 2022
2022-07-01T22:14:21
oeisdata/seq/A354/A354676.seq
e08284a02bb9e2a70a7b9e72b9d71888
A354677
a(n) = number of near-Wieferich primes with |A| <= 1000 less than 10^n.
[ "3", "24", "167", "698", "1155", "1502", "1812", "2064", "2297" ]
[ "nonn", "hard", "more" ]
5
1
1
[ "A006880", "A195988", "A246568", "A258367", "A353141", "A354675", "A354676", "A354677", "A354678" ]
null
Felix Fröhlich, Jun 02 2022
2022-07-01T22:15:15
oeisdata/seq/A354/A354677.seq
bbbff405c026db6cc7ac683ef24bd34d
A354678
a(n) = number of near-Wieferich primes with |A| <= 10000 less than 10^n.
[ "3", "24", "167", "1228", "5250", "8851", "11922", "14549", "16863" ]
[ "nonn", "hard", "more" ]
5
1
1
[ "A006880", "A195988", "A246568", "A258367", "A353141", "A354675", "A354676", "A354677", "A354678" ]
null
Felix Fröhlich, Jun 02 2022
2022-07-01T22:15:23
oeisdata/seq/A354/A354678.seq
83729d613df0ed4687a7b06817374f83
A354679
First differences of A354575.
[ "1", "3", "-2", "4", "-3", "5", "-1", "7", "-4", "-5", "11", "-7", "9", "-6", "8", "2", "-11", "13", "-9", "15", "-17", "19", "-13", "17", "-19", "23", "-15", "21", "-25", "27", "-22", "16", "-14", "6", "18", "-29", "31", "-27", "29", "-23", "25", "-21", "33", "-41", "37", "-35", "41", "-37", "43", "-40", "22", "-16", "32", "-31", "35", "10", "-51", "47", "-43", "39", "-33", "49", "-47", "45", "-55", "53", "-44", "14", "24", "-26" ]
[ "sign", "look" ]
19
1
2
[ "A354575", "A354679", "A354687", "A354688", "A354727", "A354739" ]
null
Scott R. Shannon, Jun 05 2022
2022-06-05T08:25:01
oeisdata/seq/A354/A354679.seq
191b0fddbd3bd1fc3ac103b4815e1ff1
A354680
Terms of A354169 that are not powers of 2, in order of appearance.
[ "0", "3", "12", "17", "34", "68", "136", "768", "1025", "18", "2080", "12288", "16388", "72", "32896", "196608", "262400", "524800", "1048577", "2098176", "4194306", "48", "8390656", "50331648", "67112960", "134225920", "268435460", "536887296", "1073741832", "192", "2147516416", "12884901888", "17179934720", "34359869440" ]
[ "nonn", "base" ]
53
1
2
[ "A000120", "A057716", "A354169", "A354680", "A354767", "A354798" ]
null
Rémy Sigrist and N. J. A. Sloane, Jun 06 2022
2023-11-29T13:08:01
oeisdata/seq/A354/A354680.seq
485364ea4af464096dcce9f52eb12239
A354681
Integers whose names in French contain no letter more than once.
[ "-4", "-2", "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "14", "15", "17", "19", "20", "22", "60", "100", "106", "110" ]
[ "easy", "fini", "full", "sign", "word", "less" ]
26
1
1
[ "A059916", "A117383", "A354681" ]
null
Paul Duckett, Jun 02 2022
2022-06-08T23:20:24
oeisdata/seq/A354/A354681.seq
963dfe152fbb0a9959f563b3a07bc9df
A354682
Interprimes that are products of two successive primes.
[ "6", "15", "667", "1517", "9797", "123197", "233273", "522713", "627239", "826277", "974153", "988027", "1127843", "1162003", "1209991", "2624399", "2637367", "3493157", "4235339", "4384811", "4460543", "6827753", "7784099", "10916407", "11370383", "17065157", "25009997", "26347493", "29964667", "32330587", "32387477", "33419957", "34809991", "35354867", "37088099" ]
[ "nonn" ]
12
1
1
[ "A006094", "A024675", "A174955", "A354682" ]
null
J. M. Bergot and Robert Israel, Jun 03 2022
2024-11-03T10:40:37
oeisdata/seq/A354/A354682.seq
a1ca1d1176c572f9644db47f38ba3ca3
A354683
Decimal expansion of -2 - (1 - gamma - log(2))*Pi (negated).
