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1999-12-11 03:00:00
2025-04-28 00:58:08
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A381320
Number of minimum vertex colorings in the n-Hanoi graph.
[ "6", "66", "85200", "183250434809856", "1823313150135576711941779566275453880631296", "1796015231442383417566549899388909415521140128662444489798112174969514654167314109511319978572879992886003172220405085684891648" ]
[ "nonn" ]
17
1
1
[ "A193233", "A288839", "A381320" ]
null
Eric W. Weisstein, Feb 21 2025
2025-02-21T11:48:58
oeisdata/seq/A381/A381320.seq
69375c1c5748e090f4a624691f8a016f
A381321
Numbers k such that sigma(k)/k - 1 equals (sigma(m)/m - 1)^2 for some m <= k.
[ "1", "6", "28", "216", "360", "496", "2016", "8128", "16758", "1571328", "1935360", "2678400", "33550336", "54758400", "101382400", "1685013120" ]
[ "nonn", "more" ]
41
1
2
[ "A000396", "A017666", "A243473", "A381321" ]
null
Leo Hennig, Feb 21 2025
2025-03-05T17:17:22
oeisdata/seq/A381/A381321.seq
37c7ee56cb919aad7e6e4f14f3d774c2
A381322
Least prime pn such that there is a set p1 < p2 < ... < pn of primes such that, for any distinct p and q in the set, (p + q)/2 is prime.
[ "2", "7", "19", "71", "113", "383", "509", "881", "2963", "6991", "18521", "27611" ]
[ "nonn", "hard", "more" ]
50
1
1
[ "A362629", "A381322" ]
null
Charles R Greathouse IV, Feb 25 2025
2025-03-01T12:17:10
oeisdata/seq/A381/A381322.seq
56220c553237bb4f0aefad655583f7bc
A381323
a(n) is the least nondecreasing prime p such that n is the number of primes between p (not included) and p+n*log(p).
[ "11", "37", "37", "59", "59", "59", "79", "79", "137", "151", "229", "229", "347", "367", "373", "379", "379", "397", "397", "571", "571", "571", "587", "587", "587", "587", "587", "587", "587", "587", "853", "853", "853", "877", "877", "877", "877", "877", "967", "967", "1009", "1009", "1019", "1021", "1021", "1277", "1297", "1297", "1361", "1361", "1361", "1361", "1361", "1361", "1361" ]
[ "nonn" ]
14
1
1
[ "A381293", "A381323" ]
null
Alain Rocchelli, Feb 21 2025
2025-03-02T23:55:22
oeisdata/seq/A381/A381323.seq
dfb50d9b334bf793b6d9ff1cb0648bd6
A381326
Number of (undirected) Hamiltonian cycles in the complete 4-partite graph K_{n,n,n,n}.
[ "3", "744", "1833840", "18872165376", "553245728256000", "37106744352952320000", "4936487939183251906560000", "1177983332748595472891904000000", "467912746454054494167896413962240000", "292026962339084784352431710907924480000000", "273498538086199515052362271809542396313600000000" ]
[ "nonn" ]
4
1
1
[ "A378241", "A381326" ]
null
Eric W. Weisstein, Feb 20 2025
2025-02-20T10:11:20
oeisdata/seq/A381/A381326.seq
e6cfa356b130c3cc17d02a847d33a086
A381327
a(n) is the number of nonnegative integers that can be represented by n segments in the Cistercian numeral system.
[ "1", "24", "214", "910", "2099", "2858", "2415", "1190", "289" ]
[ "nonn", "base", "fini", "full" ]
4
1
2
[ "A341737", "A381327" ]
null
Stefano Spezia, Feb 20 2025
2025-02-23T11:21:15
oeisdata/seq/A381/A381327.seq
bb226d18b8ec42bd7e6aa45b5f537dcd
A381328
a(n+1) is the least k such that k - (a(n-1)+a(n)) and k + (a(n-1)+a(n)) are primes; a(0)=0, a(1)=1.
[ "0", "1", "4", "8", "17", "28", "52", "83", "142", "232", "377", "614", "996", "1641", "2642", "4290", "6945", "11246", "18198", "29457", "47662", "77124", "124797", "201928", "326736", "528723", "855464", "1384230", "2239797", "3624050", "5863850", "9487911", "15351768", "24839684", "40191555", "65031270", "105222856", "170254137", "275477064", "445731218", "721208325", "1166939604" ]
[ "nonn" ]
11
0
3
null
null
Robert Israel, Feb 20 2025
2025-02-23T17:29:56
oeisdata/seq/A381/A381328.seq
b617f53ad18630375893df73688d3848
A381329
Number of steps for n to reach 1 under the map x -> x/2 if x is even, x -> 2*x+1 if x is prime or a perfect power, otherwise x -> gpf(x)-1 where gpf(x) = A006530(x).
[ "0", "1", "5", "2", "16", "6", "4", "3", "10", "17", "15", "7", "20", "5", "3", "4", "8", "11", "9", "18", "7", "16", "14", "8", "6", "21", "19", "6", "7", "4", "8", "5", "18", "9", "7", "12", "4", "10", "8", "19", "23", "8", "8", "17", "3", "15", "13", "9", "19", "7", "5", "22", "11", "20", "18", "7", "12", "8", "6", "5", "21", "9", "7", "6", "8", "19", "4", "10", "17", "8", "9", "13", "8", "5", "3", "11", "18" ]
[ "nonn" ]
15
1
3
[ "A006530", "A381329" ]
null
Bill McEachen, Feb 20 2025
2025-02-21T09:40:50
oeisdata/seq/A381/A381329.seq
b05dfae491689839447decd044050899
A381330
Numbers that are the sum of a prime and the square of a prime in more than one way.
[ "11", "27", "28", "32", "38", "51", "52", "54", "56", "62", "66", "68", "72", "78", "80", "86", "92", "96", "98", "108", "110", "116", "122", "126", "128", "132", "134", "138", "140", "146", "150", "152", "156", "158", "162", "164", "171", "172", "174", "176", "180", "182", "186", "188", "192", "198", "200", "204", "206", "210", "212", "216", "218", "222", "224", "228" ]
[ "nonn" ]
17
1
1
[ "A049002", "A081053", "A381330" ]
null
Chai Wah Wu, Feb 20 2025
2025-02-21T11:12:25
oeisdata/seq/A381/A381330.seq
c62065bb64d4d626b3c15dee7c9c5b74
A381331
a(1) = a(2) = 1; for n > 2, a(n) = floor((n - 2)*a(n - 1)/a(n - 2)) + GCD(n - 2, a(n - 2)).
[ "1", "1", "2", "5", "8", "7", "5", "5", "8", "13", "15", "12", "9", "21", "31", "27", "14", "9", "11", "31", "54", "35", "16", "11", "16", "35", "55", "41", "21", "15", "21", "57", "85", "48", "19", "15", "28", "70", "93", "52", "24", "22", "38", "74", "84", "51", "30", "28", "44", "79", "88", "56", "33", "34", "55", "89", "144", "91", "39", "25", "38", "96", "155", "102", "42", "28", "44", "105", "160", "104" ]
[ "nonn", "easy" ]
18
1
3
[ "A133058", "A145102", "A381331" ]
null
Ctibor O. Zizka, Feb 20 2025
2025-02-25T11:28:26
oeisdata/seq/A381/A381331.seq
2371791569243d6f4427ca43f5956317
A381332
a(n) is the number of different hooklength lists of the plane partitions of n.
[ "1", "1", "2", "4", "6", "11", "19", "31", "52", "86", "146", "231", "392", "615", "1006", "1594", "2612", "4062", "6518", "10116", "15958", "24557", "38565", "58548" ]
[ "nonn", "more" ]
14
1
3
[ "A000041", "A000219", "A094504", "A097391", "A381332" ]
null
Wouter Meeussen, Feb 20 2025
2025-02-24T21:23:56
oeisdata/seq/A381/A381332.seq
642a2e653048f3682692051a86114475
A381333
Smallest integer that is the sum of a prime and the square of a prime in n or more ways.
[ "6", "11", "56", "176", "188", "362", "398", "668", "1448", "1448", "1592", "2390", "3372", "3632", "4532", "6342", "6342", "6368", "6368", "10632", "12920", "12920", "12942", "19502", "23168", "25038", "25038", "25038", "25472", "32238", "32238", "39800", "39800", "39800", "53360", "64998", "72740", "72740", "72740", "81542", "82880", "82880" ]
[ "nonn" ]
9
1
1
[ "A001172", "A081053", "A381330", "A381333" ]
null
Chai Wah Wu, Feb 20 2025
2025-02-21T06:09:01
oeisdata/seq/A381/A381333.seq
d6c798ac83850905835654e7badb6585
A381334
Smallest integer that is the sum of a prime and the square of a prime in exactly n ways.
[ "6", "11", "56", "176", "188", "362", "398", "668", "1568", "1448", "1592", "2390", "3372", "3632", "4532", "6888", "6342", "8582", "6368", "10632", "13002", "12920", "12942", "19502", "23168", "26990", "26292", "25038", "25472", "33648", "32238", "41048", "40640", "39800", "53360", "64998", "77348", "74718", "72740", "81542", "89682", "82880" ]
[ "nonn" ]
16
1
1
[ "A081053", "A381333", "A381334" ]
null
Chai Wah Wu, Feb 20 2025
2025-02-25T01:56:05
oeisdata/seq/A381/A381334.seq
6795e1f80ed66279696475fa3401d8fd
A381335
Integers k such that there are i groups of order k+i up to isomorphism, for i=1,2,3,4,5.
