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A378101
Decimal expansion of e^(Pi^2/(6*log(2))).
[ "1", "0", "7", "3", "1", "0", "1", "5", "7", "9", "4", "8", "2", "3", "0", "8", "5", "8", "0", "3", "9", "2", "2", "3", "0", "7", "9", "9", "9", "6", "6", "5", "4", "0", "6", "0", "3", "7", "8", "1", "9", "6", "8", "4", "9", "6", "8", "4", "4", "8", "9", "0", "5", "7", "9", "0", "0", "5", "8", "0", "8", "2", "4", "8", "4", "5", "8", "1", "9", "8", "4", "2", "9", "1", "3", "3", "9", "2", "6", "2", "7", "9", "9", "9", "3", "0", "4", "5", "4", "0", "7", "7", "7", "3", "9", "1", "2", "9", "4", "9" ]
[ "nonn", "cons" ]
5
2
3
[ "A001113", "A002162", "A002388", "A013661", "A378101", "A378102" ]
null
Stefano Spezia, Nov 16 2024
2024-11-17T07:11:59
oeisdata/seq/A378/A378101.seq
066e01d7b1949fae95a01e3cd718293d
A378102
Decimal expansion of e^(-Pi^2/(6*log(2))).
[ "0", "9", "3", "1", "8", "7", "8", "2", "2", "9", "5", "3", "5", "7", "5", "8", "7", "3", "3", "6", "2", "3", "2", "8", "0", "5", "9", "9", "5", "3", "5", "2", "4", "9", "6", "6", "8", "3", "9", "0", "9", "4", "8", "7", "4", "0", "8", "2", "2", "4", "7", "8", "5", "0", "6", "7", "4", "8", "1", "6", "4", "7", "2", "0", "7", "2", "0", "2", "7", "6", "2", "0", "2", "3", "6", "7", "8", "7", "1", "3", "0", "6", "0", "6", "3", "8", "9", "0", "6", "5", "6", "8", "4", "9", "7", "1", "7", "1", "3", "1", "4" ]
[ "nonn", "cons" ]
6
0
2
[ "A001113", "A002162", "A002388", "A013661", "A378101", "A378102" ]
null
Stefano Spezia, Nov 16 2024
2025-04-03T04:07:55
oeisdata/seq/A378/A378102.seq
224a672fb0e8a6c62b38868283144bf9
A378103
Triangle read by rows: T(n,k) is the number of n-node connected unsensed planar maps with an external face and k triangular internal faces, n >= 3, 1 <= k <= 2*n - 5.
[ "1", "0", "1", "1", "0", "1", "1", "2", "1", "0", "0", "2", "4", "4", "5", "4", "0", "0", "2", "6", "10", "14", "14", "18", "16", "0", "0", "0", "7", "18", "35", "49", "63", "69", "88", "78", "0", "0", "0", "5", "28", "74", "131", "204", "274", "345", "396", "489", "457", "0", "0", "0", "0", "26", "126", "304", "574", "893", "1290", "1708", "2137", "2503", "3071", "2938", "0", "0", "0", "0", "13", "159", "582", "1396", "2613", "4274", "6270", "8709", "11433", "14227", "16905", "20667", "20118" ]
[ "nonn", "tabf" ]
15
3
8
[ "A001651", "A002713", "A003094", "A005500", "A005501", "A169808", "A377785", "A378103", "A378336", "A378340" ]
null
Ya-Ping Lu, Nov 16 2024
2024-11-25T20:44:47
oeisdata/seq/A378/A378103.seq
02df39193c58383d12a2d7a2dc64490c
A378104
Positive integers that are digitally balanced in more than one integer base b >= 2.
[ "135", "141", "147", "156", "177", "180", "198", "201", "210", "216", "225", "228", "572", "678", "684", "714", "722", "738", "2110", "2170", "2230", "2382", "2410", "2638", "2702", "2710", "2758", "2830", "2886", "8287", "8351", "8367", "8375", "8399", "8415", "8429", "8435", "8479", "8527", "8539", "8551", "8563", "8569", "8591", "8605", "8615", "8619", "8630" ]
[ "nonn", "base" ]
16
1
1
[ "A049364", "A065963", "A378000", "A378073", "A378104" ]
null
Paolo Xausa, Nov 16 2024
2024-11-21T05:23:10
oeisdata/seq/A378/A378104.seq
ac76c235324621624e722be893c3e018
A378105
Number of non-colorable strings of length n considered by the alternating coloring function.
[ "1", "2", "2", "4", "4", "8", "12", "24", "44", "88", "172", "344", "684", "1368", "2732", "5464", "10924", "21848", "43692", "87384", "174764", "349528", "699052", "1398104", "2796204", "5592408", "11184812", "22369624", "44739244", "89478488", "178956972", "357913944", "715827884", "1431655768", "2863311532", "5726623064", "11453246124", "22906492248", "45812984492" ]
[ "nonn", "easy" ]
24
0
2
[ "A001045", "A005578", "A378105" ]
null
Jonathan Garbe, Nov 16 2024
2025-01-29T12:45:23
oeisdata/seq/A378/A378105.seq
f6e44fe18828e6a870ff872816f90ef5
A378106
Lexicographically earliest sequence of distinct positive integers such that among two consecutive terms, the least term divides a positive number whose decimal expansion appears in that of the other term.
[ "1", "2", "4", "8", "16", "3", "6", "12", "24", "48", "96", "9", "18", "36", "72", "7", "14", "28", "56", "5", "10", "20", "40", "80", "160", "15", "30", "60", "120", "240", "480", "32", "64", "128", "256", "25", "50", "100", "200", "400", "800", "1600", "75", "150", "300", "600", "1200", "2400", "4800", "192", "19", "38", "76", "152", "13", "26", "52", "104", "208", "416", "41" ]
[ "nonn", "base" ]
7
1
2
[ "A342072", "A378106", "A378107" ]
null
Rémy Sigrist, Nov 16 2024
2024-11-17T13:07:40
oeisdata/seq/A378/A378106.seq
a6a9f7cd46adfbe01f43a0cab0a333e4
A378107
Lexicographically earliest sequence of distinct positive integers such that for any n > 0, either a(n+1) is a multiple of a(n) or the decimal expansion of a(n+1) appears in that of a(n).
[ "1", "2", "4", "8", "16", "6", "12", "24", "48", "96", "9", "18", "36", "3", "15", "5", "10", "20", "40", "80", "160", "60", "120", "240", "480", "960", "1920", "19", "38", "76", "7", "14", "28", "56", "112", "11", "22", "44", "88", "176", "17", "34", "68", "136", "13", "26", "52", "104", "208", "416", "41", "82", "164", "64", "128", "256", "25", "50", "100", "200", "400", "800" ]
[ "nonn", "base" ]
9
1
2
[ "A342072", "A378106", "A378107" ]
null
Rémy Sigrist, Nov 16 2024
2024-11-18T08:31:21
oeisdata/seq/A378/A378107.seq
2d67b7c2bf8db585d62cec5695c99a3a
A378108
Primes p such that neither p-1 nor p+1 are in A126706.
[ "2", "3", "5", "7", "31", "257", "131071", "618970019642690137449562111", "162259276829213363391578010288127" ]
[ "nonn", "hard", "more" ]
30
1
1
[ "A000040", "A000079", "A126706", "A141453", "A303554", "A378108" ]
null
Michael De Vlieger, Nov 26 2024
2024-11-27T18:34:27
oeisdata/seq/A378/A378108.seq
35a980fa169ebca9cf94be081278ac3f
A378109
Cogrowth sequence of the 18-element group S3 X C3 = <S,T,U | S^3, T^2, U^3, (ST)^2, [S,U], [T,U]>.
[ "1", "0", "1", "2", "3", "15", "32", "126", "351", "1094", "3321", "9801", "29768", "88452", "266085", "797162", "2390391", "7175547", "21516800", "64573362", "193700403", "581130734", "1743421725", "5230147077", "15690706952", "47071500840", "141215033961", "423644304722", "1270932117003", "3812799539655" ]
[ "nonn", "easy" ]
6
0
4
[ "A001045", "A095364", "A378031", "A378109", "A378110", "C3", "C6", "D9", "S3" ]
null
Sean A. Irvine, Nov 16 2024
2024-11-16T16:08:38
oeisdata/seq/A378/A378109.seq
9b18ab683c8f75099201c035904d04b9
A378110
Cogrowth sequence of the 18-element group S3:C3 = <S,T,U | S^3, T^3, U^2, (SU)^2, (TU)^2, [S,T]>.
[ "1", "0", "1", "2", "5", "10", "53", "98", "397", "1058", "3341", "9658", "30053", "87386", "267877", "793682", "2397437", "7162066", "21552125", "64506026", "193839445", "580889738", "1743836117", "5229312706", "15692323949", "47067796610", "141222563821", "423628907162", "1270962692165", "3812740639930" ]
[ "nonn", "easy" ]
4
0
4
[ "A001045", "A095364", "A378031", "A378109", "A378110", "C3", "C6", "D9", "S3" ]
null
Sean A. Irvine, Nov 16 2024
2024-11-16T16:08:44
oeisdata/seq/A378/A378110.seq
e2e2579e0f4697c6f6146195d266bfd8
A378111
a(n) is the least prime p such that there are exactly n squarefree numbers strictly between p and the next prime, or -1 if there is no such p.
[ "2", "5", "13", "31", "89", "139", "113", "199", "211", "317", "1759", "1381", "1951", "887", "4523", "2179", "2477", "4831", "5351", "4297", "1327", "9973", "14107", "19333", "16141", "20809", "15683", "37907", "28229", "58831", "31907", "19609", "25471", "40289", "114493", "43331", "44293", "34061", "191353", "31397", "107377", "134513", "186481", "448451", "175141", "332317", "188029" ]
[ "nonn" ]
35
0
1
[ "A000040", "A005117", "A061398", "A377430", "A378111" ]
null
Robert Israel, Nov 29 2024
2024-12-01T17:57:02
oeisdata/seq/A378/A378111.seq
49ba7b8816b1c9156f87ff76032dd391
A378112
Number A(n,k) of k-tuples (p_1, p_2, ..., p_k) of Dyck paths of semilength n, such that each p_i is never below p_{i-1} and the upper path p_k only touches the x-axis at its endpoints; square array A(n,k), n>=0, k>=0, read by antidiagonals.
[ "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "2", "2", "0", "1", "1", "3", "9", "5", "0", "1", "1", "4", "23", "55", "14", "0", "1", "1", "5", "46", "265", "400", "42", "0", "1", "1", "6", "80", "880", "3942", "3266", "132", "0", "1", "1", "7", "127", "2347", "23695", "70395", "28999", "429", "0", "1", "1", "8", "189", "5403", "105554", "824229", "1445700", "274537", "1430", "0" ]
[ "nonn", "tabl" ]
24
0
13
[ "A000012", "A000108", "A001477", "A019590", "A078920", "A101986", "A120588", "A123352", "A355281", "A368025", "A378112", "A378113", "A378114" ]
null
Alois P. Heinz, Nov 16 2024
2024-11-16T19:30:34
oeisdata/seq/A378/A378112.seq
343ca440c05d552e78c3db52e75e7672
A378113
Number of n-tuples (p_1, p_2, ..., p_n) of Dyck paths of semilength n, such that each p_i is never below p_{i-1} and the upper path p_n only touches the x-axis at its endpoints.