[ "1", "1", "5", "0", "6", "3", "0", "0", "7", "0", "8", "9", "4", "5", "8", "7", "6", "0", "8", "3", "4", "8", "8", "1", "9", "9", "5", "3", "7", "7", "0", "8", "4", "8", "9", "1", "7", "7", "5", "0", "9", "2", "1", "5", "1", "7", "6", "3", "3", "2", "1", "8", "7", "1", "8", "0", "1", "3", "0", "0", "1", "2", "6", "0", "9", "1", "5", "9", "9", "8", "6", "2", "7", "4", "7", "9", "4", "2", "4", "9", "7", "3", "5", "5", "2", "3", "6", "0", "3", "5", "9", "8", "5", "9", "9", "0", "3", "6", "0", "1", "7", "8", "5", "4", "3" ]
[ "nonn", "cons" ]
5
1
3
[ "A000796", "A001620", "A002162", "A354683" ]
null
Amiram Eldar, Jun 03 2022
2022-06-03T05:35:31
oeisdata/seq/A354/A354683.seq
6339769b633164c83c779b0d6dbfb50c
A354684
Decimal expansion of the horizontal distance between the equal-height endpoints of a suspended unit-length chain for which the area between the chord joining the endpoints and the chain has a maximum value.
[ "6", "7", "1", "6", "2", "8", "5", "3", "0", "5", "9", "0", "0", "5", "9", "6", "3", "0", "1", "7", "7", "0", "1", "1", "2", "1", "8", "8", "9", "6", "7", "6", "2", "4", "2", "4", "1", "5", "9", "8", "0", "6", "0", "2", "5", "0", "7", "0", "6", "7", "3", "3", "4", "0", "4", "4", "5", "4", "8", "3", "6", "3", "7", "8", "7", "8", "1", "5", "9", "0", "6", "6", "1", "6", "1", "0", "8", "1", "0", "2", "0", "7", "9", "5", "8", "6", "6", "0", "7", "1", "7", "8", "6", "9", "2", "3", "5", "1", "8", "5", "7", "8", "8", "0", "1" ]
[ "nonn", "cons" ]
7
0
1
[ "A225146", "A354684" ]
null
Amiram Eldar, Jun 03 2022
2022-06-03T05:37:03
oeisdata/seq/A354/A354684.seq
ff4ed23189327bd692b7da98a3a3b88c
A354685
a(n) = n! * Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * H(k), where H(k) is the k-th harmonic number.
[ "0", "1", "5", "50", "854", "22354", "833244", "41974176", "2748169584", "226916044848", "23069499189120", "2831994888419520", "413051278946186880", "70608112721914654080", "13982696139441640584960", "3175762393024883382067200", "820007850688478572529203200", "238863690100874514528150681600" ]
[ "nonn" ]
9
0
3
[ "A001008", "A002805", "A087751", "A222059", "A302548", "A354685", "A354686" ]
null
Ilya Gutkovskiy, Jun 03 2022
2022-06-04T06:41:31
oeisdata/seq/A354/A354685.seq
445bf2f46fc901cbbc9b3b025926862a
A354686
a(n) = n! * Sum_{k=1..n} Stirling1(n,k) * H(k), where H(k) is the k-th harmonic number.
[ "0", "1", "1", "-4", "38", "-646", "17124", "-651120", "33563760", "-2251415376", "190506294720", "-19843054116480", "2494435702953600", "-372324067662349440", "65089674982557308160", "-13172994619821785548800", "3055455516855073351219200", "-805168341051328705189939200" ]
[ "sign" ]
5
0
4
[ "A001008", "A002805", "A087751", "A222059", "A302547", "A354685", "A354686" ]
null
Ilya Gutkovskiy, Jun 03 2022
2022-06-03T07:41:00
oeisdata/seq/A354/A354686.seq
b7293b23b892152850e0ea9cfae56998
A354687
a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared that shares a factor with a(n-1) and the difference | a(n) - a(n-1) | is distinct from all previous differences.