[ "2814120", "22411272", "29436120" ]
[ "nonn", "hard", "more", "new" ]
10
1
1
[ "A373648", "A373649", "A373650", "A381335" ]
null
Robin Jones, Apr 19 2025
2025-04-22T08:17:10
oeisdata/seq/A381/A381335.seq
036eab0c1a2a782a8792ca25067229a9
A381336
a(n) is the smallest k > 0 for which a nondegenerate integer-sided triangle (k, k + n, c >= k + n) with an integer area exists.
[ "3", "6", "9", "12", "12", "18", "5", "7", "4", "24", "14", "36", "15", "10", "36", "14", "7", "8", "6", "21", "8", "3", "12", "5", "10", "15", "12", "20", "46", "35", "9", "28", "20", "14", "25", "16", "15", "12", "22", "21", "19", "16", "12", "6", "20", "5", "4", "10", "11", "20", "21", "30", "96", "24", "13", "9", "18", "7", "25", "63", "21", "18", "22", "9", "35", "9", "25", "21", "36", "17", "13" ]
[ "nonn" ]
14
1
1
[ "A103974", "A103975", "A188158", "A379830", "A381336", "A381337" ]
null
Felix Huber, Mar 16 2025
2025-03-24T06:14:18
oeisdata/seq/A381/A381336.seq
29022f1175b53a64c56155fe787bd5af
A381337
a(n) is the smallest c >= A381336(n) + n for which a nondegenerate integer-sided triangle (A381336(n), A381336(n) + n, c) with an integer area exists.
[ "5", "10", "15", "20", "25", "30", "13", "20", "15", "50", "25", "60", "41", "26", "75", "40", "25", "30", "29", "50", "35", "26", "37", "30", "39", "52", "45", "52", "109", "82", "41", "80", "55", "50", "65", "60", "61", "58", "61", "68", "73", "70", "65", "52", "75", "52", "53", "60", "61", "78", "75", "104", "203", "90", "75", "70", "87", "68", "101", "150", "89", "82", "91", "80", "117" ]
[ "nonn" ]
5
1
1
[ "A381336", "A381337" ]
null
Felix Huber, Mar 18 2025
2025-03-25T23:53:58
oeisdata/seq/A381/A381337.seq
61af9efd32812cc5997117034a561244
A381338
Numbers k such that (22^k - 3^k)/19 is prime.
[ "5", "31", "823", "15287", "26293", "32083", "51263", "92791" ]
[ "nonn", "hard", "more" ]
5
1
1
[ "A062587", "A062589", "A127996", "A127997", "A128344", "A204940", "A217320", "A225807", "A229542", "A375161", "A375236", "A377031", "A381338" ]
null
Robert Price, Feb 20 2025
2025-02-21T08:20:20
oeisdata/seq/A381/A381338.seq
98d87f49be98bf2d4c64ac9edc961b18
A381339
Number of vector differences between two permutations of order n, up to multiplication by nonzero rational numbers and permutations of the components.
[ "1", "1", "2", "3", "9", "28", "128", "539", "2651", "13000", "67466", "355381", "1926343", "10590537", "59234734", "335302599" ]
[ "nonn", "more", "hard" ]
14
0
3
[ "A019589", "A175176", "A362968", "A381243", "A381244", "A381339" ]
null
Max Alekseyev, Feb 20 2025
2025-02-24T08:52:00
oeisdata/seq/A381/A381339.seq
b6a7b271981b8e88279f79b33e19ed16
A381340
Decimal value of c > 1.5 for which H(2*c) = 2*H(c) for H = Hadamard's gamma function.
[ "1", "5", "0", "3", "1", "7", "6", "0", "9", "2", "3", "4", "3", "2", "7", "6", "4", "0", "3", "7", "2", "8", "6", "7", "7", "1", "3", "7", "6", "8", "8", "0", "4", "5", "0", "1", "0", "7", "8", "7", "6", "9", "6", "6", "0", "4", "1", "6", "2", "6", "6", "3", "6", "6", "7", "3", "4", "3", "0", "0", "3", "7", "0", "4", "3", "8", "8", "4", "9", "2", "8", "6", "6", "0", "4", "7", "9", "7", "9", "5", "0", "3", "5", "1", "4", "4", "1", "3", "7", "3", "5", "8", "9", "4", "7", "8", "0", "5", "0", "9", "5", "1", "8", "4", "0" ]
[ "nonn", "cons" ]
25
1
2
[ "A000796", "A381340" ]
null
Lee A. Newberg, Feb 20 2025
2025-02-26T02:15:05
oeisdata/seq/A381/A381340.seq
4fa69ae3ef11d6e794700fca0c2d3c3d
A381341
Expansion of e.g.f. exp( x * cosh(sqrt(2)*x) ).
[ "1", "1", "1", "7", "25", "81", "601", "3207", "18705", "156385", "1087441", "8962823", "84001897", "732712241", "7487525865", "78537490951", "831722893217", "9804469109953", "115549730623009", "1431784628480007", "18795444460125241", "248964703826005777", "3487888859183694329", "50283005924345951111" ]
[ "nonn" ]
10
0
4
[ "A003727", "A009189", "A185951", "A381273", "A381274", "A381275", "A381276", "A381341", "A381342" ]
null
Seiichi Manyama, Feb 20 2025
2025-02-21T05:50:01
oeisdata/seq/A381/A381341.seq
e5d3615465821a38917855251dbc4f26
A381342
Expansion of e.g.f. exp( x * cos(sqrt(2)*x) ).
[ "1", "1", "1", "-5", "-23", "-39", "361", "2675", "3697", "-90575", "-741839", "52779", "48483865", "358510985", "-1225182503", "-43006420829", "-239523048095", "2745896185953", "54532102774753", "144304368441179", "-6547928921714999", "-88336890555248327", "199686588300036553", "18186115601328322515" ]
[ "sign" ]
11
0
4
[ "A003727", "A009189", "A185951", "A381273", "A381274", "A381275", "A381276", "A381341", "A381342" ]
null
Seiichi Manyama, Feb 20 2025
2025-02-21T05:50:26
oeisdata/seq/A381/A381342.seq
73417658c65ce3a8234f0fe864932c2b
A381343
Expansion of e.g.f. exp( sin(sqrt(2)*x) / sqrt(2) ).
[ "1", "1", "1", "-1", "-7", "-15", "25", "287", "721", "-2847", "-30255", "-61697", "682761", "5861713", "3105193", "-258188513", "-1681060063", "4623681473", "135471132705", "564325398271", "-6357495670375", "-89817656595791", "-84337394884167", "7820620314702879", "67277670159083761", "-322108989883888479" ]
[ "sign" ]
15
0
5
[ "A002017", "A009210", "A009229", "A136630", "A351891", "A351892", "A381277", "A381278", "A381280", "A381343", "A381344" ]
null
Seiichi Manyama, Feb 20 2025
2025-02-21T05:50:47
oeisdata/seq/A381/A381343.seq
f2d9ee7e404acc890775e048d10bfb5c
A381344
Expansion of e.g.f. 1/( 1 - x * cosh(sqrt(2)*x) ).
[ "1", "1", "2", "12", "72", "500", "4560", "47936", "565376", "7572240", "112838400", "1844425792", "32910332928", "636463467328", "13251265570816", "295598326909440", "7034150340034560", "177843592245969152", "4760839037033054208", "134528586280018721792", "4001489050575059025920", "124973219149863342633984" ]
[ "nonn", "changed" ]
16
0
3
[ "A185951", "A205571", "A352252", "A381280", "A381281", "A381282", "A381283", "A381344", "A381345" ]
null
Seiichi Manyama, Feb 20 2025
2025-04-19T06:56:01
oeisdata/seq/A381/A381344.seq
8e2a3ae8afa8f8dda27850f694a3c4b0
A381345
Expansion of e.g.f. 1/( 1 - x * cos(sqrt(2)*x) ).
[ "1", "1", "2", "0", "-24", "-220", "-1200", "-2576", "52864", "1016208", "10909440", "57039488", "-687971328", "-26190716864", "-450123634688", "-4238375059200", "24514848522240", "2156422420074752", "54984136073084928", "799573460292407296", "42320889956270080", "-425007017470737816576", "-15563879892284330213376" ]
[ "sign" ]
11
0
3
[ "A185951", "A205571", "A352252", "A381280", "A381281", "A381282", "A381283", "A381344", "A381345" ]
null
Seiichi Manyama, Feb 20 2025
2025-02-21T05:52:14
oeisdata/seq/A381/A381345.seq
b90152390475df613285062184a8bc7e
A381346
Expansion of e.g.f. 1/( 1 - sinh(sqrt(2)*x) / sqrt(2) ).
[ "1", "1", "2", "8", "40", "244", "1808", "15632", "154240", "1712656", "21132032", "286800128", "4246266880", "68108302144", "1176458774528", "21772909267712", "429818456473600", "9015349812633856", "200218257664704512", "4693597812326094848", "115820240623410872320", "3000905720793597113344" ]
[ "nonn", "changed" ]
13
0
3
[ "A136630", "A191277", "A381284", "A381285", "A381286", "A381346", "A381347" ]
null
Seiichi Manyama, Feb 20 2025
2025-04-19T05:54:25
oeisdata/seq/A381/A381346.seq
cfd1a9134e474e5adfb6148c8bc6b4b7
A381347
Expansion of e.g.f. 1/( 1 - sin(sqrt(2)*x) / sqrt(2) ).
[ "1", "1", "2", "4", "8", "4", "-112", "-1184", "-9088", "-59504", "-310528", "-643136", "14701568", "323581504", "4554426368", "51666451456", "458243735552", "2004840714496", "-37024075153408", "-1386061762251776", "-29290212127670272", "-483475390212586496", "-6224109737622372352", "-45231727252157947904" ]
[ "sign" ]
10
0
3
[ "A136630", "A191277", "A263249", "A381284", "A381285", "A381286", "A381346", "A381347" ]
null
Seiichi Manyama, Feb 20 2025
2025-02-21T05:53:48
oeisdata/seq/A381/A381347.seq
373d9e2e1b098953f5f387a6af40ce71
A381348
Irregular triangle read by rows in which row n lists the largest subset of Z/nZ fixed by x -> x^2.