[ "1", "1", "2", "23", "880", "105554", "40446551", "50637232553", "209584899607676", "2881189188022646406", "131778113962930341491415", "20065327661524165382215337625", "10173706896856510992170168595911888", "17178054578218938036671513200907244799852", "96590987238453485101729361602126273065518820938" ]
[ "nonn" ]
16
0
3
[ "A000108", "A355400", "A378112", "A378113" ]
null
Alois P. Heinz, Nov 16 2024
2024-11-21T10:22:20
oeisdata/seq/A378/A378113.seq
ebe136530643114d5cb18eba48770611
A378114
Number of 3-tuples (p_1, p_2, p_3) of Dyck paths of semilength n, such that each p_i is never below p_{i-1} and the upper path p_3 only touches the x-axis at its endpoints.
[ "1", "1", "3", "23", "265", "3942", "70395", "1445700", "33188889", "834702890", "22656163450", "656075013591", "20085981787831", "645418018740113", "21637970282382744", "753157297564682541", "27105935164769925549", "1005184072184843625837", "38295251586474334236780", "1495061191885030011433707" ]
[ "nonn" ]
14
0
3
[ "A000108", "A006149", "A378112", "A378114" ]
null
Alois P. Heinz, Nov 16 2024
2024-11-21T10:19:50
oeisdata/seq/A378/A378114.seq
9f092d559d6b1c82474f7e8bf60daeef
A378115
Numbers k such that (23^k + 2^k)/25 is prime.
[ "3", "19", "61", "97", "397", "1511" ]
[ "nonn", "hard", "more" ]
6
1
1
[ "A057187", "A057188", "A062587", "A062589", "A127996", "A127997", "A128344", "A204940", "A217320", "A225807", "A228922", "A229542", "A375161", "A375236", "A377031", "A377856", "A378115" ]
null
Robert Price, Nov 16 2024
2025-02-16T08:34:07
oeisdata/seq/A378/A378115.seq
d79722fc383cdfd1c864324ad64039df
A378116
Lexicographically earliest sequence of distinct positive integers such that a(a(n)) shares a factor with a(a(n)-2) while not sharing a factor with a(a(n)-1).
[ "3", "4", "9", "8", "7", "6", "35", "12", "25", "11", "15", "22", "14", "33", "16", "21", "18", "49", "20", "63", "26", "27", "19", "24", "95", "28", "45", "32", "31", "30", "217", "34", "77", "36", "55", "38", "39", "40", "51", "44", "42", "121", "46", "99", "50", "57", "43", "48", "215", "52", "75", "56", "54", "91", "58", "65", "62", "85", "60", "119", "64", "105", "68", "69", "70", "61", "71", "122", "213", "74", "81", "73", "78", "365", "76", "115", "82", "125", "83", "80", "249", "86", "87", "88", "93", "92", "111", "94", "84" ]
[ "nonn" ]
9
1
1
[ "A027746", "A064413", "A098550", "A121053", "A378030", "A378098", "A378116" ]
null
Scott R. Shannon, Nov 17 2024
2024-11-30T08:50:52
oeisdata/seq/A378/A378116.seq
02b775ed4f8339f7e7279d2971763da3
A378117
Lexicographically earliest sequence of nonnegative integers a(0), a(1), ..., such that a(n) is the number of pairs of adjacent terms whose sum is n.
[ "0", "1", "1", "2", "1", "3", "2", "3", "2", "4", "2", "5", "2", "5", "3", "5", "4", "5", "4", "5", "5", "5", "6", "5", "6", "5", "6", "6", "6", "7", "6", "7", "6", "7", "7", "7", "7", "8", "7", "8", "7", "8", "8", "8", "8", "8", "9", "8", "9", "8", "9", "9", "9", "9", "9", "10", "9", "10", "9", "10", "10", "10", "10", "10", "10", "11", "10", "11", "10", "11", "11", "11", "11", "11", "11", "11", "12", "11", "12" ]
[ "nonn" ]
8
0
4
[ "A001462", "A307707", "A378117" ]
null
Rémy Sigrist and N. J. A. Sloane, Nov 17 2024
2024-11-17T06:31:41
oeisdata/seq/A378/A378117.seq
422f2f17649068f8ce4cd53ad7297a01
A378118
a(n) is the multinomial coefficient given by the previous terms, i.e., a(n) = (a(1)+...+a(n-1))!/(a(1)!*...*a(n-1)!).
[ "1", "1", "2", "12", "21840", "2814355154336774377799951925175856161820370339122436787831200" ]
[ "nonn" ]
4
1
3
null
null
Pontus von Brömssen, Nov 17 2024
2024-11-17T07:13:48
oeisdata/seq/A378/A378118.seq
b9aebf3267e5ce9edf25bf38d025e94c
A378119
a(n) is the smallest positive k such that the digit sums of k and k + 1 are both divisible by n, or -1 if no such pair exists.
[ "1", "19", "-1", "39", "49999", "-1", "69999", "79", "-1", "18999999999", "2899999", "-1", "48999", "5899999999999", "-1", "78999999999", "8899", "-1", "19899999999999999999", "298999999999", "-1", "49899999", "598999999999999999999", "-1", "79899999999999999", "898999", "-1", "19989999999999999999999999999", "29989999999999999", "-1" ]
[ "sign", "base" ]
26
1
2
[ "A007953", "A051885", "A378119" ]
null
Barney Maunder-Taylor, Nov 16 2024
2024-12-28T15:49:24
oeisdata/seq/A378/A378119.seq
ff6a5fcbfd232e0d16879b785ddf0445
A378120
a(n) = (A000217(n) + A005132(n))/2.
[ "0", "1", "3", "6", "6", "11", "17", "24", "24", "33", "33", "44", "44", "57", "57", "72", "72", "89", "107", "126", "126", "147", "147", "147", "171", "171", "197", "197", "225", "225", "255", "255", "287", "320", "354", "354", "390", "390", "390", "429", "429", "470", "470", "513", "513", "558", "558", "605", "605", "654", "654", "705", "705", "758", "758", "813", "813" ]
[ "nonn" ]
14
0
3
[ "A000217", "A005132", "A377748", "A378120" ]
null
Paul Curtz, Nov 17 2024
2024-11-18T18:27:52
oeisdata/seq/A378/A378120.seq
73d0450d10b42b0d36904961962b9008
A378121
Numbers missing from all Fibonacci/tribonacci sequences that start with 1, 1, 1.
[ "19", "41", "49", "59", "67", "107", "109", "161", "177", "179", "197", "201", "205", "211", "223", "227", "229", "239", "247", "263", "269", "277", "295", "301", "307", "317", "323", "327", "335", "349", "353", "361", "367", "394", "409", "413", "421", "447", "449", "454", "467", "475", "499", "502", "509", "526", "529", "533", "538", "541", "557", "566", "577", "601", "603", "607" ]
[ "nonn" ]
18
1
1
[ "A000045", "A000213", "A378121" ]
null
Erich Friedman, Nov 17 2024
2024-11-19T01:03:57
oeisdata/seq/A378/A378121.seq
421ea98f38c0a2440cc33cb78ecc4fb0
A378122
a(n) = number of prime divisors of the sum of the first n primes.
[ "1", "1", "2", "1", "2", "1", "2", "2", "2", "2", "2", "1", "3", "1", "2", "2", "3", "2", "2", "2", "2", "2", "3", "2", "3", "2", "2", "2", "3", "2", "3", "2", "3", "2", "2", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "2", "3", "3", "3", "2", "4", "2", "2", "3", "4", "2", "2", "1", "3", "2", "3", "1", "2", "2", "3", "3", "3", "3", "3", "2", "3", "2", "2", "3", "4", "2", "3", "3", "2", "2", "2", "4", "3", "3" ]
[ "nonn" ]
5
1
3
[ "A000040", "A008334", "A008335", "A071215", "A378122", "A378123" ]
null
Clark Kimberling, Nov 17 2024
2024-11-20T09:50:56
oeisdata/seq/A378/A378122.seq
afe7db9eb8dabf79f40f8c85517656a7
A378123
a(n) = number of prime divisors of the sum of the first n odd primes.
[ "1", "1", "2", "2", "2", "2", "2", "2", "1", "2", "3", "2", "2", "2", "1", "3", "1", "2", "2", "3", "2", "2", "1", "2", "2", "2", "1", "2", "2", "2", "1", "3", "2", "3", "2", "2", "3", "3", "2", "3", "3", "3", "2", "4", "2", "2", "2", "3", "4", "3", "2", "3", "1", "3", "1", "3", "2", "3", "2", "5", "1", "5", "2", "4", "1", "3", "2", "3", "3", "3", "1", "3", "2", "3", "1", "3", "2", "3", "2", "4", "3", "3", "2", "2", "2", "4" ]
[ "nonn" ]
8
1
3
[ "A000040", "A001221", "A008334", "A008335", "A071148", "A071215", "A378122", "A378123" ]
null
Clark Kimberling, Nov 17 2024
2024-11-20T09:51:03
oeisdata/seq/A378/A378123.seq
8c00064d1cc3265f67e1418ceb6506a9
A378124
Decimal expansion of Pi^2/(12*log(phi)).
[ "1", "7", "0", "9", "1", "5", "7", "9", "8", "5", "3", "0", "5", "6", "2", "1", "9", "2", "6", "4", "6", "3", "8", "1", "5", "6", "9", "3", "6", "2", "0", "3", "2", "9", "5", "4", "2", "9", "7", "9", "0", "3", "4", "7", "1", "6", "1", "6", "8", "8", "5", "0", "0", "8", "4", "2", "4", "6", "2", "7", "6", "7", "7", "7", "4", "0", "4", "6", "2", "4", "2", "7", "9", "3", "9", "1", "5", "6", "3", "6", "2", "4", "4", "6", "0", "3", "6", "4", "0", "2", "2", "8", "9", "5", "1", "6", "5", "4", "5", "9" ]
[ "nonn", "cons" ]
8
1
2
[ "A001622", "A002388", "A002390", "A013661", "A072691", "A174607", "A247039", "A378124" ]
null
Stefano Spezia, Nov 17 2024
2024-11-18T07:35:05
oeisdata/seq/A378/A378124.seq
743137defa80c19d0d04d217f2bc5031
A378125
Triangle T(n, k) read by rows. Let m be a nonzero rational number then T(n, m mod (n+1)) is the n-th coefficient in the Hasse-Weil L-series (q^(n+1) in the q-expansion) associated to the elliptic equation -4*x^3 + ((m+1)^2 + 8)*x^2 - 2*(m+3)*x + 1 - y^2 = 0.