[ "1", "2", "4", "8", "14", "6", "3", "12", "22", "10", "5", "20", "34", "16", "32", "52", "13", "26", "48", "15", "36", "9", "33", "44", "18", "46", "23", "69", "21", "28", "58", "24", "56", "7", "42", "78", "27", "72", "30", "55", "11", "66", "104", "38", "19", "76", "116", "29", "87", "141", "39", "91", "35", "85", "17", "102", "40", "100", "25", "90", "153", "45", "114", "50", "120", "192", "51", "68", "142", "54", "130", "208", "60" ]
[ "nonn" ]
23
1
2
[ "A064413", "A352763", "A354087", "A354687", "A354688", "A354721", "A354731" ]
null
Scott R. Shannon, Jun 03 2022
2022-06-04T13:04:11
oeisdata/seq/A354/A354687.seq
8f2e552e6c6dcaf5b80c5b2157ebbf56
A354688
a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared that is coprime to a(n-1) and the difference | a(n) - a(n-1) | is distinct from all previous differences.
[ "1", "2", "5", "3", "7", "12", "19", "4", "13", "21", "8", "25", "6", "17", "11", "23", "9", "29", "39", "10", "31", "15", "37", "14", "41", "16", "47", "65", "18", "53", "20", "57", "83", "22", "61", "27", "55", "79", "24", "67", "26", "71", "33", "73", "43", "75", "119", "30", "89", "32", "81", "28", "93", "35", "86", "149", "34", "101", "45", "91", "127", "36", "107", "38", "111", "49", "97", "139", "40", "117", "167", "42", "121", "46" ]
[ "nonn" ]
21
1
2
[ "A093714", "A352588", "A354687", "A354688", "A354721", "A354731" ]
null
Scott R. Shannon, Jun 03 2022
2022-06-04T13:04:52
oeisdata/seq/A354/A354688.seq
7f94672c78a7710e8ad7b696a9b185aa
A354689
Smallest Euler pseudoprime to base n.
[ "9", "341", "121", "341", "217", "185", "25", "9", "91", "9", "133", "65", "21", "15", "341", "15", "9", "25", "9", "21", "65", "21", "33", "25", "217", "9", "65", "9", "15", "49", "15", "25", "545", "21", "9", "35", "9", "39", "133", "39", "21", "451", "21", "9", "133", "9", "65", "49", "25", "21", "25", "51", "9", "55", "9", "33", "25", "57", "15", "341", "15", "9", "341", "9", "33", "65" ]
[ "nonn" ]
9
1
1
[ "A006970", "A090086", "A298756", "A326614", "A354689" ]
null
Jinyuan Wang, Jun 03 2022
2025-02-16T08:34:03
oeisdata/seq/A354/A354689.seq
f7499aed86a71e1166bbe54cd58e5f17
A354690
Number of unrooted labeled binary trees satisfying a path-length criterion concerning three labeled leaves.
[ "1", "2", "8", "54", "468", "4950", "62640", "920430", "15373260", "287746830", "5965860600", "135691860150", "3359026786500", "89901262801350", "2586669802516800", "79617014497770750", "2610359828029453500", "90821198300068986750", "3342059240460417477000", "129683329092674014407750" ]
[ "nonn" ]
31
3
2
[ "A001147", "A354690" ]
null
Noah A Rosenberg, Jun 03 2022
2022-09-10T06:00:32
oeisdata/seq/A354/A354690.seq
4ffffab9561a8511c843c4a5829ee8ac
A354691
Numbers k with the property that 4*p+q and 4*q+p are primes, where p = prime(k) and q = prime(k+1).