[ "0", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "3", "4", "0", "1", "2", "4", "0", "1", "0", "1", "4", "7", "0", "1", "5", "6", "0", "1", "3", "4", "5", "9", "0", "1", "4", "9", "0", "1", "3", "9", "0", "1", "2", "4", "7", "8", "9", "11", "0", "1", "6", "10", "0", "1", "0", "1", "0", "1", "4", "7", "9", "10", "13", "16", "0", "1", "4", "5", "6", "7", "9", "11", "16", "17", "0", "1", "5", "16", "0", "1", "4", "7", "9", "15", "16", "18" ]
[ "nonn", "tabf" ]
67
1
12
[ "A002145", "A096008", "A096088", "A277847", "A309414", "A381348" ]
null
Aloe Poliszuk, Feb 20 2025
2025-04-07T23:39:10
oeisdata/seq/A381/A381348.seq
9a7a8b84f955dcb4585412294c0ed775
A381349
Triangle read by rows: T(n,k) is the number of distinct tuples E each corresponding to some k-ary word W = (w_1, ..., w_n), where E is a tuple (e_1, ..., e_{n-1}) with e_i being the number of pairs of equal letters (w_j,w_k) in W such that j + i = k.
[ "1", "1", "2", "1", "3", "4", "1", "6", "9", "10", "1", "10", "22", "26", "27", "1", "20", "54", "73", "78", "79", "1", "36", "163", "249", "269", "275", "276", "1", "72", "447", "791", "915", "942", "949", "950", "1", "135", "1350", "3136", "3776", "3899", "3934", "3942", "3943", "1", "272", "4088", "11315", "14849", "15650", "15811", "15855", "15864", "15865" ]
[ "nonn", "tabl" ]
26
1
3
[ "A000312", "A006606", "A120910", "A226873", "A381349" ]
null
John Tyler Rascoe, Feb 21 2025
2025-02-26T12:57:02
oeisdata/seq/A381/A381349.seq
fc24668ea882154443664407866cfdb1
A381350
Number of subsets of 8 integers between 1 and n such that their sum is 2 modulo n.
[ "1", "5", "15", "42", "99", "217", "429", "808", "1430", "2438", "3978", "6308", "9690", "14550", "21318", "30664", "43263", "60115", "82225", "111038", "148005", "195143", "254475", "328752", "420732", "534076", "672452", "840648", "1043460", "1287036", "1577532", "1922736", "2330445", "2810385", "3372291", "4028178", "4790071", "5672645" ]
[ "nonn", "easy" ]
23
9
2
[ "A011796", "A031164", "A056594", "A381289", "A381290", "A381291", "A381350" ]
null
Xavier Roulleau, Feb 21 2025
2025-02-28T05:59:12
oeisdata/seq/A381/A381350.seq
10f5d73d18d895ff9848fad2f6de90e0
A381351
Number of subsets of 9 integers between 1 and n such that their sum is 3 modulo n.
[ "1", "5", "19", "55", "143", "335", "715", "1430", "2703", "4862", "8398", "14000", "22610", "35530", "54484", "81719", "120175", "173592", "246675", "345345", "476913", "650325", "876525", "1168710", "1542684", "2017356", "2615103", "3362260", "4289780", "5433736", "6835972", "8544965", "10616489", "13114465" ]
[ "nonn", "easy" ]
15
10
2
[ "A011796", "A031164", "A032194", "A381289", "A381290", "A381291", "A381351" ]
null
Xavier Roulleau, Feb 21 2025
2025-02-28T17:57:25
oeisdata/seq/A381/A381351.seq
b9a9008af33da66654a2a5182e028552
A381353
G.f. A(x) satisfies [x^n] A(x)^prime(n) = 0 for n > 1.
[ "1", "1", "-1", "2", "-5", "13", "-31", "48", "129", "-2035", "12963", "-20703", "-782282", "14675113", "-177056253", "1716591959", "-14243243451", "103606488776", "-627394591646", "1811555482942", "35994203030869", "-1017785909530332", "17383954047181972", "-240466278357060336", "2883144103957621596", "-30796354831853056598", "299839265871265461201" ]
[ "sign" ]
15
0
4
[ "A381353", "A381355" ]
null
Paul D. Hanna, Mar 11 2025
2025-03-12T08:14:10
oeisdata/seq/A381/A381353.seq
9af71cc415bfb3b727a355a5986d3b9f
A381354
G.f. satisfies x = Sum_{n>=1} -(-1)^(n mod 3) * x^n * abs(1/A(x)^n), where abs(F(x)) equals the series expansion formed by the unsigned coefficients in F(x).
[ "1", "1", "4", "14", "44", "130", "496", "1586", "5128", "17764", "59492", "196368", "659330", "2226166", "7396070", "24876724", "83420692", "279644938", "935867180", "3146178556", "10534161782", "35369902036", "118498115768", "398015733448", "1333108657368", "4477017033638", "15004173961698", "50369493608278", "168842274387828", "566766393991544" ]
[ "nonn" ]
6
0
3
null
null
Paul D. Hanna, Mar 02 2025
2025-03-02T22:51:01
oeisdata/seq/A381/A381354.seq
547221eaa130a275beb697256b4a5755
A381355
G.f. A(x) = x*F'(x)/F(x) where F(x) is the g.f. of A381353 that satisfies [x^n] F(x)^prime(n) = 0 for n > 1.
[ "1", "-3", "10", "-35", "121", "-390", "1037", "-1083", "-14030", "137837", "-382106", "-8791718", "199408912", "-2701500413", "28888970650", "-262327310011", "2080772422210", "-13882125053550", "52262449086711", "642274567089685", "-21939026363969530", "405884590698374334", "-5979931388627873195", "75930802310040533922", "-856565474619901407729" ]
[ "sign" ]
13
1
2
[ "A381353", "A381355" ]
null
Paul D. Hanna, Mar 11 2025
2025-03-12T08:14:18
oeisdata/seq/A381/A381355.seq
19cd41988dbc6816cdff8435a9556bf2
A381356
Limit of rows in irregular triangle A381587.
[ "1", "3", "1", "3", "1", "3", "1", "1", "1", "5", "1", "1", "1", "1", "1", "7", "1", "3", "1", "1", "1", "1", "1", "7", "1", "1", "1", "5", "1", "3", "1", "1", "1", "1", "1", "7", "1", "1", "1", "3", "1", "5", "1", "1", "1", "5", "1", "3", "1", "1", "1", "1", "1", "7", "1", "1", "1", "3", "1", "1", "1", "3", "1", "5", "1", "1", "1", "3", "1", "5", "1", "1", "1", "5", "1", "3", "1", "1", "1", "1", "1", "7", "1", "1", "1", "3", "1", "1", "1", "3", "1", "1", "1", "3", "1", "3", "1", "5" ]
[ "nonn" ]
11
1
2
[ "A306346", "A381356", "A381587" ]
null
Paul D. Hanna, Mar 03 2025
2025-03-04T13:47:57
oeisdata/seq/A381/A381356.seq
1ded855ce0d8e15439f1475b87b17073
A381357
Row lengths of irregular triangle A381587.
[ "1", "1", "1", "2", "4", "6", "10", "16", "26", "42", "66", "102", "156", "238", "364", "560", "868", "1354", "2120", "3322", "5198", "8112", "12624", "19602", "30400", "47138", "73138", "113598", "176630", "274858" ]
[ "nonn", "more" ]
17
1
4
[ "A381357", "A381358", "A381587" ]
null
Paul D. Hanna, Mar 03 2025
2025-03-03T13:02:45
oeisdata/seq/A381/A381357.seq
fd162d496723f343a0f3ed2211a456b8
A381358
Row sums of irregular triangle A381587.
[ "1", "1", "2", "3", "5", "9", "15", "25", "41", "67", "109", "175", "277", "433", "671", "1035", "1595", "2463", "3817", "5937", "9259", "14457", "22569", "35193", "54795", "85195", "132333", "205471", "319069", "495699" ]
[ "nonn", "more" ]
16
1
3
[ "A381357", "A381358", "A381587" ]
null
Paul D. Hanna, Mar 03 2025
2025-03-03T13:02:40
oeisdata/seq/A381/A381358.seq
439a5119c1277219a233e8e72b410f3d
A381359
E.g.f. A(x) satisfies 1 - A'(x)^2 + 4*A(x)^3 = 0.
[ "1", "12", "720", "129600", "51321600", "37977984000", "47113228800000", "90796614543360000", "256892229695692800000", "1021474451008342425600000", "5513370502054734544896000000", "39267642006336798923489280000000", "360478517037545726209161953280000000", "4181620210850033164370074219315200000000" ]
[ "nonn" ]
50
0
2
[ "A104133", "A104134", "A381359", "A381360" ]
null
Paul D. Hanna, Mar 06 2025
2025-04-02T05:16:11
oeisdata/seq/A381/A381359.seq
c50489419af8a69f3036d0b36d333931
A381360
E.g.f. satisfies A(x) = exp( Integral abs(1/A(x)) dx ), where abs(F(x)) equals the series expansion formed by the unsigned coefficients in F(x).
[ "1", "1", "2", "4", "12", "40", "160", "720", "3680", "20800", "129600", "880000", "6476800", "51321600", "435776000", "3946624000", "37977984000", "386949376000", "4161608704000", "47113228800000", "560034421760000", "6974121256960000", "90796614543360000", "1233482823823360000", "17455222222028800000", "256892229695692800000" ]
[ "nonn" ]
37
0
3
[ "A104133", "A104134", "A381359", "A381360", "A381361", "T0", "T1", "T2" ]
null
Paul D. Hanna, Feb 25 2025
2025-02-28T09:48:25
oeisdata/seq/A381/A381360.seq
abe41131e33e94563726c9d9f7bab2e1
A381362
G.f. A(x) satisfies 1/2 = Sum_{n=-oo..+oo} x^n*A(x)^n * (A(x)^n + x)^(2*n-1) * (x^n + A(x))^(2*n-1).