[ "1", "-1", "-2", "0", "-3", "-1", "1", "2", "1", "2", "-1", "-2", "-1", "-3", "1", "0", "6", "1", "0", "3", "2", "1", "-1", "-3", "1", "-2", "-2", "-2", "-1", "0", "-1", "0", "-1", "0", "-1", "0", "0", "6", "-2", "0", "6", "-2", "0", "6", "-2", "1", "4", "1", "6", "-1", "2", "2", "2", "3", "-2", "-1", "-5", "4", "3", "1", "-2", "-4", "-5", "-3", "-1", "1", "0", "-6", "-1", "0", "-3", "-2", "0", "-6", "-1", "0", "-3", "-2", "1", "-2", "-7", "0", "2", "-2", "-1", "0", "-5", "-2", "-5", "3", "4", "-1", "2", "3", "-2", "2", "4", "2", "-2", "1", "6", "-1", "4", "2", "4" ]
[ "sign", "tabl" ]
34
0
3
[ "A001615", "A006571", "A007653", "A251913", "A377441", "A378125" ]
null
Thomas Scheuerle, Nov 17 2024
2024-12-08T04:00:44
oeisdata/seq/A378/A378125.seq
6676f0e2cffbb8e07a7c67ea25b58166
A378126
Array read by antidiagonals: T(n, m) is the maximal size of partitions of (n, m) into sums of distinct pairs of nonnegative integers, excluding (0, 0).
[ "0", "1", "1", "1", "2", "1", "2", "2", "2", "2", "2", "3", "3", "3", "2", "2", "3", "3", "3", "3", "2", "3", "3", "4", "4", "4", "3", "3", "3", "4", "4", "4", "4", "4", "4", "3", "3", "4", "4", "4", "5", "4", "4", "4", "3", "3", "4", "5", "5", "5", "5", "5", "5", "4", "3", "4", "4", "5", "5", "5", "5", "5", "5", "5", "4", "4", "4", "5", "5", "5", "6", "6", "6", "6", "5", "5", "5", "4", "4", "5", "5", "6", "6", "6", "6" ]
[ "nonn", "tabl" ]
20
0
5
[ "A003056", "A054242", "A086435", "A201377", "A378126", "A378379" ]
null
Jimin Park, Nov 17 2024
2024-12-12T23:08:17
oeisdata/seq/A378/A378126.seq
60677d4b420d45f7372a319ca4f38ec8
A378127
Inverse permutation to A377137.
[ "1", "3", "4", "2", "6", "5", "10", "9", "11", "8", "12", "7", "14", "15", "13", "20", "21", "19", "22", "18", "23", "17", "24", "16", "27", "26", "28", "25", "35", "34", "36", "33", "37", "32", "38", "31", "39", "30", "40", "29", "43", "44", "42", "45", "41", "53", "54", "52", "55", "51", "56", "50", "57", "49", "58", "48", "59", "47", "60", "46", "64", "63", "65", "62", "66", "61", "76", "75", "77", "74", "78", "73", "79", "72", "80", "71", "81", "70", "82", "69", "83", "68", "84", "67", "88", "89", "87", "90", "86", "91" ]
[ "nonn", "tabf" ]
9
1
2
[ "A064455", "A209278", "A265225", "A377137", "A378127" ]
null
Boris Putievskiy, Nov 17 2024
2024-12-01T14:39:32
oeisdata/seq/A378/A378127.seq
efad55da735d6fa0d7cc0accc8f12741
A378128
Decimal expansion of 2/L, where L is the lemniscate constant (A062539).
[ "7", "6", "2", "7", "5", "9", "7", "6", "3", "5", "0", "1", "8", "1", "3", "1", "8", "8", "0", "6", "2", "3", "2", "5", "9", "8", "0", "9", "6", "3", "6", "1", "5", "7", "9", "3", "2", "9", "2", "6", "2", "9", "2", "3", "7", "3", "4", "8", "0", "7", "2", "9", "1", "5", "2", "1", "7", "0", "7", "1", "5", "9", "8", "2", "6", "4", "4", "2", "2", "6", "9", "2", "9", "5", "6", "2", "5", "6", "1", "9", "2", "1", "9", "5", "4", "6", "6", "1", "4", "6" ]
[ "nonn", "cons", "easy" ]
12
0
1
[ "A010466", "A062539", "A085565", "A175575", "A377999", "A378128", "A378129", "A378130", "A378131", "A378132" ]
null
Paolo Xausa, Nov 17 2024
2024-11-20T17:41:19
oeisdata/seq/A378/A378128.seq
560518abf76cd81a79b27bb4957b9424
A378129
Decimal expansion of log(L^2/Pi), where L is the lemniscate constant (A062539).
[ "7", "8", "3", "1", "8", "8", "7", "8", "5", "4", "1", "3", "6", "7", "3", "5", "5", "2", "9", "4", "3", "8", "9", "0", "6", "9", "3", "7", "9", "8", "2", "2", "2", "0", "5", "6", "1", "8", "0", "4", "2", "0", "2", "3", "1", "5", "4", "0", "0", "5", "3", "2", "9", "6", "6", "1", "0", "6", "6", "1", "9", "1", "8", "7", "1", "1", "3", "8", "8", "6", "4", "5", "0", "2", "4", "0", "5", "9", "0", "3", "8", "4", "7", "9", "4", "5", "8", "7", "4", "4" ]
[ "nonn", "cons", "easy" ]
7
0
1
[ "A002388", "A062539", "A068465", "A371855", "A377999", "A378128", "A378129", "A378130", "A378131", "A378132" ]
null
Paolo Xausa, Nov 17 2024
2024-11-19T00:53:35
oeisdata/seq/A378/A378129.seq
7633fdcb2e211daec3030f0541b6473e
A378130
Decimal expansion of 24*L^2/(5^(7/4)*Pi^2), where L is the lemniscate constant (A062539).
[ "9", "9", "9", "9", "9", "6", "3", "8", "3", "1", "5", "9", "0", "8", "4", "1", "2", "7", "7", "7", "2", "7", "6", "3", "4", "9", "9", "1", "8", "4", "7", "0", "6", "1", "1", "2", "8", "0", "8", "9", "4", "3", "4", "8", "8", "7", "7", "0", "3", "5", "9", "6", "6", "1", "3", "2", "9", "0", "9", "5", "9", "5", "0", "4", "9", "2", "6", "8", "1", "5", "2", "7", "3", "9", "9", "2", "1", "6", "4", "9", "2", "2", "9", "9", "3", "7", "4", "7", "9", "1" ]
[ "nonn", "cons", "easy" ]
11
0
1
[ "A008977", "A062539", "A091670", "A377999", "A378128", "A378129", "A378130", "A378131", "A378132" ]
null
Paolo Xausa, Nov 18 2024
2025-03-31T01:46:43
oeisdata/seq/A378/A378130.seq
9c783aea9509237c9899e8903d2efb30
A378131
Decimal expansion of sqrt(1 + sqrt(3))*L/(Pi*12^(1/8)), where L is the lemniscate constant (A062539).
[ "1", "0", "1", "1", "2", "0", "4", "6", "9", "5", "5", "3", "7", "6", "9", "0", "0", "9", "0", "5", "7", "2", "8", "5", "5", "9", "8", "8", "5", "6", "9", "6", "2", "5", "8", "0", "3", "2", "8", "3", "5", "3", "6", "6", "5", "8", "4", "7", "9", "5", "8", "1", "9", "2", "0", "4", "2", "2", "3", "1", "0", "8", "1", "0", "3", "5", "4", "7", "3", "8", "0", "6", "8", "3", "0", "1", "1", "5", "6", "1", "0", "6", "0", "4", "5", "1", "2", "1", "7", "7" ]
[ "nonn", "cons", "easy" ]
8
1
5
[ "A000796", "A062539", "A068465", "A090388", "A377999", "A378128", "A378129", "A378130", "A378131", "A378132" ]
null
Paolo Xausa, Nov 18 2024
2024-11-19T00:53:55
oeisdata/seq/A378/A378131.seq
7d0f65d43df479c3e0fe4f636f1b0c1e
A378132
Decimal expansion of L^4/15, where L is the lemniscate constant (A062539).
[ "3", "1", "5", "1", "2", "1", "2", "0", "0", "2", "1", "5", "3", "8", "9", "7", "5", "3", "8", "2", "1", "7", "6", "8", "9", "9", "4", "2", "2", "4", "8", "6", "8", "8", "5", "5", "6", "6", "4", "5", "5", "1", "9", "3", "5", "4", "5", "1", "4", "8", "5", "2", "4", "3", "8", "4", "7", "0", "5", "4", "0", "3", "5", "7", "3", "8", "4", "2", "5", "9", "8", "3", "7", "6", "8", "2", "7", "4", "6", "1", "2", "1", "6", "1", "0", "8", "6", "9", "4", "3" ]
[ "nonn", "cons", "easy", "changed" ]
9
1
1
[ "A062539", "A068465", "A092732", "A377999", "A378128", "A378129", "A378130", "A378131", "A378132" ]
null
Paolo Xausa, Nov 18 2024
2025-04-25T21:08:48
oeisdata/seq/A378/A378132.seq
dd0d1f742bb7cbab00c9cbf124ce400b
A378133
Irregular triangle T(n,k) = P(n)*2^k, n >= 0, k = 0..floor(log_2 prime(k+1)), where P = A002110.
[ "1", "2", "4", "6", "12", "24", "30", "60", "120", "210", "420", "840", "1680", "2310", "4620", "9240", "18480", "30030", "60060", "120120", "240240", "480480", "510510", "1021020", "2042040", "4084080", "8168160", "9699690", "19399380", "38798760", "77597520", "155195040", "223092870", "446185740", "892371480", "1784742960", "3569485920" ]
[ "nonn", "tabf", "easy" ]
10
0
2
[ "A000079", "A002110", "A060735", "A088860", "A098388", "A102476", "A378133", "A378144" ]
null
Michael De Vlieger, Nov 17 2024
2025-03-23T13:55:05
oeisdata/seq/A378/A378133.seq
5509e6297d7b7fb403896f0bf0440b81
A378134
a(n) is the smallest prime p such that (2*p)^(2^n) + 1 is also prime.
[ "2", "2", "2", "2", "37", "281", "137", "2129", "139", "23", "1231", "1279", "17477" ]
[ "nonn", "more" ]
15
0
1
[ "A005384", "A019434", "A052291", "A378134", "A378143", "A378146" ]
null
Juri-Stepan Gerasimov, Nov 17 2024
2024-12-03T12:42:20
oeisdata/seq/A378/A378134.seq
ea2dacc2e3bd4d654a0b26a55b20d31a
A378135
a(n) = p(n*p(n)), where p(x) = least prime > x.
[ "2", "3", "7", "17", "23", "37", "43", "79", "89", "101", "113", "149", "157", "223", "239", "257", "277", "331", "347", "439", "461", "487", "509", "673", "701", "727", "757", "787", "821", "907", "937", "1151", "1187", "1223", "1259", "1297", "1361", "1523", "1559", "1601", "1657", "1777", "1811", "2027", "2069", "2129", "2179", "2503", "2549", "2609", "2657" ]
[ "nonn" ]
22
0
1
[ "A000040", "A013636", "A151800", "A378135", "A378136", "A378137" ]
null
Clark Kimberling, Nov 20 2024
2025-01-08T05:43:20
oeisdata/seq/A378/A378135.seq
b0d9f7e9836df48d6783156f5468c264
A378136
a(n) = p(2*n*p(n)), where p(x) = least prime > x.