[ "2", "23", "74", "86", "91", "96", "97", "99", "100", "105", "133", "174", "280", "305", "357", "372", "504", "554", "562", "565", "660", "668", "686", "716", "733", "741", "789", "796", "859", "885", "909", "925", "993", "1021", "1103", "1131", "1136", "1144", "1191", "1215", "1234", "1248", "1285", "1326", "1334", "1414", "1503", "1559", "1577", "1590", "1607", "1656", "1738", "1751", "1822", "1847", "1894", "1929", "2088", "2090" ]
[ "nonn" ]
8
1
1
null
null
Zak Seidov, Jun 03 2022
2022-06-04T19:40:51
oeisdata/seq/A354/A354691.seq
714c9ddca39ba59fa98dba4bd6023952
A354692
Smallest Euler-Jacobi pseudoprime to all natural bases up to prime(n) - 1 that is not a base prime(n) Euler-Jacobi pseudoprime.
[ "9", "561", "10585", "1729", "488881", "399001", "2433601", "1857241", "6189121", "549538081", "50201089", "14469841", "86566959361", "311963097601", "369838909441", "31929487861441", "6389476833601", "8493512837546881", "31585234281457921", "10120721237827201", "289980482095624321", "525025434548260801", "91230634325542321" ]
[ "nonn" ]
11
1
1
[ "A002110", "A007324", "A047713", "A285549", "A354692", "A354694" ]
null
Jinyuan Wang, Jun 03 2022
2025-02-16T08:34:03
oeisdata/seq/A354/A354692.seq
acabdbb9aa42deae46a4560fb95fd3b7
A354693
Number of unlabeled prime posets with n elements.
[ "1", "0", "0", "1", "4", "28", "234", "2585", "36326", "646405", "14528011", "412212506" ]
[ "nonn", "more" ]
13
1
5
[ "A000112", "A003430", "A202182", "A354693" ]
null
Salah Uddin Mohammad, Jun 03 2022
2022-07-27T11:53:23
oeisdata/seq/A354/A354693.seq
de2c20578c24435134e009c8d81507b8
A354694
Least Euler pseudoprime to base 2 through base prime(n).
[ "341", "1729", "1729", "46657", "46657", "162401", "399001", "399001", "399001", "399001", "488881", "3057601", "3057601", "3828001", "3828001", "3828001", "3828001", "3828001", "3828001", "3828001", "3828001", "3828001", "3828001", "3828001", "3828001", "17098369", "17098369", "17098369", "17098369", "17236801", "17236801" ]
[ "nonn" ]
6
1
1
[ "A002110", "A007324", "A083876", "A271221", "A354694" ]
null
Jinyuan Wang, Jun 04 2022
2025-02-16T08:34:03
oeisdata/seq/A354/A354694.seq
d08ae370802443545cd29808bc3a4b3a
A354695
G.f. A(x) satisfies: A(x) = 1 + x * A(x^3/(1 - x)^3) / (1 - x)^3.
[ "1", "1", "3", "6", "11", "21", "42", "87", "189", "432", "1018", "2415", "5694", "13297", "30768", "70626", "161011", "364977", "823536", "1851706", "4152972", "9298653", "20800758", "46516437", "104044590", "232856189", "521601174", "1169670645", "2626188319", "5904269526", "13292581605", "29968831278", "67663806228" ]
[ "nonn" ]
8
0
3
[ "A119685", "A351816", "A352045", "A354695", "A354696" ]
null
Seiichi Manyama, Jun 03 2022
2022-06-03T12:59:31
oeisdata/seq/A354/A354695.seq
cb315e13a3328a934c1cf9f75ee980cb
A354696
G.f. A(x) satisfies: A(x) = 1 + x * A(x^4/(1 - x)^4) / (1 - x)^4.
[ "1", "1", "4", "10", "20", "36", "64", "120", "240", "499", "1060", "2314", "5252", "12360", "29632", "70992", "168096", "392465", "905940", "2075314", "4730052", "10735516", "24258688", "54553000", "122076240", "271914499", "603183508", "1333268098", "2937818900", "6455143760", "14146816640", "30929336736", "67473335104" ]
[ "nonn" ]
8
0
3
[ "A119685", "A351817", "A352066", "A354695", "A354696" ]
null
Seiichi Manyama, Jun 03 2022
2022-06-03T12:59:36
oeisdata/seq/A354/A354696.seq
bbba2b71a29ac969e835548e446094c2
A354697
a(n) is the least integer that can be written in two or more ways as the product of the integers in two subsets of its A070824(a(n)) nontrivial divisors, each of size n and with empty intersection.