[ "1", "2", "46", "862", "20414", "526106", "14519710", "419293310", "12527971550", "384222183226", "12030729376882", "383113013296770", "12372095284443242", "404291094649795558", "13345757405802263098", "444433438912442427974", "14914705697211799893458", "503945427634033914776682", "17131542722554038753304418" ]
[ "nonn" ]
7
0
2
[ "A380066", "A381362", "A381363", "A381364", "A381365" ]
null
Paul D. Hanna, Feb 21 2025
2025-02-21T09:28:35
oeisdata/seq/A381/A381362.seq
bb95510c37088e863da61b4848b43132
A381363
G.f. A(x) satisfies 1/2 = Sum_{n=-oo..+oo} x^n*A(x)^n * (A(x)^n + x)^(3*n-1) * (x^n + A(x))^(3*n-1).
[ "1", "2", "66", "1986", "70750", "2773026", "115646874", "5037785442", "226634621738", "10451025646474", "491480704359206", "23483727916864770", "1136978797530782274", "55661780274825593226", "2750906179870011022678", "137071833496453114753202", "6878951603092645315764426", "347398329676557462113960102", "17642408607091724771432417962" ]
[ "nonn" ]
7
0
2
[ "A380066", "A381362", "A381363", "A381364", "A381365" ]
null
Paul D. Hanna, Feb 21 2025
2025-02-22T01:25:51
oeisdata/seq/A381/A381363.seq
b8b1101cb7686c2cdf1111393b9c8a9e
A381364
G.f. A(x) satisfies 1/3 = Sum_{n=-oo..+oo} x^n*A(x)^n * (A(x)^n + 2*x)^(n-1) * (x^n + 2*A(x))^(n-1).
[ "1", "6", "69", "1185", "25971", "638664", "16870146", "469957290", "13643527371", "409333196409", "12617508055164", "397955799543372", "12805103784047244", "419461854027499095", "13966745624480483286", "472195682273425114437", "16198043820079506200952", "563559268046248762052514", "19883430320804741832966096" ]
[ "nonn" ]
9
0
2
[ "A380066", "A381362", "A381363", "A381364", "A381365" ]
null
Paul D. Hanna, Feb 21 2025
2025-02-21T11:49:43
oeisdata/seq/A381/A381364.seq
797a50e7b87c7933a53888a94e7e3ac7
A381365
G.f. A(x) satisfies 1/3 = Sum_{n=-oo..+oo} x^n*A(x)^n * (A(x)^n + 2*x)^(2*n-1) * (x^n + 2*A(x))^(2*n-1).
[ "1", "6", "267", "13686", "850848", "58650900", "4328042982", "334965057171", "26856046274793", "2212709064827217", "186314651055503493", "15969595037968661298", "1389302975474149478955", "122403732968608536815772", "10902910239945431586012588", "980514346017575408715296385" ]
[ "nonn" ]
8
0
2
[ "A380066", "A381362", "A381363", "A381364", "A381365" ]
null
Paul D. Hanna, Feb 21 2025
2025-02-21T11:49:46
oeisdata/seq/A381/A381365.seq
270e95dcc9f4056241c852ff71291fbf
A381366
Number of possible configurations of an n dimensional Rubik's simplex.
[ "3732480", "253603223500400479331942400000", "66038535945066815418194228229716898861828197815802983951534337590785326501068800000000000000000" ]
[ "nonn" ]
21
3
1
[ "A079746", "A381366", "A381367" ]
null
Michel Marcus, Feb 21 2025
2025-03-03T13:33:06
oeisdata/seq/A381/A381366.seq
1c9cbde846475853954c2b391d3d78df
A381367
Number of possible configurations of an n dimensional Rubik's hypercube.
[ "43252003274489856000", "1756772880709135843168526079081025059614484630149557651477156021733236798970168550600274887650082354207129600000000000000" ]
[ "nonn" ]
28
3
1
[ "A075152", "A381366", "A381367" ]
null
Michel Marcus, Feb 21 2025
2025-03-03T13:33:13
oeisdata/seq/A381/A381367.seq
c60a1bc3ceb1d12e2d499973d306ea7b
A381368
a(n) is the least k > n for which prime(n) + prime(k) is a square.
[ "4", "6", "5", "10", "16", "9", "8", "102", "13", "20", "30", "28", "17", "26", "16", "58", "33", "23", "55", "21", "54", "142", "30", "28", "49", "48", "139", "35", "91", "47", "45", "44", "56", "135", "54", "40", "39", "252", "51", "49", "78", "128", "62", "76", "75", "126", "245", "71", "55", "69", "54", "68", "120", "137", "81", "65", "63", "238", "171", "96", "62", "76", "108", "209" ]
[ "nonn", "easy" ]
13
1
1
[ "A000040", "A000290", "A259232", "A381368" ]
null
Felix Huber, Mar 02 2025
2025-03-08T08:47:33
oeisdata/seq/A381/A381368.seq
46f734916389ad17436990030dd3a579
A381369
A(n,k) is the sum over all partitions of [n] of k^j for a partition with j inversions; square array A(n,k), n>=0, k>=0, read by antidiagonals.
[ "1", "1", "1", "1", "1", "2", "1", "1", "2", "4", "1", "1", "2", "5", "8", "1", "1", "2", "6", "15", "16", "1", "1", "2", "7", "28", "52", "32", "1", "1", "2", "8", "47", "204", "203", "64", "1", "1", "2", "9", "72", "628", "2344", "877", "128", "1", "1", "2", "10", "103", "1552", "17327", "43160", "4140", "256", "1", "1", "2", "11", "140", "3276", "84416", "1022983", "1291952", "21147", "512" ]
[ "nonn", "tabl" ]
23
0
6
[ "A000110", "A011782", "A125810", "A125812", "A125813", "A125814", "A125815", "A381369", "A381373", "A381426" ]
null
Alois P. Heinz, Feb 21 2025
2025-03-15T18:45:03
oeisdata/seq/A381/A381369.seq
54bc89daf523b3ce68c834e8ab47ae86
A381370
Smallest number with reciprocal of period length n in base 9.
[ "1", "2", "5", "7", "32", "11", "35", "547", "17", "19", "25", "23", "224", "398581", "29", "31", "128", "103", "95", "1597", "352", "43", "115", "47", "97", "151", "53", "109", "928", "59", "155", "683", "256", "161", "515", "71", "608", "18427", "7985", "79", "187", "83", "203", "431", "89", "181", "235", "1223", "896", "491", "101" ]
[ "nonn", "base" ]
35
0
2
[ "A003060", "A379642", "A381370" ]
null
Erich Friedman, Feb 25 2025
2025-02-28T15:13:50
oeisdata/seq/A381/A381370.seq
5ebf40419438d62c70340bd3107f5186
A381371
Let M_n be the n X n matrix M_(i,j)=1/(i+j+i*j); a(n) is the denominator of det(M_n).
[ "1", "3", "600", "13340250", "50970747366000", "192735375681129362668125", "15380836671854204397523000341517500", "139074458529886561401033709221959285413905785765625", "690389384806889736952966420263657968347961857742117270950740703125" ]
[ "nonn", "easy", "frac" ]
13
0
2
[ "A069740", "A381371" ]
null
Stefano Spezia, Feb 21 2025
2025-02-23T04:48:27
oeisdata/seq/A381/A381371.seq
c9cf846630790428696395ce5ab0d43f
A381372
Smaller of two consecutive primes p and q, both ending with 3, such that q-p = 10n, or -1 if no such primes exist.
[ "283", "3413", "7253", "19333", "45893", "142993", "399283", "542603", "818723", "396733", "3240983", "10863973", "32788543", "8917523", "17652013", "92593183", "80935103", "92510963", "257789053", "481691513", "20831323", "47326693", "607010093", "1461724573", "387096133", "1496441363", "2298026803", "1855047163" ]
[ "nonn", "base" ]
33
1
1
[ "A140791", "A380785", "A381372" ]
null
Jean-Marc Rebert, Feb 23 2025
2025-03-08T17:30:56
oeisdata/seq/A381/A381372.seq
3752b79840f5ab843ab66f86735ee9b9
A381373
Sum over all partitions of [n] of n^j for a partition with j inversions.
[ "1", "1", "2", "7", "72", "3276", "915848", "2011878835", "42723411900032", "10608257527069388539", "35808039364308986083608352", "1828963737334508176477805993389490", "1618534282345584818909121118371843799592960", "28472613161534902071627567919297331348486838233018341" ]
[ "nonn" ]
22
0
3
[ "A062173", "A120325", "A125810", "A381369", "A381373", "A381427" ]
null
Alois P. Heinz, Feb 21 2025
2025-03-15T18:44:34
oeisdata/seq/A381/A381373.seq
cb69fe6a6895dfad3594a346c866f31f
A381374
Little Hankel transform of A317614: a(n) = A317614(n+1)^2 - A317614(n)*A317614(n+2).
[ "1", "1", "97", "49", "769", "289", "2977", "961", "8161", "2401", "18241", "5041", "35617", "9409", "63169", "16129", "104257", "25921", "162721", "39601", "242881", "58081", "349537", "82369", "487969", "113569", "663937", "152881", "883681", "201601", "1153921", "261121", "1481857", "332929", "1875169", "418609", "2342017", "519841", "2891041" ]
[ "nonn", "easy" ]
4
1
3
[ "A056221", "A056222", "A239607", "A317614", "A374668", "A381374" ]
null
Stefano Spezia, Feb 21 2025
2025-02-23T11:21:36
oeisdata/seq/A381/A381374.seq
ac6351f19a77d7fd144f3f21dcd64ae3
A381376
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cosh(x * A(x)^2) ).