[ "2", "5", "13", "31", "41", "71", "89", "157", "179", "199", "223", "293", "313", "443", "479", "521", "547", "647", "691", "877", "929", "967", "1013", "1361", "1399", "1451", "1511", "1567", "1627", "1801", "1861", "2297", "2371", "2447", "2521", "2591", "2671", "3037", "3119", "3203", "3299", "3527", "3613", "4049", "4139", "4231", "4327", "4987", "5099" ]
[ "nonn" ]
18
0
1
[ "A000040", "A013636", "A151800", "A378135", "A378136" ]
null
Clark Kimberling, Nov 20 2024
2025-01-08T05:43:37
oeisdata/seq/A378/A378136.seq
59ca2fa134f95900c8f817f1c00c554e
A378137
a(n) = p(n^2*p(n)), where p(x) is the least prime > x.
[ "2", "3", "13", "47", "83", "179", "257", "541", "709", "907", "1103", "1579", "1873", "2879", "3343", "3833", "4357", "5501", "6163", "8311", "9203", "10151", "11149", "15349", "16729", "18127", "19609", "21143", "22739", "26083", "27901", "35569", "37889", "40343", "42773", "45329", "47963", "56131", "59207", "62383", "65609", "72287" ]
[ "nonn" ]
17
0
1
[ "A000040", "A151800", "A378135", "A378136", "A378137" ]
null
Clark Kimberling, Dec 21 2024
2025-01-11T05:27:10
oeisdata/seq/A378/A378137.seq
a3b11b72b276399d122e6ba7d287be8d
A378138
The distinct values, in order of appearance, of A381087.
[ "2", "1", "6", "31", "64", "331", "814", "1607", "4107", "5129", "10283", "12819", "16163", "40108", "80313", "100153", "256379", "1281895", "2571143", "3130008" ]
[ "nonn", "base" ]
16
0
1
[ "A011532", "A378138", "A381087", "A381183" ]
null
Scott R. Shannon, Feb 16 2025
2025-02-20T08:38:12
oeisdata/seq/A378/A378138.seq
1c00e421a69b303330ee5ff9ddec67dc
A378139
Smallest prime number such that the number of distinct prime factors with multiplicity of its 9's complement is equal to n. If no such number exists, return -1.
[ "2", "3", "23", "11", "19", "263", "167", "103", "487", "1039", "7951", "5903", "28319", "107071", "67231", "590399", "180799", "344639", "1480319", "12181759", "4757119", "10871039", "1611391", "140167679", "203082239", "228248063", "530237951", "1812718591", "5302379519", "13295347711", "12758476799", "132953477119", "1410065407" ]
[ "nonn", "base" ]
42
1
1
[ "A000040", "A001221", "A001222", "A061601", "A377471", "A378139" ]
null
Jean-Marc Rebert, Jan 08 2025
2025-01-29T13:13:54
oeisdata/seq/A378/A378139.seq
5104dd8362858169760da8a4c8556fc6
A378140
a(n) is the least palindrome that has exactly n palindromic divisors other than itself and 1.
[ "1", "4", "6", "232", "44", "636", "66", "484", "888", "616", "2442", "2112", "4224", "6006", "2772", "26862", "23232", "232232", "46464", "297792", "66066", "88088", "222222", "252252", "213312", "21122112", "234432", "606606", "828828", "444444", "279972", "21211212", "666666", "2444442", "2114112", "2578752", "888888", "4228224", "42422424", "23555532", "54999945", "82711728" ]
[ "nonn", "base" ]
11
0
2
[ "A071276", "A071277", "A087997", "A378140" ]
null
Robert Israel, Jan 08 2025
2025-01-10T12:06:22
oeisdata/seq/A378/A378140.seq
df9c4909d26302b44f56fe6a2f9e97d8
A378141
For any n > 0, a(n) is the least positive integer such that the XOR difference triangle with bottom row (a(1), ..., a(n)) has distinct values.
[ "1", "2", "4", "8", "16", "32", "9", "18", "64", "128", "39", "75", "156", "256", "76", "137", "259" ]
[ "nonn", "base", "fini", "full" ]
11
1
2
[ "A099884", "A378141", "A380112" ]
null
Rémy Sigrist, Jan 09 2025
2025-01-17T09:12:21
oeisdata/seq/A378/A378141.seq
3d240c89a1d6fcc00a36669c82e27665
A378142
a(n) = n + floor(n*s/r) + floor(n*t/r), where r=2^(1/4), s=2^(1/2), t=2^(3/4).
[ "3", "6", "10", "13", "17", "21", "24", "28", "31", "35", "39", "42", "46", "49", "53", "57", "61", "64", "67", "71", "74", "79", "82", "85", "89", "92", "97", "100", "104", "107", "110", "115", "118", "122", "125", "128", "133", "136", "140", "143", "146", "150", "154", "158", "161", "165", "168", "172", "176", "179", "183", "186", "190", "194", "197", "201", "204" ]
[ "nonn" ]
14
1
1
[ "A000027", "A010767", "A184812", "A378142", "A378185", "A379510" ]
null
Clark Kimberling, Jan 13 2025
2025-01-20T22:45:51
oeisdata/seq/A378/A378142.seq
20670a5c95a920c7ccfc88661800f092
A378143
a(n) is the smallest prime of the form (2*p)^(2^n) + 1 for some prime p.
[ "5", "17", "257", "65537", "808551180810136214718004658177", "9807585394417153072393128067370344132933540474708183331242417216238928121991128579833857" ]
[ "nonn" ]
13
0
1
[ "A005384", "A019434", "A052291", "A222008", "A286678", "A378134", "A378143", "A378146" ]
null
Juri-Stepan Gerasimov, Nov 17 2024
2024-12-03T12:43:37
oeisdata/seq/A378/A378143.seq
9561033b206f965a9d67eb8fe9dc1c6e
A378144
a(n) = P(n) * 2^floor(log_2(prime(n+1))) = A002110(n) * A000079(A098388(n+1)).
[ "1", "4", "24", "120", "1680", "18480", "480480", "8168160", "155195040", "3569485920", "103515091680", "6417935684160", "237463620313920", "9736008432870720", "418648362613440960", "19676473042831725120", "1042853071270081431360", "61528331204934804450240", "7506456407002046142929280", "502932579269137091576261760" ]
[ "nonn", "easy" ]
11
0
2
[ "A000079", "A002110", "A060735", "A098388", "A378133", "A378144" ]
null
Michael De Vlieger, Nov 17 2024
2024-11-20T06:46:39
oeisdata/seq/A378/A378144.seq
984385d9cbcd2d49a73367c97e43f2b0
A378145
Riordan triangle (1 + x * C(x), x * C(x)), where C(x) is g.f. of A000108.
[ "1", "1", "1", "1", "2", "1", "2", "4", "3", "1", "5", "10", "8", "4", "1", "14", "28", "23", "13", "5", "1", "42", "84", "70", "42", "19", "6", "1", "132", "264", "222", "138", "68", "26", "7", "1", "429", "858", "726", "462", "240", "102", "34", "8", "1", "1430", "2860", "2431", "1573", "847", "385", "145", "43", "9", "1", "4862", "9724", "8294", "5434", "3003", "1430", "583", "198", "53", "10", "1" ]
[ "nonn", "easy", "tabl" ]
11
0
5
[ "A000007", "A000108", "A004070", "A068875", "A120588", "A378145" ]
null
Werner Schulte, Nov 17 2024
2024-12-08T17:12:07
oeisdata/seq/A378/A378145.seq
a653fb601aeec145f087e5106f67dbeb
A378146
Primes p such that 16*p^4 + 1 is prime.
[ "2", "3", "17", "23", "37", "41", "53", "59", "71", "97", "127", "139", "167", "233", "263", "277", "283", "379", "389", "457", "521", "563", "571", "601", "619", "661", "691", "743", "797", "809", "811", "823", "853", "859", "877", "967", "971", "997", "1051", "1063", "1103", "1187", "1277", "1289", "1321", "1367", "1399", "1433", "1451", "1499" ]
[ "nonn" ]
10
1
1
[ "A005384", "A052291", "A378134", "A378143", "A378146" ]
null
Juri-Stepan Gerasimov, Nov 17 2024
2024-12-03T12:43:49
oeisdata/seq/A378/A378146.seq
336ebde1caec38af1be651f90f2b5637
A378147
The lexicographically earliest infinite simple continued fraction such that the concatenation of its terms has the same succession of digits as its decimal expansion.
[ "0", "3", "29", "5", "710", "9", "8", "9", "2", "10", "6", "7", "2", "3", "8", "6", "8", "5", "3", "3", "2", "3", "5", "1", "5", "9", "4", "8", "8", "2", "50", "4", "8", "2", "5", "2", "7", "20", "3", "1", "5", "4", "8", "5", "5", "7", "9", "9", "1", "90", "2", "8", "8", "3", "6", "5", "5", "2", "50", "3", "9", "5", "4", "1", "80", "3", "1", "9", "3", "5", "8", "7", "1", "1", "7", "7", "8", "5", "9", "2", "4", "2", "5", "4" ]
[ "base", "cofr", "nonn" ]
11
0
2
null
null
Dominic McCarty, Jan 07 2025
2025-01-09T19:13:12
oeisdata/seq/A378/A378147.seq
82bd070287cde497c4cbb81bb130d295
A378148
a(n) is the number of distinct trapezoids having integer sides and height with exactly one pair of parallel sides and area n.
[ "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "1", "0", "1", "2", "1", "0", "3", "0", "1", "2", "1", "0", "3", "0", "1", "2", "1", "0", "4", "0", "2", "2", "1", "1", "5", "0", "1", "2", "3", "0", "5", "0", "2", "3", "1", "0", "6", "0", "2", "2", "2", "0", "7", "1", "3", "2", "1", "0", "9", "0", "1", "3", "3", "2", "8", "0", "3", "2", "3", "0", "10", "0", "1", "5", "3", "0", "9", "0", "6", "3", "1", "0", "10", "2", "1", "2" ]
[ "nonn" ]
22
1
15
[ "A024406", "A027750", "A103606", "A214602", "A340858", "A340859", "A340860", "A365049", "A374594", "A378148", "A378149", "A378150" ]
null
Felix Huber, Dec 02 2024
2024-12-03T12:50:30
oeisdata/seq/A378/A378148.seq
534988c1437dae9f54377bc78146cfd3
A378149
a(n) is the number of distinct integer-sided right trapezoids with exactly one pair of parallel sides and area n.
[ "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "1", "0", "1", "1", "0", "0", "2", "0", "0", "1", "1", "0", "1", "0", "1", "1", "0", "0", "3", "0", "1", "1", "1", "1", "2", "0", "1", "1", "2", "0", "4", "0", "0", "2", "1", "0", "3", "0", "2", "1", "0", "0", "4", "1", "1", "1", "1", "0", "3", "0", "1", "2", "1", "1", "5", "0", "1", "1", "2", "0", "4", "0", "1", "3", "1", "0", "5", "0", "2", "2", "1", "0", "3", "1", "1", "1" ]
[ "nonn" ]
10
1
18
[ "A027750", "A214602", "A340858", "A340859", "A340860", "A374594", "A378148", "A378149", "A378150" ]
null
Felix Huber, Dec 04 2024
2024-12-23T22:18:49
oeisdata/seq/A378/A378149.seq
5a708aa867b6c0bc05c3e61c5682255a
A378150
a(n) is the number of distinct integer-sided isosceles trapezoids with exactly one pair of parallel sides and area n.