[ "12", "120", "720", "10080", "110880", "1814400", "26611200", "518918400", "10378368000", "261534873600", "5928123801600", "168951528345600", "4505374089216000", "152056375511040000", "4663062182338560000", "167870238564188160000", "6463004184721244160000", "249902828475888107520000", "10495918795987300515840000" ]
[ "nonn", "hard" ]
40
2
1
[ "A002182", "A025487", "A354457", "A354697" ]
null
Hugo Pfoertner, Jun 03 2022
2024-05-14T13:40:52
oeisdata/seq/A354/A354697.seq
060625ee719380482cdb54a726da4a74
A354698
T(n,k) is the number of points with integer coordinates strictly inside the triangle with vertices (0,0), (n,0), (n,k), where T(n,k) is a triangle read by rows, 2 <= k <= n.
[ "0", "1", "1", "1", "3", "3", "2", "4", "6", "6", "2", "4", "7", "10", "10", "3", "6", "9", "12", "15", "15", "3", "7", "9", "14", "17", "21", "21", "4", "7", "12", "16", "19", "24", "28", "28", "4", "9", "13", "16", "22", "27", "31", "36", "36", "5", "10", "15", "20", "25", "30", "35", "40", "45", "45", "5", "10", "15", "22", "25", "33", "37", "43", "49", "55", "55", "6", "12", "18", "24", "30", "36", "42", "48", "54", "60", "66", "66" ]
[ "nonn", "tabl", "easy" ]
16
2
5
[ "A000217", "A004526", "A074148", "A117571", "A354698" ]
null
Hugo Pfoertner, Jun 06 2022
2022-06-08T10:16:18
oeisdata/seq/A354/A354698.seq
e043fa1341e9d0b9831dfa543913ac0b
A354699
T(w,h) is the number of non-congruent triangles with distinct side lengths whose vertices with integer coordinates (x_i, y_i) all lie on the perimeter of a rectangle of width w and height h, with max(x_i)-min(x_i) = w and max(y_i)-min(y_i) = h.
[ "0", "2", "1", "4", "5", "3", "5", "6", "7", "4", "7", "8", "8", "9", "6", "8", "9", "10", "11", "12", "7", "10", "11", "12", "13", "14", "15", "9", "11", "12", "13", "13", "15", "16", "17", "10", "13", "14", "14", "16", "17", "18", "19", "20", "12", "14", "15", "16", "17", "18", "18", "20", "20", "22", "13", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "15", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "16" ]
[ "nonn", "tabl" ]
8
1
2
[ "A354699", "A354700" ]
null
Hugo Pfoertner, Jun 07 2022
2024-12-19T11:53:22
oeisdata/seq/A354/A354699.seq
9e53365b43d7c13ddbb8cc69af65f388
A354700
T(w,h) is the number of non-congruent quadrilaterals whose vertices with integer coordinates (x_i, y_i) all lie on the perimeter of a rectangle of width w and height h, with no 3 points on the same edge of the rectangle, max(x_i) - min(x_i) = w and max(y_i) - min(y_i) = h, such that the 6 distances between the 4 vertices are distinct.
[ "0", "0", "0", "1", "4", "5", "2", "16", "36", "21", "8", "33", "69", "116", "71", "13", "52", "126", "201", "317", "181", "22", "84", "191", "299", "445", "639", "366", "28", "110", "249", "373", "581", "839", "1105", "585", "43", "157", "330", "529", "806", "1094", "1463", "1856", "1009", "50", "190", "407", "653", "1014", "1360", "1853", "2295", "2958", "1562" ]
[ "nonn", "tabl" ]
12
1
5
[ "A353532", "A354699", "A354700", "A354701" ]
null
Hugo Pfoertner, Jun 07 2022
2024-12-19T11:53:22
oeisdata/seq/A354/A354700.seq
12966b0e530aeca4fc49ad63d7fa9b6f