[ "1", "1", "2", "9", "96", "1385", "22080", "403417", "8829184", "227956689", "6667822080", "215780258441", "7674505073664", "298885308910201", "12661212551163904", "578940699178779225", "28400662193828659200", "1488075298726340008097", "82965096417136263561216", "4904558063539270185865609" ]
[ "nonn" ]
10
0
3
[ "A185951", "A381171", "A381300", "A381376", "A381377" ]
null
Seiichi Manyama, Feb 22 2025
2025-02-22T09:56:27
oeisdata/seq/A381/A381376.seq
c201a3992186501df7158c7f1727cefe
A381377
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cosh(x * A(x)) )^2.
[ "1", "2", "6", "30", "288", "4090", "68160", "1292774", "28627200", "739821618", "21729070080", "708442911022", "25365382259712", "992297344710698", "42173572623716352", "1934344590577340790", "95175474351245230080", "5000227637170108004194", "279428527333796676894720", "16552583621200571079876158" ]
[ "nonn" ]
10
0
2
[ "A185951", "A381206", "A381376", "A381377" ]
null
Seiichi Manyama, Feb 22 2025
2025-02-22T09:56:23
oeisdata/seq/A381/A381377.seq
c2a04d877b7bb3fda8b4679d34087bbb
A381378
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cos(x * A(x)^2) ).
[ "1", "1", "2", "3", "-48", "-1135", "-18240", "-231637", "-1356544", "53849889", "3026119680", "100808786419", "2429052865536", "26284690243825", "-1539261873164288", "-140633348417624805", "-7196339681250508800", "-258335768147494234303", "-4225401456668904259584", "307227604973975435785571" ]
[ "sign" ]
11
0
3
[ "A185951", "A364980", "A381376", "A381378", "A381382", "A381384" ]
null
Seiichi Manyama, Feb 22 2025
2025-02-22T09:56:19
oeisdata/seq/A381/A381378.seq
9b7ca9ee67a9815b6bd673d76df8d3ae
A381379
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cos(x * A(x)) )^2.
[ "1", "2", "6", "18", "-48", "-2630", "-52800", "-824054", "-8682240", "54462258", "7410631680", "305163480578", "8935815871488", "167137193150954", "-1440976761090048", "-349400091225243270", "-22113174143289262080", "-960586728800597050526", "-26252145855684866211840", "255024367557922004307442" ]
[ "sign" ]
11
0
2
[ "A185951", "A381378", "A381379" ]
null
Seiichi Manyama, Feb 22 2025
2025-02-22T09:55:53
oeisdata/seq/A381/A381379.seq
bb005ec8894f84ea3f8ad276407a4f5d
A381380
Decimal expansion of the area of a ruled surface formed by moving a segment of length sqrt(6), the ends of which lie on the diagonals of opposite faces of a unit cube oriented at right angles to each other.
[ "2", "7", "2", "7", "0", "5", "4", "7", "7", "3", "8", "1", "2", "0", "4", "8", "9", "8", "8", "4", "3", "5", "1", "5", "5", "6", "7", "9", "0", "2", "0", "2", "5", "9", "8", "4", "2", "8", "3", "4", "6", "4", "7", "7", "1", "9", "9", "0", "3", "1", "3", "8", "7", "4", "0", "0", "3", "1", "0", "7", "1", "1", "8", "9", "3", "9", "5", "3", "9", "5", "1", "4", "0", "1", "3", "6", "7", "1", "4", "8", "4", "8", "4", "4", "9", "4", "0", "4", "0", "1", "1" ]
[ "nonn", "cons" ]
39
1
1
null
null
Nicolay Avilov, Feb 22 2025
2025-04-10T08:04:42
oeisdata/seq/A381/A381380.seq
e7bd0a34272302ba4fc638c20888c62b
A381381
a(n) is the smallest positive integer m such that for all integers k >= m an n-free 1-partition of k exists.
[ "154", "155", "126", "183", "97", "101", "91", "108", "92", "98", "78", "81", "108", "78", "78", "91", "78", "106", "81", "92", "78", "80", "78", "78", "78", "81", "78", "108", "78", "78", "92" ]
[ "nonn", "more" ]
5
3
1
null
null
Michel Marcus, Feb 22 2025
2025-02-22T09:55:20
oeisdata/seq/A381/A381381.seq
ce9fe94b2a64a1a97c1a0194297cf32b
A381382
E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)^2) / A(x)^2 ).
[ "1", "1", "2", "7", "48", "541", "7600", "120891", "2178176", "45053401", "1065957888", "28344376303", "831973593088", "26647344263541", "925300511922176", "34668496386129763", "1394928344160731136", "59986286728056665905", "2744940504174063714304", "133158543838350039763671" ]
[ "nonn" ]
10
0
3
[ "A136630", "A364980", "A381376", "A381378", "A381382", "A381384" ]
null
Seiichi Manyama, Feb 22 2025
2025-02-22T09:55:49
oeisdata/seq/A381/A381382.seq
cf220dc3ac6ee14d81c58f072931c347
A381383
E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)) / A(x) )^2.
[ "1", "2", "6", "26", "176", "1842", "25552", "417146", "7727232", "162203810", "3855123968", "102712106202", "3024863555584", "97316416451282", "3393616911181824", "127581806046438074", "5147059194652983296", "221843071154521998402", "10172731970828970557440", "494451746675777509028762" ]
[ "nonn" ]
10
0
2
[ "A136630", "A381382", "A381383" ]
null
Seiichi Manyama, Feb 22 2025
2025-02-22T09:55:46
oeisdata/seq/A381/A381383.seq
a50dbebeccbda1ffdc04b30578e45898
A381384
E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)^2) / A(x)^2 ).
[ "1", "1", "2", "5", "0", "-299", "-5840", "-90791", "-1210496", "-11174519", "71397888", "8367496301", "327020705792", "9709296136541", "226223975684096", "2946493117173761", "-87437164233621504", "-9675847870039338095", "-535455805780063748096", "-22518479178045130002731", "-706013052362778282033152" ]
[ "sign" ]
10
0
3
[ "A136630", "A364980", "A381376", "A381378", "A381382", "A381384" ]
null
Seiichi Manyama, Feb 22 2025
2025-02-22T09:55:43
oeisdata/seq/A381/A381384.seq
32f6d179eb6b8349585d9431e5b9ae74
A381385
E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)) / A(x) )^2.
[ "1", "2", "6", "22", "64", "-398", "-14768", "-288458", "-4695168", "-62117470", "-385004032", "15463485398", "923640068096", "33487329741842", "957927747201024", "20185023268062070", "95909717192212480", "-21197461265149558718", "-1619210077600334151680", "-82170388240550451506282", "-3226620083793471277105152" ]
[ "sign" ]
11
0
2
[ "A136630", "A381384", "A381385" ]
null
Seiichi Manyama, Feb 22 2025
2025-02-22T09:55:39
oeisdata/seq/A381/A381385.seq
acb0bf2c9b4585bfbac4d2784f7dc98a
A381386
E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)^2) ).
[ "1", "1", "6", "73", "1360", "34321", "1095584", "42350673", "1923628032", "100430070721", "5926517800192", "390116250605401", "28341322114027520", "2252512575040254801", "194421212092585943040", "18110799663166635386017", "1810994441189833169698816", "193488658627430346315888385", "21997611392941496027173879808" ]
[ "nonn" ]
17
0
3
[ "A136630", "A381386", "A381387" ]
null
Seiichi Manyama, Feb 22 2025
2025-02-24T08:09:17
oeisdata/seq/A381/A381386.seq
c28dc96940a20b82ba86badde60366e5
A381387
E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)) )^2.
[ "1", "2", "14", "182", "3520", "91002", "2954400", "115638014", "5303063552", "278979672050", "16565016146176", "1095997724407302", "79966475806040064", "6379010456725968362", "552344502268240535552", "51595059327775839277646", "5171865567269556457308160", "553764742712510134123863522" ]
[ "nonn" ]
16
0
2
[ "A136630", "A381386", "A381387" ]
null
Seiichi Manyama, Feb 22 2025
2025-02-24T08:09:04
oeisdata/seq/A381/A381387.seq
4dbd0694002c32a2e46bb5d02075359d
A381388
E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)^2) ).
[ "1", "1", "6", "71", "1280", "31201", "961184", "35838991", "1569696768", "79007365921", "4494170889472", "285130996517399", "19963494971809792", "1529055924661457921", "127179971644212387840", "11416028319985437309215", "1099976414821996358795264", "113239907265894992879189185", "12404749306625020735299780608" ]
[ "nonn" ]
16
0
3
[ "A136630", "A381388", "A381389" ]
null
Seiichi Manyama, Feb 22 2025
2025-02-24T08:00:33
oeisdata/seq/A381/A381388.seq
05a84eff6c314cd2d18f8de388cc131a
A381389
E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)) )^2.
[ "1", "2", "14", "178", "3344", "83722", "2628000", "99358810", "4398573568", "223280915090", "12788876882176", "816044058415298", "57411735641690112", "4415467258014111002", "368568207039291072512", "33186631279383615035242", "3206409506796711229521920", "330893672854541429428877602" ]
[ "nonn" ]
16
0
2
[ "A136630", "A381388", "A381389" ]
null
Seiichi Manyama, Feb 22 2025
2025-02-24T07:59:58
oeisdata/seq/A381/A381389.seq
afaabb186ac2c850e9b37ef88545f60a
A381390
a(n) = 12*n^2 + 4*n + 1.