[ "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "1", "0", "1", "1", "0", "0", "2", "0", "0", "1", "1", "0", "1", "0", "1", "1", "0", "0", "2", "0", "0", "1", "1", "0", "1", "0", "1", "1", "0", "0", "2", "0", "0", "1", "1", "0", "2", "0", "2", "1", "0", "0", "3", "0", "0", "1", "2", "1", "2", "0", "1", "1", "1", "0", "5", "0", "0", "2", "1", "0", "2", "0", "3", "1", "0", "0", "4", "1", "0", "1", "2" ]
[ "nonn" ]
8
1
24
[ "A027750", "A214602", "A340858", "A340859", "A340860", "A374594", "A378148", "A378149", "A378150" ]
null
Felix Huber, Dec 02 2024
2024-12-03T12:50:40
oeisdata/seq/A378/A378150.seq
eb7c8680603ca732cd6a9deba0f88054
A378151
G.f. A(x) satisfies A(x) = 1 + (x * (1+x) * A(x))^3.
[ "1", "0", "0", "1", "3", "3", "4", "18", "45", "72", "153", "450", "1066", "2172", "5142", "13381", "31752", "72333", "176475", "441909", "1065528", "2551465", "6292857", "15620439", "38229235", "93698523", "232545105", "578019090", "1430290512", "3548336724", "8851036863", "22092054588", "55093739760", "137681640450" ]
[ "nonn" ]
10
0
5
[ "A000045", "A115055", "A256169", "A378151", "A378152", "A378153" ]
null
Seiichi Manyama, Nov 18 2024
2024-11-18T07:33:10
oeisdata/seq/A378/A378151.seq
f4050fbea66f4bb5698e5e46b991524e
A378152
G.f. A(x) satisfies A(x) = 1 + (x * (1+x) * A(x))^4.
[ "1", "0", "0", "0", "1", "4", "6", "4", "5", "32", "112", "224", "302", "488", "1564", "4872", "11034", "19664", "37128", "95824", "266659", "635740", "1306682", "2706524", "6503711", "16794992", "40634744", "90066416", "197648134", "465436936", "1152867388", "2790870536", "6434526866", "14640368240", "34415925816", "83509570992" ]
[ "nonn" ]
7
0
6
[ "A000045", "A256169", "A378151", "A378152" ]
null
Seiichi Manyama, Nov 18 2024
2024-11-18T07:33:18
oeisdata/seq/A378/A378152.seq
f21b296ab5ead705eaf47f7f4ac599b0
A378153
G.f. A(x) satisfies A(x) = 1 + (x * (1+x))^3 * A(x)^2.
[ "1", "0", "0", "1", "3", "3", "3", "12", "30", "45", "75", "192", "436", "798", "1554", "3542", "7740", "15543", "32183", "70794", "153252", "321431", "684123", "1491504", "3232672", "6928779", "14957787", "32615388", "70991040", "153985890", "335256886", "733206840", "1603258134", "3503385568", "7671749664", "16837946850" ]
[ "nonn" ]
10
0
5
[ "A000108", "A115055", "A378151", "A378153" ]
null
Seiichi Manyama, Nov 18 2024
2024-11-18T09:44:43
oeisdata/seq/A378/A378153.seq
ea00cf30d139587f41e5b10aa4e06168
A378154
Array read by rows: T(n,k) for k <= min(n,10) is the number of digital types of length n with exactly k distinct decimal digits without common prime factors of a different digital type.
[ "1", "1", "1", "0", "3", "1", "0", "4", "6", "1", "0", "15", "25", "10", "1", "0", "12", "84", "65", "15", "1", "0", "63", "301", "350", "140", "21", "1", "0", "80", "868", "1672", "1050", "266", "28", "1", "0", "171", "2745", "7770", "6951", "2646", "462", "36", "1", "0", "370", "8680", "33505", "42405", "22827", "5880", "750", "45", "0", "0", "1023", "28501", "145750", "246730", "179487", "63987", "11880", "1155", "55" ]
[ "nonn", "base", "tabf" ]
92
1
5
[ "A008277", "A164864", "A267013", "A376918", "A377727", "A378154", "A378199", "A378511", "A378761" ]
null
Dmytro Inosov, Nov 18 2024
2025-01-03T23:28:26
oeisdata/seq/A378/A378154.seq
e5bd5cc6d730b0c66bf83a776ef51f3b
A378155
G.f. A(x) satisfies A(x) = ( 1 + x * A(x)^(2/3) * (1 + A(x)^(2/3)) )^3.
[ "1", "6", "48", "452", "4680", "51504", "591312", "7002864", "84926304", "1049402944", "13165069824", "167239042176", "2146912312064", "27808372643328", "362981425115904", "4769884412086016", "63050983340533248", "837805424714425344", "11184489029495865344", "149935005483457542144", "2017560365768892739584" ]
[ "nonn" ]
5
0
2
[ "A219534", "A371693", "A378155", "A378156" ]
null
Seiichi Manyama, Nov 18 2024
2024-11-18T09:45:03
oeisdata/seq/A378/A378155.seq
6b09119341ae3bae46db2ab6e3b44302
A378156
G.f. A(x) satisfies A(x) = ( 1 + x * A(x)^(1/2) * (1 + A(x)^(1/2)) )^4.
[ "1", "8", "72", "720", "7728", "87104", "1017184", "12200640", "149429504", "1861059328", "23498407680", "300110580224", "3870135336192", "50323754919936", "659085377250816", "8686436702866432", "115120162870534144", "1533214282017157120", "20510220228874399744", "275462154992599851008", "3712900128220039372800" ]
[ "nonn" ]
8
0
2
[ "A219534", "A371693", "A378155", "A378156" ]
null
Seiichi Manyama, Nov 18 2024
2024-11-18T09:44:57
oeisdata/seq/A378/A378156.seq
53f91991e6574aa06668088457f65593
A378157
The least prime dividing !n = A000166(n).
[ "2", "3", "2", "5", "2", "7", "2", "3", "2", "11", "2", "13", "2", "3", "2", "17", "2", "11", "2", "3", "2", "23", "2", "5", "2", "3", "2", "29", "2", "31", "2", "3", "2", "5", "2", "11", "2", "3", "2", "11", "2", "43", "2", "3", "2", "47", "2", "7", "2", "3", "2", "53", "2", "5", "2", "3", "2", "11", "2", "61", "2", "3", "2", "5", "2", "67", "2", "3", "2", "71", "2", "73", "2", "3", "2", "7", "2", "79", "2", "3", "2" ]
[ "nonn" ]
9
3
1
[ "A000166", "A020639", "A152024", "A195207", "A195208", "A195209", "A195210", "A378157", "A378158", "A378159" ]
null
Amiram Eldar, Nov 18 2024
2024-11-19T00:58:56
oeisdata/seq/A378/A378157.seq
b0ef3420dafeb8bc6d60cd40624a3899
A378158
Numbers k such that lpf(!k) < lpf(k-1), where lpf(k) = A020639(k) and !k = A000166(k).
[ "20", "38", "42", "60", "90", "104", "108", "110", "114", "132", "138", "152", "164", "170", "174", "192", "194", "198", "240", "242", "258", "284", "294", "324", "338", "350", "360", "368", "390", "398", "434", "438", "450", "462", "482", "488", "500", "504", "510", "522", "524", "528", "542", "548", "564", "570", "588", "600", "602", "614", "618", "632", "642", "644", "648" ]
[ "nonn" ]
7
1
1
[ "A000166", "A020639", "A337986", "A378157", "A378158" ]
null
Amiram Eldar, Nov 18 2024
2024-11-19T00:59:04
oeisdata/seq/A378/A378158.seq
2d0c3185c4ba0fbd83258db37c66cc83
A378159
The least prime dividing A000255(n); a(1) = 1.
[ "1", "3", "11", "53", "3", "13", "11", "3", "1468457", "11", "3", "1373", "34361893981", "3", "17713", "2130617", "3", "11", "13", "3", "11", "617", "3", "37", "11", "3", "179", "14633", "3", "76463", "97", "3", "337", "1049", "3", "11", "7237598635049", "3", "67", "11", "3", "22742406079421034331584846001936724930824184898296683", "11", "3", "13" ]
[ "nonn" ]
8
1
2
[ "A000255", "A020639", "A301423", "A378157", "A378159" ]
null
Amiram Eldar, Nov 18 2024
2024-11-19T00:59:13
oeisdata/seq/A378/A378159.seq
5bd947ca70f81b083854bed0c2c7d49c
A378160
The number of distinct prime factors of !n = A000166(n).
[ "0", "1", "1", "2", "2", "3", "3", "4", "2", "3", "2", "4", "3", "3", "4", "3", "3", "4", "5", "5", "4", "7", "5", "6", "4", "5", "7", "6", "6", "7", "4", "4", "4", "8", "4", "6", "4", "5", "6", "6", "4", "7", "2", "4", "7", "8", "6", "5", "7", "6", "7", "7", "4", "6", "9", "6", "6", "6", "6", "6", "4", "4", "5", "4", "3", "6", "6", "6", "6", "6", "7", "7", "4", "8", "6", "5", "8", "6", "4", "4", "5", "8", "4", "7", "7", "8", "6" ]
[ "nonn" ]
13
2
4
[ "A000166", "A001221", "A152024", "A195207", "A195208", "A195209", "A195210", "A301423", "A378157", "A378160", "A378161", "A378162" ]
null
Amiram Eldar, Nov 18 2024
2024-12-08T20:41:07
oeisdata/seq/A378/A378160.seq
de71ae45201be14ed22aeb5fb8113a97
A378161
The number of prime factors of !n = A000166(n), counted with multiplicity.
[ "0", "1", "2", "3", "2", "4", "3", "6", "5", "3", "3", "6", "3", "3", "5", "6", "3", "8", "5", "6", "5", "8", "5", "9", "5", "5", "11", "7", "6", "9", "4", "8", "6", "8", "4", "10", "5", "5", "7", "8", "4", "8", "2", "7", "12", "8", "6", "9", "8", "7", "8", "8", "4", "10", "10", "8", "7", "6", "6", "8", "4", "4", "8", "9", "3", "8", "6", "7", "7", "6", "7", "13", "4", "8", "8", "6", "9", "7", "4", "7", "10", "8", "4", "9", "7" ]
[ "nonn" ]
12
2
3
[ "A000166", "A001222", "A152024", "A195207", "A195208", "A195209", "A195210", "A301423", "A378157", "A378160", "A378161", "A378162" ]
null
Amiram Eldar, Nov 18 2024
2024-12-08T20:41:02
oeisdata/seq/A378/A378161.seq
f378866177aa70099a894f0171207822
A378162
Number k such that !k = A000166(k) is squarefree.