[ "1", "17", "57", "121", "209", "321", "457", "617", "801", "1009", "1241", "1497", "1777", "2081", "2409", "2761", "3137", "3537", "3961", "4409", "4881", "5377", "5897", "6441", "7009", "7601", "8217", "8857", "9521", "10209", "10921", "11657", "12417", "13201", "14009", "14841", "15697", "16577", "17481", "18409", "19361", "20337", "21337" ]
[ "nonn", "easy" ]
22
0
2
[ "A001082", "A381390" ]
null
Aaron David Fairbanks, Mar 06 2025
2025-03-07T09:13:20
oeisdata/seq/A381/A381390.seq
c52e5028ff9e1b31d4bd0daaa3f8f3ea
A381391
Number of k <= 10^n that are neither squarefree nor prime powers (i.e., k is in A126706).
[ "0", "29", "367", "3866", "39098", "391838", "3920154", "39205902", "392069187", "3920718974", "39207261564", "392072817656", "3920728751139", "39207289143932", "392072896183208", "3920728975677128", "39207289797472001", "392072898095046811", "3920728981307675534", "39207289814141997459", "392072898144605471040" ]
[ "nonn" ]
17
1
2
[ "A011557", "A071172", "A126706", "A229099", "A267574", "A372403", "A380403", "A381391" ]
null
Michael De Vlieger, Feb 22 2025
2025-02-23T12:17:10
oeisdata/seq/A381/A381391.seq
329dbf5110320cc85d555a7e410b41cb
A381392
Decimal expansion of the double zeta(3/2,2).
[ "9", "3", "1", "8", "2", "4", "4", "9", "0", "4", "2", "5", "0", "3", "4", "0", "9", "8", "5", "5", "1", "6", "1", "5", "1", "1", "0", "7", "0", "3", "6", "4", "3", "0", "5", "1", "7", "0", "7", "5", "0", "5", "7", "9", "4", "6", "3", "4", "6", "8", "7", "6", "9", "9", "5", "7", "6", "6", "2", "7" ]
[ "nonn", "cons" ]
7
0
1
null
null
R. J. Mathar, Feb 22 2025
2025-02-22T13:47:50
oeisdata/seq/A381/A381392.seq
bf6b6fa1e59b4f02100bbfcbbeddeeae
A381393
Decimal expansion of the double zeta(5/2,5/2).
[ "3", "8", "1", "3", "3", "0", "1", "5", "3", "1", "1", "1", "6", "0", "9", "2", "6", "0", "5", "7", "1", "8", "8", "1", "8", "7", "5", "4", "3", "0", "9", "8", "9", "2", "9", "3", "2", "8", "0", "8", "8", "6", "5", "3", "8", "1", "3", "4", "9", "0", "3", "1", "1", "6", "6", "4", "9", "3", "0", "3", "8" ]
[ "nonn", "cons" ]
7
0
1
null
null
R. J. Mathar, Feb 22 2025
2025-02-22T13:47:57
oeisdata/seq/A381/A381393.seq
9e0128b3709df62c37ef34f3474da6cc
A381394
Decimal expansion of the double zeta(2,8).
[ "0", "0", "4", "1", "2", "2", "4", "6", "9", "6", "7", "8", "3", "9", "9", "8", "3", "2", "2", "2", "4", "0", "4", "6", "9", "5", "6", "8", "3", "8", "6", "9", "4", "2", "0", "8", "8", "5", "5", "8", "1", "2", "6", "2", "7", "3", "5", "8", "4", "6", "8", "5", "6", "9", "2", "8", "5", "2", "4", "5", "5", "1", "7", "9", "2", "8", "7", "1", "7", "1", "1", "1", "2", "7", "7", "4", "0", "6", "3", "8", "8", "3", "3", "1", "2", "7", "5", "9", "4", "5", "3", "4", "5", "2", "4", "3", "4", "1", "7", "3", "8", "8", "1", "7", "4" ]
[ "nonn", "cons" ]
12
0
3
null
null
R. J. Mathar, Feb 22 2025
2025-02-26T02:15:20
oeisdata/seq/A381/A381394.seq
4af27c554a521e76372c16ead02e4c67
A381395
Decimal expansion of the double zeta(3,7).
[ "0", "0", "8", "4", "1", "9", "6", "6", "8", "5", "0", "3", "0", "9", "6", "3", "3", "2", "4", "2", "3", "9", "6", "8", "5", "7", "9", "7", "1", "4", "6", "7", "0", "6", "5", "0", "6", "3", "6", "9", "1", "7", "8", "7", "5", "0", "6", "3", "9", "5", "8", "0", "9", "2", "2", "7", "2", "5", "7", "4", "5", "1", "6", "6", "3", "5", "9", "0", "4", "6", "9", "0", "0", "4", "7", "9", "1", "5", "3", "3", "7", "7", "7", "9", "6", "2", "7", "3", "5", "3", "9", "2", "3", "3", "7", "1", "5", "8", "7", "5", "5", "0", "6", "4", "7" ]
[ "nonn", "cons" ]
12
0
3
null
null
R. J. Mathar, Feb 22 2025
2025-02-26T02:14:09
oeisdata/seq/A381/A381395.seq
e452f8e1d27c52d951ec119233f9c00a
A381396
Decimal expansion of the double zeta(4,6).
[ "0", "1", "7", "4", "5", "5", "1", "9", "4", "7", "5", "0", "8", "3", "5", "0", "2", "4", "7", "3", "5", "7", "4", "0", "6", "3", "9", "3", "8", "6", "6", "6", "8", "4", "1", "3", "7", "3", "1", "8", "5", "9", "2", "8", "2", "9", "0", "9", "5", "2", "1", "4", "3", "1", "0", "0", "6", "1", "5", "6", "7", "0", "1", "1", "3", "3", "3", "8", "9", "2", "4", "1", "8", "5", "2", "8", "7", "7", "4", "4", "4", "7", "4", "6", "9", "2", "0", "7", "2", "2", "6", "9", "0", "2", "3", "3", "4", "5", "4", "1", "2", "1", "0", "5", "4" ]
[ "nonn", "cons" ]
15
0
3
null
null
R. J. Mathar, Feb 22 2025
2025-02-26T02:13:55
oeisdata/seq/A381/A381396.seq
c5ca7354ad2196ecd637054300b7f767
A381397
Decimal expansion of the double zeta(2,10).
[ "0", "0", "0", "9", "9", "9", "2", "0", "6", "7", "8", "7", "2", "0", "9", "6", "9", "1", "8", "4", "0", "4", "3", "3", "8", "0", "1", "4", "8", "8", "2", "1", "5", "8", "3", "7", "6", "0", "9", "1", "4", "1", "0", "1", "9", "2", "3", "2", "8", "1", "9", "4", "0", "9", "6", "8", "4", "8", "8", "2", "2", "2", "0", "6", "8", "5", "6", "7", "2", "1", "8", "5", "3", "2", "7", "1", "8", "5", "9", "1", "2", "5", "6", "3", "0", "3", "5", "0", "3", "6", "5", "4", "0", "1", "2", "7", "7", "7", "5", "8", "9", "8", "6", "4", "7" ]
[ "cons", "nonn" ]
12
0
4
null
null
R. J. Mathar, Feb 22 2025
2025-02-26T02:13:33
oeisdata/seq/A381/A381397.seq
fd45c783ab1737c76415a7e14d429998
A381398
Irregular triangle read by rows, where row n lists the elements of the set of bases and exponents (including exponents = 1) in the prime factorization of n.
[ "1", "2", "1", "3", "2", "1", "5", "1", "2", "3", "1", "7", "2", "3", "2", "3", "1", "2", "5", "1", "11", "1", "2", "3", "1", "13", "1", "2", "7", "1", "3", "5", "2", "4", "1", "17", "1", "2", "3", "1", "19", "1", "2", "5", "1", "3", "7", "1", "2", "11", "1", "23", "1", "2", "3", "2", "5", "1", "2", "13", "3", "1", "2", "7", "1", "29", "1", "2", "3", "5", "1", "31", "2", "5", "1", "3", "11", "1", "2", "17", "1", "5", "7", "2", "3" ]
[ "nonn", "tabf", "easy" ]
11
2
2
[ "A035306", "A081812", "A381201", "A381202", "A381203", "A381204", "A381205", "A381212", "A381398", "A381399", "A381402" ]
null
Paolo Xausa, Feb 22 2025
2025-02-25T11:39:24
oeisdata/seq/A381/A381398.seq
9e36de8d47fc4b46be9d5828da530ecc
A381399
a(n) is the number of prime elements in the set of bases and exponents in the prime factorization of n.
[ "0", "1", "1", "1", "1", "2", "1", "2", "2", "2", "1", "2", "1", "2", "2", "1", "1", "2", "1", "2", "2", "2", "1", "2", "2", "2", "1", "2", "1", "3", "1", "2", "2", "2", "2", "2", "1", "2", "2", "3", "1", "3", "1", "2", "3", "2", "1", "2", "2", "2", "2", "2", "1", "2", "2", "3", "2", "2", "1", "3", "1", "2", "3", "1", "2", "3", "1", "2", "2", "3", "1", "2", "1", "2", "3", "2", "2", "3", "1", "2", "1", "2", "1", "3", "2", "2", "2", "3", "1", "3" ]
[ "nonn", "easy" ]
9
1
6
[ "A115588", "A381398", "A381399", "A381400", "A381401" ]
null
Paolo Xausa, Feb 22 2025
2025-02-25T11:39:39
oeisdata/seq/A381/A381399.seq
896e076ede099ef465aa8bf4f3270e43
A381400
Numbers k >= 2 such that A115588(k) != A381399(k).
[ "64", "81", "256", "320", "405", "448", "512", "567", "625", "704", "729", "832", "891", "1024", "1053", "1088", "1216", "1280", "1377", "1472", "1539", "1600", "1792", "1856", "1863", "1875", "1984", "2240", "2349", "2368", "2401", "2511", "2560", "2624", "2752", "2816", "2835", "2997", "3008", "3072", "3136", "3321", "3328", "3392", "3483", "3520" ]
[ "nonn", "easy" ]
10
1
1
[ "A115588", "A381399", "A381400" ]
null
Paolo Xausa, Feb 22 2025
2025-02-25T11:39:46
oeisdata/seq/A381/A381400.seq
006f70f48b149e23778557ac6a9dd944
A381401
a(n) is the number of (possibly non-distinct) prime elements in the multiset of bases and exponents in the prime factorization of n.
[ "0", "1", "1", "2", "1", "2", "1", "2", "2", "2", "1", "3", "1", "2", "2", "1", "1", "3", "1", "3", "2", "2", "1", "3", "2", "2", "2", "3", "1", "3", "1", "2", "2", "2", "2", "4", "1", "2", "2", "3", "1", "3", "1", "3", "3", "2", "1", "2", "2", "3", "2", "3", "1", "3", "2", "3", "2", "2", "1", "4", "1", "2", "3", "1", "2", "3", "1", "3", "2", "3", "1", "4", "1", "2", "3", "3", "2", "3", "1", "2", "1", "2", "1", "4", "2", "2", "2", "3", "1", "4" ]
[ "nonn", "easy" ]
10
1
4
[ "A106490", "A349281", "A381398", "A381399", "A381401" ]
null
Paolo Xausa, Feb 24 2025
2025-02-25T11:40:01
oeisdata/seq/A381/A381401.seq
7511e01fbfa8bebf5279c8aa2db8b366
A381402
Numbers k such that the set P of bases and exponents in the prime factorization of k (including exponents = 1) contains all numbers from min(P) to max(P).
[ "2", "4", "6", "8", "9", "12", "18", "24", "27", "36", "48", "54", "72", "81", "108", "144", "162", "216", "240", "324", "432", "625", "648", "720", "810", "1200", "1296", "1620", "2000", "2025", "2160", "2592", "3125", "3240", "3600", "3750", "3888", "4050", "5000", "5625", "6000", "6480", "7500", "8100", "10125", "10800", "11250", "12960", "15000", "15625" ]
[ "nonn" ]
9
1
1
[ "A381398", "A381402" ]
null
Paolo Xausa, Feb 24 2025
2025-02-25T11:40:10
oeisdata/seq/A381/A381402.seq
d223725322e93214e7c069e867a74326
A381403
a(n) is the mode of the multiset of bases and exponents (including exponents = 1) in the prime factorization of n (using smallest mode if multimodal).
[ "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "2", "1", "1", "1", "3", "2", "1", "3", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "2", "1", "2", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn", "easy" ]
8
2
3
[ "A035306", "A381178", "A381403", "A381404" ]
null
Paolo Xausa, Feb 27 2025
2025-03-01T12:19:17
oeisdata/seq/A381/A381403.seq
4da4d87791f215885cfe3bb3df4c5c53
A381404
a(n) is the mode of the multiset of bases and exponents (including exponents = 1) in the prime factorization of n (using largest mode if multimodal).
[ "2", "3", "2", "5", "1", "7", "3", "3", "1", "11", "2", "13", "1", "1", "4", "17", "2", "19", "2", "1", "1", "23", "3", "5", "1", "3", "2", "29", "1", "31", "5", "1", "1", "1", "2", "37", "1", "1", "5", "41", "1", "43", "2", "5", "1", "47", "4", "7", "2", "1", "2", "53", "3", "1", "7", "1", "1", "59", "2", "61", "1", "7", "6", "1", "1", "67", "2", "1", "1", "71", "3", "73", "1", "5", "2", "1", "1", "79", "5", "4", "1", "83", "2", "1", "1" ]
[ "nonn", "easy" ]
7
2
1
[ "A000040", "A035306", "A381178", "A381403", "A381404" ]
null
Paolo Xausa, Feb 27 2025
2025-03-01T12:19:27
oeisdata/seq/A381/A381404.seq
d7a290f17f27b7290e2482387f306d15
A381405
a(0) = 0; for n > 0, a(n) is the smallest unused number such that a(n) AND a(n-1) = 0, where AND is the binary AND operation, while the binary weight of a(n) does not equal that of a(n-1).
[ "0", "1", "6", "8", "3", "4", "9", "2", "5", "16", "7", "24", "32", "10", "21", "34", "13", "18", "37", "64", "11", "20", "35", "12", "19", "36", "25", "66", "28", "33", "14", "17", "38", "65", "22", "40", "23", "72", "39", "80", "15", "48", "67", "60", "128", "26", "68", "27", "96", "29", "98", "129", "30", "97", "130", "41", "86", "136", "49", "78", "144", "42", "85", "138", "53", "74", "132", "43", "84", "139", "52", "75", "148", "99", "140", "51", "76", "147", "44", "83", "160", "31", "192", "45", "82", "141", "50", "77", "146", "101" ]
[ "nonn", "base" ]
11
0
3
[ "A000120", "A057168", "A061712", "A129760", "A381405", "A381406" ]
null
Scott R. Shannon, Feb 22 2025
2025-02-23T09:31:51
oeisdata/seq/A381/A381405.seq
8ff8321eaf2757c0cbea68cfbf38f246
A381406
a(0) = 0; for n > 0, a(n) is the smallest unused number such that a(n) OR a(n-1) = 2^k - 1, where OR is the binary OR operation and k>=1, while the binary weight of a(n) does not equal that of a(n-1).
[ "0", "1", "3", "2", "5", "7", "4", "11", "6", "13", "10", "15", "8", "23", "9", "14", "17", "30", "19", "12", "27", "20", "31", "16", "47", "18", "29", "22", "43", "21", "46", "25", "39", "24", "55", "26", "45", "50", "61", "34", "63", "28", "51", "44", "59", "36", "91", "37", "58", "69", "62", "33", "94", "35", "60", "67", "124", "71", "56", "79", "48", "95", "32", "127", "38", "57", "70", "121", "54", "41", "86", "107", "52", "75", "117", "42", "53", "74", "119", "40", "87", "104", "151", "105", "118", "73", "126", "49", "78", "115" ]
[ "nonn", "base" ]
8
0
3
[ "A000120", "A057168", "A061712", "A086799", "A381405", "A381406" ]
null
Scott R. Shannon, Feb 22 2025
2025-02-23T09:31:44
oeisdata/seq/A381/A381406.seq
3d0f4fc151aea751b533403cd84ad8c5
A381407
E.g.f. A(x) satisfies A(x) = exp( x * cosh(x * A(x)^2) ).
[ "1", "1", "1", "4", "61", "756", "8581", "125168", "2577849", "60269968", "1469636041", "39496750272", "1212192326005", "41147125079360", "1496063100479949", "58263746530145536", "2447130544401729649", "110270888250759852288", "5279535712822539622033", "267412182631190346232832" ]
[ "nonn" ]
9
0
4
[ "A185951", "A381376", "A381407" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-23T08:01:19
oeisdata/seq/A381/A381407.seq
2dab5a899ea74255110b38292d16a613
A381408
E.g.f. A(x) satisfies A(x) = exp( 2 * x * cosh(x * A(x)) ).
[ "1", "2", "4", "14", "160", "2202", "28384", "419302", "8238080", "193340978", "4860711424", "132391420350", "4045976651776", "137295166640842", "5028417873133568", "197042617602645398", "8292209178735935488", "374117497443421923426", "17958577129581151387648", "912189896002576287703918" ]
[ "nonn" ]
8
0
2
[ "A185951", "A381407", "A381408" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-23T08:02:20
oeisdata/seq/A381/A381408.seq
2eda360000f38173cbc6ec6e22643dc1
A381409
E.g.f. A(x) satisfies A(x) = exp( x * cos(x * A(x)^2) ).
[ "1", "1", "1", "-2", "-59", "-744", "-6419", "-6096", "1504553", "47199232", "911415481", "7309642880", "-338340409043", "-21607316073472", "-725479564376475", "-13094500078091264", "245361657851526353", "35579148236923486208", "1875350389057457406193", "57582879572195726819328" ]
[ "sign" ]
9
0
4
[ "A185951", "A381378", "A381409" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-23T08:03:24
oeisdata/seq/A381/A381409.seq
f9a88ef59c2279da734c4d6a4d1053ea
A381410
E.g.f. A(x) satisfies A(x) = exp( 2 * x * cos(x * A(x)) ).
[ "1", "2", "4", "2", "-128", "-2118", "-23456", "-125046", "2962432", "134260082", "3203705344", "43519495186", "-465102608384", "-58643045328086", "-2434321489723392", "-60275924271785062", "-100012292095737856", "89170947715367242466", "5992924139510968483840", "233532153884059053483042" ]
[ "sign" ]
10
0
2
[ "A185951", "A381409", "A381410" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-23T08:04:15
oeisdata/seq/A381/A381410.seq
df79fc6439776817f1beb78991310ed6
A381411
E.g.f. A(x) satisfies A(x) = exp( sinh(x * A(x)^2) / A(x)^2 ).
[ "1", "1", "1", "2", "21", "252", "2645", "29248", "420777", "7789008", "160214281", "3480537568", "82299294077", "2172147323712", "63112534885725", "1969853583132672", "65473850077772881", "2323179959573426432", "88007266294215935121", "3540245668453458467328", "150353926528453088942821" ]
[ "nonn" ]
8
0
4
[ "A136630", "A381411" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-23T08:05:28
oeisdata/seq/A381/A381411.seq
1ac98da2661026b6f18fcbdecaf90089
A381412
E.g.f. A(x) satisfies A(x) = exp( 2 * sinh(x * A(x)) / A(x) ).