[ "0", "2", "3", "6", "8", "11", "14", "15", "18", "20", "24", "27", "30", "32", "35", "36", "39", "42", "44", "47", "48", "54", "59", "60", "62", "63", "66", "68", "71", "72", "74", "75", "80", "83", "84", "86", "87", "90", "92", "95", "96", "98", "102", "104", "107", "108", "110", "114", "116" ]
[ "nonn", "more" ]
9
1
2
[ "A000166", "A005117", "A378160", "A378161", "A378162" ]
null
Amiram Eldar, Nov 18 2024
2024-11-26T02:20:56
oeisdata/seq/A378/A378162.seq
9371766d7e7605e8df742f5b5c6aff9a
A378163
Triangle read by rows: T(n,k) is the number of subgroups of S_n isomorphic to S_k, where S_n is the n-th symmetric group.
[ "1", "1", "1", "1", "3", "1", "1", "9", "4", "1", "1", "25", "20", "5", "1", "1", "75", "160", "60", "12", "1", "1", "231", "910", "560", "84", "7", "1", "1", "763", "5936", "5740", "560", "56", "8", "1", "1", "2619", "53424", "58716", "3276", "336", "72", "9", "1", "1", "9495", "397440", "734160", "79632", "4620", "480", "90", "10", "1", "1", "35695", "3304620", "8337120", "1105104", "39732", "3300", "660", "110", "11", "1", "1", "140151", "35023120", "133212420", "16571808", "1400784", "20592", "4950", "880", "132", "12", "1", "1", "568503", "322852816", "1769490580", "176344740", "16253952", "130416", "33462", "7150", "1144", "156", "13", "1" ]
[ "nonn", "tabl", "hard" ]
29
1
5
[ "A000085", "A001189", "A281097", "A378163", "A378279", "A378280", "A378281" ]
null
Jianing Song, Nov 18 2024
2024-11-29T23:50:57
oeisdata/seq/A378/A378163.seq
83938ec4b2bc2aeb3cf7650318084a0d
A378164
Smaller of consecutive terms b < c of A076467 such that the quality q=log(rad(c))/log(rad((c-b)*b*c)) of the abc-triple c-b,b,c with gcd(c-b,b,c)=1 sets a new record.
[ "1", "81", "1296", "2187", "1419857" ]
[ "nonn", "hard", "more" ]
9
1
2
[ "A007947", "A076467", "A377933", "A377934", "A378164", "A378165", "A378166", "A378167" ]
null
Hugo Pfoertner, Nov 18 2024
2024-11-27T17:56:59
oeisdata/seq/A378/A378164.seq
e04aee8926bae92d739f42687d97a374
A378165
Differences between adjacent terms of A076467 that correspond to the locations of abc-quality records of A378164.
[ "7", "44", "35", "10", "23440" ]
[ "nonn", "hard", "more" ]
5
1
1
[ "A076467", "A378164", "A378165" ]
null
Hugo Pfoertner, Nov 19 2024
2024-11-27T15:58:13
oeisdata/seq/A378/A378165.seq
173cdd271ef5854493d1e25a686f16eb
A378166
Terms c = A076467(k) such that the distinct prime factors of b = A076467(k-1) and of c-b are subsets of the prime factors of c, i.e., rad(c)/rad((c-b)*b*c) = 1.
[ "16", "64", "2744", "474552", "157529610000", "407165596771032", "1491025241529616", "173903694695292024", "661905356066769705912", "14918256451377811247508792", "19801061641727872277815512", "2718924063971620383558231552" ]
[ "nonn", "hard", "more" ]
16
1
1
[ "A007947", "A076467", "A378164", "A378165", "A378166", "A378167" ]
null
Hugo Pfoertner, Nov 20 2024
2024-11-29T05:11:38
oeisdata/seq/A378/A378166.seq
28ceb153dc9856615f4e6e1bf3b347b9
A378167
Differences between adjacent terms of A076467 that correspond to the locations described by A378166.
[ "8", "32", "343", "17576", "65610000", "11329982936", "26102469128", "315404039943", "152838610998696", "7327416190396311", "146668341275463896", "1097750613982270976" ]
[ "nonn", "hard", "more" ]
13
1
1
[ "A076467", "A378164", "A378165", "A378166", "A378167" ]
null
Hugo Pfoertner, Nov 20 2024
2024-11-29T05:11:28
oeisdata/seq/A378/A378167.seq
6548d06414d6b76172ee306bae69f5a3
A378168
a(n) is the number of squares <= 10^n that are not higher powers, i.e., terms of A076467.
[ "2", "6", "24", "87", "292", "959", "3089", "9875", "31410", "99633", "315589", "998889", "3160340", "9996605", "31616816", "99989509", "316209268", "999967330", "3162219896", "9999897769", "31622595517", "99999679010", "316227196708", "999998989804", "3162275866962", "9999996815862", "31622770946248", "99999989953079" ]
[ "nonn" ]
23
1
1
[ "A000290", "A001597", "A070428", "A076467", "A089579", "A378168" ]
null
Hugo Pfoertner, Nov 20 2024
2024-11-21T19:11:46
oeisdata/seq/A378/A378168.seq
f6cb397caa32fa1149fc7a0fda30ddc5
A378169
Number of free polyominoes with n cells with at most 3 collinear cell centers on any line in the plane.
[ "1", "1", "2", "4", "9", "18", "37", "62", "86", "78", "61", "34", "14", "4", "1" ]
[ "nonn", "fini", "full" ]
8
1
3
[ "A000105", "A377756", "A377942", "A378169" ]
null
Dave Budd, Nov 18 2024
2024-12-03T12:41:31
oeisdata/seq/A378/A378169.seq
c4ae08098911471541a865c92a1cddbe
A378170
Number of subsets of the first n nonzero tetrahedral numbers whose sum is a nonzero tetrahedral number.
[ "1", "2", "3", "5", "7", "8", "11", "13", "19", "34", "45", "72", "113", "171", "262", "388", "638", "1128", "1928", "3370", "5584", "9691", "17129", "30493", "54785", "94510", "169817", "308491", "559176", "1019487", "1816043", "3333698", "6153695", "11384025", "21100254", "38262081", "71096456", "132675454", "247900732", "463959984" ]
[ "nonn" ]
9
1
2
[ "A000292", "A377123", "A378170", "A378171" ]
null
Ilya Gutkovskiy, Nov 18 2024
2024-11-19T00:53:04
oeisdata/seq/A378/A378170.seq
2cc7fbe7dff1c54c136af77cc2e1690b
A378171
Number of subsets of the first n positive cubes whose sum is a positive cube.
[ "1", "2", "3", "4", "6", "7", "8", "11", "12", "18", "23", "32", "42", "67", "99", "150", "247", "391", "635", "1098", "1865", "2927", "4932", "9109", "14825", "26926", "48452", "83758", "148387", "263258", "468595", "840912", "1559322", "2785642", "5146754", "9454946", "16756330", "31372080", "57754175", "105385375", "196773661", "368705288", "671572482" ]
[ "nonn" ]
8
1
2
[ "A000578", "A126111", "A336815", "A339615", "A378170", "A378171" ]
null
Ilya Gutkovskiy, Nov 18 2024
2024-11-19T00:53:12
oeisdata/seq/A378/A378171.seq
3fa8a3833fc7fc8815be5357e326d241
A378172
Numbers m such that k = 4*m is powerful while both 4*m-1 and 4*m+1 are squarefree.
[ "1", "4", "8", "9", "18", "27", "32", "36", "49", "50", "54", "64", "98", "100", "108", "121", "125", "162", "216", "225", "242", "243", "288", "289", "324", "338", "343", "392", "400", "432", "441", "450", "486", "500", "512", "648", "675", "676", "729", "784", "800", "841", "864", "882", "900", "1000", "1058", "1089", "1125", "1152", "1250", "1296", "1323", "1350" ]
[ "nonn", "easy" ]
5
1
2
[ "A001694", "A005117", "A335851", "A378172" ]
null
Michael De Vlieger, Nov 24 2024
2024-11-27T18:34:35
oeisdata/seq/A378/A378172.seq
080ae511a364c1a91bc17ab51f7070e4
A378173
Array read by antidiagonals: T(n,k) is the number of proper antichain partitions of the rectangular poset of size n X k.
[ "1", "1", "1", "1", "2", "1", "1", "5", "5", "1", "1", "14", "38", "14", "1", "1", "42", "372", "372", "42", "1", "1", "132", "4282", "14606", "4282", "132", "1", "1", "429", "55149" ]
[ "nonn", "tabl", "more" ]
9
1
5
[ "A060854", "A299968", "A374985", "A378173" ]
null
Ludovic Schwob, Nov 18 2024
2024-11-20T09:47:47
oeisdata/seq/A378/A378173.seq
9e4b4390927455c8a09807e4f94b51fa
A378174
Maximum number of clues in a n X n crossword puzzle where each word is at least 4 letters long and the puzzle has 180-degree rotational symmetry and no interlock.
[ "0", "0", "0", "8", "10", "12", "14", "16", "20", "36", "40", "44", "52", "64", "80", "88", "96", "108", "122", "144", "156", "166", "184", "198", "228", "244", "258", "280", "294", "332" ]
[ "nonn", "more" ]
21
1
4
[ "A243826", "A378174" ]
null
Abigail Schnitzer, Nov 18 2024
2024-11-19T08:59:21
oeisdata/seq/A378/A378174.seq
0208cc24514acaea05de60a6331b258e
A378175
Triangle T(n,k) read by rows in which n-th row lists in increasing order all multiplicative partitions mu of n (with factors > 1) encoded as Product_{j in mu} prime(j); n>=1, 1<=k<=A001055(n).
[ "1", "3", "5", "7", "9", "11", "13", "15", "17", "19", "21", "27", "23", "25", "29", "33", "31", "35", "37", "39", "45", "41", "43", "51", "47", "55", "49", "53", "57", "63", "81", "59", "61", "65", "69", "75", "67", "71", "77", "87", "99", "73", "85", "79", "93", "83", "89", "91", "95", "105", "111", "117", "135", "97", "121", "101", "123", "103", "115", "125", "107", "119", "129", "153" ]
[ "nonn", "tabf" ]
28
1
2
[ "A000040", "A001055", "A005408", "A006450", "A064988", "A215366", "A318871", "A377852", "A378175", "A378176" ]
null
Alois P. Heinz, Nov 18 2024
2024-11-20T05:23:22
oeisdata/seq/A378/A378175.seq
15f44c9c587d10b3c624761a51b70995
A378176
Sum over all multiplicative partitions mu of n (with factors > 1) of the encoding as Product_{j in mu} prime(j).
[ "1", "3", "5", "16", "11", "28", "17", "67", "48", "62", "31", "156", "41", "94", "102", "303", "59", "270", "67", "334", "158", "172", "83", "743", "218", "224", "343", "508", "109", "707", "127", "1173", "292", "316", "336", "1651", "157", "364", "372", "1587", "179", "1091", "191", "926", "960", "448", "211", "3468", "516", "1202", "528", "1198", "241", "2209" ]
[ "nonn" ]
17
1
2
[ "A000040", "A001055", "A006450", "A145519", "A377853", "A378175", "A378176" ]
null
Alois P. Heinz, Nov 18 2024
2024-11-20T05:20:09
oeisdata/seq/A378/A378176.seq
d8de005bf0340b2f35d2d1657763f248
A378177
Triangle read by rows: T(n,k) is the number of subgroups of S_n isomorphic to S_k up to conjugacy, where S_n is the n-th symmetric group.
[ "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "1", "3", "4", "4", "2", "1", "1", "3", "5", "5", "3", "1", "1", "1", "4", "7", "10", "4", "2", "1", "1", "1", "4", "10", "13", "5", "2", "2", "1", "1", "1", "5", "12", "22", "9", "4", "2", "2", "1", "1", "1", "5", "15", "27", "11", "4", "3", "2", "2", "1", "1", "1", "6", "20", "47", "17", "9", "3", "3", "2", "2", "1", "1", "1", "6", "23", "56", "19", "9", "4", "3", "3", "2", "2", "1", "1" ]
[ "nonn", "tabl", "hard", "more" ]
11
1
8
[ "A004526", "A378177", "A378266", "A378273", "A378274" ]
null
Jianing Song, Nov 18 2024
2024-11-27T18:56:57
oeisdata/seq/A378/A378177.seq
5e045eb2002b908995c755fbf8004f92
A378178
Number of powerful k between consecutive perfect (or proper) prime powers.
[ "0", "0", "0", "0", "0", "0", "1", "0", "1", "2", "0", "0", "1", "4", "0", "1", "1", "0", "6", "0", "1", "3", "2", "2", "3", "7", "1", "5", "3", "4", "1", "0", "0", "2", "6", "4", "7", "2", "5", "3", "6", "1", "3", "11", "2", "2", "0", "10", "2", "13", "6", "3", "7", "2", "3", "5", "14", "7", "2", "1", "1", "3", "11", "2", "2", "17", "3", "8", "1", "11", "9", "2", "6", "0", "11", "1", "0", "20", "5", "4", "4", "24", "23" ]
[ "nonn", "easy" ]
11
1
10
[ "A001694", "A246547", "A286708", "A378178" ]
null
Michael De Vlieger, Nov 24 2024
2024-11-27T18:34:56
oeisdata/seq/A378/A378178.seq
fc9671a2507fe8e090dac8e43192430a
A378179
Squarefree numbers k whose neighbors are neither squarefree nor prime powers.
[ "19", "51", "53", "55", "89", "91", "97", "149", "151", "161", "163", "197", "199", "233", "235", "241", "249", "251", "269", "271", "293", "295", "305", "307", "337", "339", "341", "349", "377", "379", "413", "415", "449", "451", "485", "487", "489", "491", "521", "523", "551", "557", "559", "577", "579", "593", "595", "629", "631", "638", "649", "651", "665", "667" ]
[ "nonn", "easy" ]
12
1
1
[ "A005117", "A013929", "A024619", "A073247", "A126706", "A378179" ]
null
Michael De Vlieger, Nov 24 2024
2024-11-27T18:35:16
oeisdata/seq/A378/A378179.seq
e263d8ba6f22e30476e66f7671e01d1e
A378180
Irregular triangle where row n lists m such that rad(m) | n and bigomega(m) < bigomega(n), where rad = A007947 and bigomega = A001222.
[ "1", "1", "1", "2", "1", "1", "2", "3", "1", "1", "2", "4", "1", "3", "1", "2", "5", "1", "1", "2", "3", "4", "6", "9", "1", "1", "2", "7", "1", "3", "5", "1", "2", "4", "8", "1", "1", "2", "3", "4", "6", "9", "1", "1", "2", "4", "5", "10", "25", "1", "3", "7", "1", "2", "11", "1", "1", "2", "3", "4", "6", "8", "9", "12", "18", "27", "1", "5", "1", "2", "13", "1", "3", "9", "1", "2", "4", "7", "14", "49", "1", "1", "2", "3", "4", "5", "6", "9", "10", "15", "25" ]
[ "nonn", "tabf", "easy" ]
5
2
4
[ "A000961", "A001221", "A001222", "A007947", "A010846", "A024619", "A027750", "A162306", "A376248", "A376567", "A377070", "A378180", "A378181", "A378183" ]
null
Michael De Vlieger, Nov 19 2024
2024-11-24T09:38:43
oeisdata/seq/A378/A378180.seq
6d0ffd5943c009272375b3aa52e25bdf
A378181
a(1) = 0, a(n) = binomial(bigomega(n) + omega(n) - 1, omega(n)), where bigomega = A001222 and omega = A001221.
[ "0", "1", "1", "2", "1", "3", "1", "3", "2", "3", "1", "6", "1", "3", "3", "4", "1", "6", "1", "6", "3", "3", "1", "10", "2", "3", "3", "6", "1", "10", "1", "5", "3", "3", "3", "10", "1", "3", "3", "10", "1", "10", "1", "6", "6", "3", "1", "15", "2", "6", "3", "6", "1", "10", "3", "10", "3", "3", "1", "20", "1", "3", "6", "6", "3", "10", "1", "6", "3", "10", "1", "15", "1", "3", "6", "6", "3", "10", "1", "15", "4", "3", "1" ]
[ "nonn", "easy" ]
5
1
4
[ "A000005", "A001221", "A001222", "A007947", "A010846", "A024619", "A378180", "A378181" ]
null
Michael De Vlieger, Nov 19 2024
2024-11-24T09:38:54
oeisdata/seq/A378/A378181.seq
b04db543c14632da2d51fb9032b408bd
A378182
Sum of row n of A378180.
[ "0", "1", "1", "3", "1", "6", "1", "7", "4", "8", "1", "25", "1", "10", "9", "15", "1", "25", "1", "47", "11", "14", "1", "90", "6", "16", "13", "77", "1", "80", "1", "31", "15", "20", "13", "90", "1", "22", "17", "250", "1", "116", "1", "161", "58", "26", "1", "301", "8", "47", "21", "215", "1", "90", "17", "554", "23", "32", "1", "490", "1", "34", "90", "63", "19", "212", "1", "347", "27", "152" ]
[ "nonn", "easy" ]
5
1
4
[ "A000203", "A007947", "A024619", "A244974", "A376567", "A377071", "A378180", "A378182" ]
null
Michael De Vlieger, Nov 20 2024
2024-11-24T09:39:06
oeisdata/seq/A378/A378182.seq
7b1314bf88000b36763b9e38174a8f40
A378183
a(n) = rad(n)^binomial(omega(n) + bigomega(n) - 1, bigomega(n) - 2), where rad = A007947, bigomega = A001222, and omega = A001221.
[ "1", "1", "1", "2", "1", "6", "1", "8", "3", "10", "1", "1296", "1", "14", "15", "64", "1", "1296", "1", "10000", "21", "22", "1", "60466176", "5", "26", "27", "38416", "1", "24300000", "1", "1024", "33", "34", "35", "60466176", "1", "38", "39", "10000000000", "1", "130691232", "1", "234256", "50625", "46", "1", "3656158440062976", "7", "10000", "51", "456976", "1" ]
[ "nonn", "easy" ]
5
1
4
[ "A001221", "A001222", "A006881", "A007947", "A007955", "A024619", "A243103", "A377073", "A377379", "A378180", "A378183" ]
null
Michael De Vlieger, Nov 19 2024
2024-11-24T09:39:16
oeisdata/seq/A378/A378183.seq
360fc0960797c130a9117e6ed54c04f7
A378184
With p(n) = A002144(n) = n-th Pythagorean prime, a(n) is the least k such p(n) + k is a Pythagorean prime and 2 p(n) + k + 1 is a non-Pythagorean prime; or a(n) = 0 if there is no such k.
[ "8", "4", "12", "8", "4", "20", "20", "28", "16", "12", "4", "8", "4", "24", "36", "8", "16", "20", "16", "76", "36", "4", "24", "16", "56", "8", "16", "36", "20", "4", "56", "16", "40", "20", "76", "8", "64", "8", "40", "40", "16", "8", "4", "48", "12", "20", "36", "24", "16", "116", "76", "4", "24", "20", "20", "100", "100", "84", "56", "52", "64", "16", "8", "4", "24", "12", "44", "56" ]
[ "nonn" ]
9
1
1
[ "A000041", "A002144", "A002145", "A378184" ]
null
Clark Kimberling, Jan 11 2025
2025-01-14T09:49:28
oeisdata/seq/A378/A378184.seq
0bb890c46dfad9606bbec0c25917711f
A378185
a(n) = n + floor(n*r/s) + floor(n*r/t), where r=2^(1/4), s=2^(1/2), t=2^(3/4).
[ "2", "5", "8", "11", "14", "18", "20", "23", "26", "29", "33", "36", "38", "41", "44", "48", "51", "54", "56", "59", "62", "66", "69", "72", "75", "77", "81", "84", "87", "90", "93", "96", "99", "102", "105", "108", "112", "114", "117", "120", "123", "126", "130", "132", "135", "138", "141", "145", "148", "151", "153", "156", "160", "163", "166", "169", "171", "174", "178" ]
[ "nonn" ]
10
1
1
[ "A000027", "A184812", "A378142", "A378185", "A379510" ]
null
Clark Kimberling, Jan 13 2025
2025-01-13T20:29:47
oeisdata/seq/A378/A378185.seq
1c240dd9d6b7d145e44139d41dd20b95
A378186
With p(n) = A002145(n) = n-th non-Pythagorean prime, a(n) is the least k such p(n) + k is a non-Pythagorean prime and 2 p(n) + k - 5 is a Pythagorean prime; and a(n) = 0 if there is no such k .
[ "4", "4", "12", "4", "20", "16", "16", "12", "24", "64", "12", "4", "20", "28", "20", "64", "20", "40", "16", "16", "24", "20", "20", "28", "16", "16", "12", "68", "12", "20", "40", "100", "4", "36", "16", "12", "20", "100", "4", "36", "20", "72", "4", "48", "16", "12", "24", "100", "32", "4", "20", "76", "40", "8", "16", "12", "8", "40", "64", "196", "16", "12", "60", "68", "52", "20" ]
[ "nonn" ]
5
1
1
[ "A000041", "A002144", "A002145", "A378186", "A378187" ]
null
Clark Kimberling, Jan 13 2025
2025-01-14T09:49:57
oeisdata/seq/A378/A378186.seq
4163cf37e9e74acbafdcfce918cd5e0e
A378187
With p(n) = A002145(n) = n-th non-Pythagorean prime, a(n) is the least k such p(n) + k is a non-Pythagorean prime and 2 p(n) + k - 3 is a Pythagorean prime; and a(n) = 0 if there is no such k.
[ "4", "12", "12", "12", "24", "12", "24", "12", "12", "36", "12", "24", "48", "24", "60", "12", "48", "72", "12", "36", "192", "12", "60", "24", "12", "48", "12", "12", "108", "48", "60", "24", "72", "72", "168", "36", "24", "12", "84", "48", "24", "48", "108", "24", "24", "36", "12", "12", "12", "24", "60", "48", "60", "156", "48", "60", "84", "12", "24", "60", "84", "12", "84", "36" ]
[ "nonn" ]
4
1
1
[ "A000041", "A002144", "A002145", "A378186", "A378187" ]
null
Clark Kimberling, Jan 13 2025
2025-01-14T09:50:08
oeisdata/seq/A378/A378187.seq
33105482965849ea6b502fbc66c2f7f0
A378188
Record values in A205561.