[ "1", "2", "4", "10", "64", "754", "9024", "109050", "1544960", "27480162", "567449600", "12641553258", "303021248512", "7982668175954", "231306526932992", "7245659221444186", "242226980924424192", "8623216994933650114", "327015684198600278016", "13169904418920596839626", "560434137147666884198400" ]
[ "nonn" ]
10
0
2
[ "A136630", "A381411", "A381412" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-23T08:08:47
oeisdata/seq/A381/A381412.seq
87187aa495a470f7c2e4f7346a3d2419
A381413
E.g.f. A(x) satisfies A(x) = exp( sin(x * A(x)^2) / A(x)^2 ).
[ "1", "1", "1", "0", "-19", "-248", "-2355", "-14504", "69113", "4886848", "117560921", "1925294976", "14523966437", "-478472693632", "-28832809713435", "-921278399444480", "-18983574162924687", "-55161522627854336", "18306724696454977713", "1118400460045234098176", "41755736397548337559133" ]
[ "sign" ]
10
0
5
[ "A136630", "A381413" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-23T08:09:50
oeisdata/seq/A381/A381413.seq
289356fa2437c003aa7be638570c3c3a
A381414
E.g.f. A(x) satisfies A(x) = exp( 2 * sin(x * A(x)) / A(x) ).
[ "1", "2", "4", "6", "-32", "-686", "-8256", "-72394", "-200448", "11160866", "373370880", "7696016614", "100295200768", "-338643776142", "-77999443329024", "-3211092423560938", "-85537972638318592", "-1169784729390416830", "33029632126142382080", "3381750252027454249926", "158090250687453045194752" ]
[ "sign" ]
11
0
2
[ "A136630", "A381413", "A381414" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-23T08:16:51
oeisdata/seq/A381/A381414.seq
28ddd9dedacea9a7e733890c6555910b
A381415
E.g.f. A(x) satisfies A(x) = exp( sinh(x * A(x)^2) ).
[ "1", "1", "5", "50", "765", "15852", "415441", "13182976", "491502521", "21061603152", "1020066862269", "55107133707232", "3285531022228725", "214295961023511616", "15179005200468020489", "1160334809344169734144", "95214513195493336071537", "8347897781857074205573376", "778804910740650550851809013" ]
[ "nonn" ]
9
0
3
[ "A136630", "A162650", "A381415" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-23T08:17:43
oeisdata/seq/A381/A381415.seq
12a0d418ade02fcdc6c8ab1c587fb6ad
A381416
E.g.f. A(x) satisfies A(x) = exp( 2 * sinh(x * A(x)) ).
[ "1", "2", "12", "130", "2080", "44354", "1185856", "38188546", "1439993088", "62261776002", "3037542875136", "165090563653250", "9892965209886720", "648064548551770562", "46075919968420085760", "3533725068594022938626", "290804441398399410503680", "25561250854199444302177538", "2390133356713125694150017024" ]
[ "nonn" ]
10
0
2
[ "A136630", "A381415", "A381416" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-23T08:19:14
oeisdata/seq/A381/A381416.seq
4142c63f71fca5c75fa490d6488e974b
A381417
E.g.f. A(x) satisfies A(x) = exp( sin(x * A(x)^2) ).
[ "1", "1", "5", "48", "693", "13432", "327561", "9639224", "332476361", "13157303104", "587704852749", "29250533304960", "1605304225302525", "96313936238637184", "6271774683977444817", "440545491471769836032", "33204015428071302059025", "2672942015998405569765376", "228892490007003118401996565" ]
[ "nonn" ]
10
0
3
[ "A136630", "A381417" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-23T08:20:10
oeisdata/seq/A381/A381417.seq
d94fbfb1afacda5730ebfd44f716697b
A381418
E.g.f. A(x) satisfies A(x) = exp( 2 * sin(x * A(x)) ).
[ "1", "2", "12", "126", "1920", "38594", "966336", "29013502", "1016725248", "40756464002", "1840019388416", "92407718510206", "5110719354064896", "308687318601431618", "20219267260662005760", "1427631259848921544702", "108098847179804608299008", "8738141126983786551626498", "751078053821468153074155520" ]
[ "nonn" ]
11
0
2
[ "A136630", "A381417", "A381418" ]
null
Seiichi Manyama, Feb 23 2025
2025-02-23T08:20:57
oeisdata/seq/A381/A381418.seq
008a0199281e04968c7620b0fe3a694f
A381419
a(1) = 1; for n > 1, a(n) is the smallest unused positive number that is coprime to a(n-1) and has a different binary weight than a(n-1).
[ "1", "3", "2", "5", "4", "7", "6", "11", "8", "9", "13", "10", "19", "12", "23", "14", "15", "16", "17", "21", "20", "27", "22", "29", "18", "25", "24", "31", "26", "33", "28", "39", "32", "35", "34", "37", "30", "41", "36", "43", "38", "45", "44", "47", "40", "49", "46", "55", "42", "53", "48", "59", "50", "51", "52", "57", "56", "61", "54", "65", "58", "63", "62", "67", "60", "73", "64", "69", "68", "71", "66", "79", "70", "83" ]
[ "nonn", "base" ]
23
1
2
[ "A000120", "A027748", "A093714", "A109451", "A381419", "A381420", "A381821" ]
null
Scott R. Shannon, Feb 23 2025
2025-03-11T08:23:12
oeisdata/seq/A381/A381419.seq
a2164401b3acce9f5f8c2a35614d4ef6
A381420
a(1) = 1, a(2) = 3; for n > 2, a(n) is the smallest unused positive number that shares a factor with a(n-1) and has a different binary weight than a(n-1).
[ "1", "3", "15", "5", "25", "10", "2", "6", "4", "12", "8", "14", "16", "18", "21", "9", "27", "24", "22", "20", "26", "30", "28", "32", "34", "38", "36", "39", "13", "65", "35", "40", "42", "33", "11", "55", "44", "46", "48", "45", "50", "54", "52", "58", "56", "60", "62", "64", "66", "51", "17", "85", "68", "70", "63", "7", "77", "49", "91", "78", "69", "23", "115", "75", "72", "57", "19", "95", "76", "80", "74", "86", "82", "90" ]
[ "nonn", "base" ]
18
1
2
[ "A000120", "A027748", "A064413", "A093714", "A109451", "A381419", "A381420" ]
null
Scott R. Shannon, Feb 23 2025
2025-03-11T09:01:23
oeisdata/seq/A381/A381420.seq
be0919296bee9db1993b0ff3e41177a0
A381421
a(n) = Sum_{k=0..n} (k+1) * binomial(2*k,2*n-2*k).
[ "1", "2", "5", "22", "68", "206", "631", "1870", "5467", "15836", "45416", "129260", "365565", "1028122", "2877697", "8021010", "22274476", "61653850", "170152275", "468347046", "1286055927", "3523777912", "9635982160", "26302324504", "71674754873", "195015074610", "529846108989", "1437657038030", "3896050721940" ]
[ "nonn", "easy", "changed" ]
44
0
2
[ "A034839", "A108479", "A381421", "A382230", "A382470", "A382471", "A382472", "A382473", "A382474" ]
null
Seiichi Manyama, Mar 28 2025
2025-04-23T10:47:06
oeisdata/seq/A381/A381421.seq
0607d5af75c0fae02cb24434f9706fee
A381422
Expansion of g.f. = exp( Sum_{n>=1} A066802(n)*x^n/n )
[ "1", "20", "662", "26780", "1205961", "58050204", "2924165436", "152231599628", "8125577046740", "442293253888592", "24457749066666142", "1370114821790970340", "77591333270514869230", "4434803157977731784808", "255492958449660158603448", "14820943641891118200315756", "864962304943085638764540396" ]
[ "nonn", "new" ]
8
0
2
[ "A066802", "A155200", "A156216", "A229451", "A229452", "A255881", "A381422" ]
null
Karol A. Penson, Apr 22 2025
2025-04-22T14:08:40
oeisdata/seq/A381/A381422.seq
58c4a2fb5484e6eea761550803ab7b1c
A381423
Exponent of x of maximal coefficient in Hermite polynomial of order n.
[ "0", "1", "2", "3", "4", "1", "2", "3", "4", "5", "2", "3", "4", "5", "6", "3", "4", "5", "6", "7", "4", "5", "6", "7", "4", "5", "6", "7", "8", "5", "6", "7", "8", "5", "6", "7", "8", "9", "6", "7", "8", "9", "6", "7", "8", "9", "10", "7", "8", "9", "10", "7", "8", "9", "10", "11", "8", "9", "10", "11", "8", "9", "10", "11", "12", "9", "10", "11", "12", "9", "10", "11", "12", "9", "10", "11", "12", "13", "10" ]
[ "nonn" ]
8
0
3
[ "A277280", "A381423" ]
null
Mike Sheppard, Feb 23 2025
2025-03-06T12:00:16
oeisdata/seq/A381/A381423.seq
3d54c74672e02eb8874df7b89e462da8
A381424
Truncated hex numbers: a(n) = 24*n^2 + 6*n + 1.
[ "1", "31", "109", "235", "409", "631", "901", "1219", "1585", "1999", "2461", "2971", "3529", "4135", "4789", "5491", "6241", "7039", "7885", "8779", "9721", "10711", "11749", "12835", "13969", "15151", "16381", "17659", "18985", "20359", "21781", "23251", "24769", "26335", "27949", "29611", "31321", "33079", "34885", "36739", "38641" ]
[ "nonn", "easy" ]
17
0
2
[ "A003215", "A005892", "A007742", "A381424" ]
null
Aaron David Fairbanks, Feb 23 2025
2025-03-06T12:53:01
oeisdata/seq/A381/A381424.seq
54b9334730d474ddfb6a0c9db05fd296