[ "2", "3", "4", "5", "8", "10", "20", "22", "24", "29", "34", "36", "49", "59", "72", "76", "90", "108", "110", "144", "162", "173", "175", "189", "281", "410", "413", "473", "478", "511", "512", "513", "539", "555", "632", "639", "783", "790", "794", "820", "944", "1096", "1153", "1178", "1226", "1264", "1413", "1438", "1622", "1633", "1689", "1717", "1801", "1892", "1982", "2002", "2057", "2446", "2521", "2592" ]
[ "nonn" ]
11
1
1
[ "A205561", "A378188", "A378189" ]
null
Robert Israel, Nov 19 2024
2025-03-31T01:47:06
oeisdata/seq/A378/A378188.seq
4493b8ee1f8ab7862a4be1ec3d26bc87
A378189
Positions of records in A205561.
[ "1", "3", "5", "7", "13", "17", "37", "83", "137", "173", "193", "269", "311", "479", "607", "673", "1019", "1427", "1523", "1613", "3391", "3527", "4817", "5021", "5623", "9887", "14891", "15823", "21701", "22727", "24439", "26399", "27581", "28771", "29339", "35491", "37967", "49207", "51157", "52639", "54799", "64303", "93077", "104323", "115279", "116981", "117881", "135209", "157177" ]
[ "nonn" ]
7
1
2
[ "A205561", "A378188", "A378189" ]
null
Robert Israel, Nov 19 2024
2024-11-21T09:05:18
oeisdata/seq/A378/A378189.seq
cab4395e1efce653238f153a53d7de60
A378190
Number of planar maps with an external face and n internal triangular faces.
[ "1", "2", "6", "24", "100", "586", "3725", "26532", "198081", "1539550", "12274565", "99959181", "827795678", "6954099320", "59138955508", "508331799502", "4410651891166", "38590663253312", "340173195849485", "3018768835038348", "26952060900042852", "241960993507098580", "2183134755112963493", "19788571100313277286" ]
[ "nonn" ]
5
1
2
[ "A002713", "A169808", "A377785", "A378103", "A378190" ]
null
Ya-Ping Lu, Nov 19 2024
2024-12-12T23:15:51
oeisdata/seq/A378/A378190.seq
ddd7e0c4172ae9f60803488ea3299207
A378191
a(n) is the number of integer bases >= 2 in which n is digitally balanced.
[ "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "1", "1", "1", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "1", "0", "0", "0", "0", "1", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "nonn", "base" ]
14
0
null
[ "A049364", "A065963", "A378000", "A378073", "A378080", "A378104", "A378191" ]
null
Paolo Xausa, Nov 19 2024
2024-11-20T09:45:07
oeisdata/seq/A378/A378191.seq
1c0fae1d03809ae02a5ce682c98bfa8d
A378192
a(1) = 1. For n > 1, a(n) is the number of terms a(i); 1 <= i <= n-1 such that phi(a(i)) = phi(a(n-1)), where phi is Euler's totient function A000010.
[ "1", "1", "2", "3", "1", "4", "2", "5", "1", "6", "3", "4", "5", "2", "7", "1", "8", "3", "6", "7", "2", "9", "3", "8", "4", "9", "4", "10", "5", "6", "11", "1", "10", "7", "5", "8", "9", "6", "12", "10", "11", "2", "11", "3", "13", "1", "12", "12", "13", "2", "13", "3", "14", "7", "8", "14", "9", "10", "15", "1", "14", "11", "4", "15", "2", "15", "3", "16", "4", "17", "1", "16", "5", "16", "6", "18", "12", "17" ]
[ "nonn" ]
19
1
3
[ "A000010", "A000027", "A000040", "A006093", "A378192" ]
null
David James Sycamore, Nov 19 2024
2024-11-20T09:43:57
oeisdata/seq/A378/A378192.seq
5ab06cda50e40ee29b55b0fd2685ad76
A378193
Rectangular array read by descending antidiagonals: row n shows the integers m such that the number of Pythagorean primes (including multiplicities) that divide m is n-1.
[ "1", "2", "5", "3", "10", "25", "4", "13", "50", "125", "6", "15", "65", "250", "625", "7", "17", "75", "325", "1250", "3125", "8", "20", "85", "375", "1625", "6250", "15625", "9", "26", "100", "425", "1875", "8125", "31250", "78125", "11", "29", "130", "500", "2125", "9375", "40625", "156250", "390625", "12", "30", "145", "650", "2500", "10625", "46875", "203125", "781250", "1953125" ]
[ "nonn", "tabl" ]
11
1
2
[ "A002144", "A002145", "A083025", "A378193", "A378194" ]
null
Clark Kimberling, Jan 14 2025
2025-01-27T05:07:27
oeisdata/seq/A378/A378193.seq
bd8832c4dcca710c8013679f4b1df529
A378194
Rectangular array, read by descending antidiagonals: row n shows the integers m such that the number of primes of the form 4k+3 (including multiplicities) that divide m is n-1.
[ "1", "2", "3", "4", "6", "9", "5", "7", "18", "27", "8", "11", "21", "54", "81", "10", "12", "33", "63", "162", "243", "13", "14", "36", "99", "189", "486", "729", "16", "15", "42", "108", "297", "567", "1458", "2187", "17", "19", "45", "126", "324", "891", "1701", "4374", "6561", "20", "22", "49", "135", "378", "972", "2673", "5103", "13122", "19683", "25", "23", "57", "147", "405", "1134", "2916", "8019", "15309", "39366", "59049", "26", "24", "66", "171", "441", "1215", "3402", "8748", "24057", "45927", "118098", "177147" ]
[ "nonn", "tabl" ]
11
1
2
[ "A000244", "A002144", "A002145", "A025192", "A065339", "A072437", "A376961", "A378193", "A378194" ]
null
Clark Kimberling, Jan 14 2025
2025-01-28T07:54:01
oeisdata/seq/A378/A378194.seq
e5fec8a25627170709bd245e5393588e
A378195
Number of 2-colorings of length n without an arithmetic progression of length 3
[ "1", "2", "4", "6", "10", "14", "20", "16", "6", "0" ]
[ "nonn" ]
6
0
2
[ "A005346", "A378195", "A378196", "A378197" ]
null
Ethan Ji, Nov 19 2024
2024-12-03T12:45:42
oeisdata/seq/A378/A378195.seq
c593a13d5ed36373cd72fb7a090ab701
A378196
Number of 2-colorings of length n without an arithmetic progression of length 4
[ "1", "2", "4", "8", "14", "26", "48", "78", "132", "230", "356", "548", "842", "1078", "1344", "1764", "1744", "1850", "1948", "1708", "1442", "1342", "1032", "702", "524", "316", "168", "136", "136", "144", "152", "160", "168", "176", "28", "0" ]
[ "nonn" ]
5
0
2
[ "A005346", "A378195", "A378196", "A378197" ]
null
Ethan Ji, Nov 19 2024
2024-12-03T12:45:51
oeisdata/seq/A378/A378196.seq
ca2c80a236ab20e230473a5ca0547188
A378197
Number of 2-colorings of length n without an arithmetic progression of length 5.
[ "1", "2", "4", "8", "16", "30", "58", "112", "216", "400", "740", "1398", "2638", "4710", "8444", "15118", "27690", "48406", "84382", "146928", "255844", "402998", "625824", "956370", "1447476", "2066828", "3225856", "5020232", "7823236", "10975318", "15264202", "21500308", "30004914", "39030820", "50728472", "65402746", "88886116" ]
[ "nonn" ]
14
0
2
[ "A005346", "A378195", "A378196", "A378197" ]
null
Ethan Ji, Nov 19 2024
2024-11-23T03:37:17
oeisdata/seq/A378/A378197.seq
d4200d18c77865c34397f3f4fd5959f0
A378198
Table T(n, k) read by upward antidiagonals. T(n,1) = A375602(n), T(n,2) = A375602(A375602(n)), T(n,3) = A375602(A375602(A375602(n))) and so on.
[ "1", "2", "1", "4", "2", "1", "3", "3", "2", "1", "5", "4", "4", "2", "1", "6", "5", "3", "3", "2", "1", "7", "6", "5", "4", "4", "2", "1", "10", "7", "6", "5", "3", "3", "2", "1", "13", "16", "7", "6", "5", "4", "4", "2", "1", "16", "14", "9", "7", "6", "5", "3", "3", "2", "1", "8", "9", "17", "13", "7", "6", "5", "4", "4", "2", "1", "11", "10", "13", "12", "14", "7", "6", "5", "3", "3", "2", "1", "14", "8", "16", "14", "11", "17", "7", "6", "5", "4", "4", "2", "1", "17", "17", "10", "9", "17", "8", "12", "7", "6", "5", "3", "3", "2", "1", "19", "12", "12", "16", "13", "12", "10", "11", "7" ]
[ "nonn", "tabl" ]
9
1
2
[ "A000027", "A002817", "A006003", "A370655", "A373498", "A374447", "A374494", "A374531", "A375602", "A375725", "A378198" ]
null
Boris Putievskiy, Nov 19 2024
2024-12-03T12:46:07
oeisdata/seq/A378/A378198.seq
cb8967636c15b0a7ab7452b03a4b8715
A378199
Number of digit patterns of length n such that all integers of that digital type share a common prime factor of a different digital type.
[ "0", "0", "1", "4", "1", "26", "1", "175", "365", "1513", "1", "52611", "989", "426897", "3072870", "11132038", "1", "879525398", "316025138" ]
[ "nonn", "base", "more" ]
31
1
4
[ "A164864", "A267013", "A376918", "A377727", "A378154", "A378199", "A378761" ]
null
Dmytro Inosov, Nov 19 2024
2025-01-06T15:12:41
oeisdata/seq/A378/A378199.seq
185c2b69480f461562058e04b04309b4
A378200
Square array read by upward antidiagonals: T(n,k) = ((k + n - 1)^2 + (k - n + 1)*(-1)^n + (1 - k - n)*(-1)^k + (1 - k - n)*(-1)^(k + n) + 2)/2.
[ "1", "5", "2", "6", "3", "4", "12", "9", "14", "7", "15", "8", "13", "10", "11", "23", "20", "25", "18", "27", "16", "28", "17", "26", "19", "24", "21", "22", "38", "35", "40", "33", "42", "31", "44", "29", "45", "30", "43", "32", "41", "34", "39", "36", "37", "57", "54", "59", "52", "61", "50", "63", "48", "65", "46", "66", "47", "64", "49", "62", "51", "60", "53", "58", "55", "56" ]
[ "nonn", "tabl" ]
36
1
2
[ "A000027", "A000384", "A016813", "A370655", "A373498", "A374447", "A374494", "A374531", "A375602", "A375725", "A376214", "A378200", "A378684", "A378705", "A378762", "A379342", "A379343", "A380245", "A380815", "A380817", "A381662", "A381663", "A381664" ]
null
Boris Putievskiy, Nov 19 2024
2025-03-29T18:09:30
oeisdata/seq/A378/A378200.seq
d5af225e0199853529dbb41ddb60224c