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1999-12-11 03:00:00
2025-04-28 00:58:08
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A382249
a(n) is the smallest starting prime of a sequence of exactly n consecutive primes that are alternately of the form 6*k+1 and 6*k-1 or vice versa.
[ "23", "19", "17", "13", "11", "7", "5", "97", "89", "877", "863", "859", "857", "853", "839", "829", "827", "823", "821", "811", "809", "3954889", "15186331", "15186323", "15186319", "77011331", "77011303", "77011289", "288413249", "288413233", "288413219", "288413173", "288413159", "62585146739", "114058236679", "143014298851", "143014298831", "143014298809" ]
[ "nonn", "changed" ]
25
1
1
[ "A057620", "A057622", "A382249" ]
null
Jean-Marc Rebert, Mar 19 2025
2025-04-25T20:41:22
oeisdata/seq/A382/A382249.seq
40965a2920dfb9aca2f3433176c9a761
A382250
Irregular 3-dimensional table, where layer n is an irregular 2D table with A000041(n) columns, each of which lists the n-bit binary numbers whose run lengths correspond to a given partition.
[ "0", "0", "0", "1", "0", "1", "3", "2", "0", "1", "7", "2", "4", "6", "3", "5", "0", "1", "15", "2", "8", "14", "3", "7", "4", "6", "12", "5", "9", "11", "13", "10", "0", "1", "31", "2", "16", "30", "3", "15", "4", "6", "8", "14", "24", "28", "5", "17", "23", "29", "7", "9", "11", "13", "19", "25", "27", "10", "18", "20", "22", "26", "12", "21", "0", "1", "63", "2", "32", "62", "3", "31", "4", "6", "16", "30", "48", "60", "5", "33", "47", "61", "7", "15", "8", "14" ]
[ "nonn" ]
16
0
7
[ "A000005", "A000041", "A000079", "A007088", "A101211", "A175020", "A175021", "A318927", "A382250" ]
null
Ali Sada and M. F. Hasler, Mar 24 2025
2025-03-26T22:03:28
oeisdata/seq/A382/A382250.seq
290427b8036e01cb6349ee92289c091a
A382252
Triangle T(n,k) = numerator of (n+k)/(1+n*k), 0 <= k <= n >= 0, read by rows.
[ "0", "1", "1", "2", "1", "4", "3", "1", "5", "3", "4", "1", "2", "7", "8", "5", "1", "7", "1", "3", "5", "6", "1", "8", "9", "2", "11", "12", "7", "1", "3", "5", "11", "1", "13", "7", "8", "1", "10", "11", "4", "13", "2", "5", "16", "9", "1", "11", "3", "13", "7", "3", "1", "17", "9", "10", "1", "4", "13", "14", "5", "16", "17", "2", "19", "20", "11", "1", "13", "7", "1", "2", "17", "3", "19", "1", "7", "11", "12", "1", "14", "15", "16", "17", "18", "19", "20", "21", "2", "23", "24" ]
[ "nonn", "tabl", "frac", "new" ]
9
0
4
[ "A000012", "A001477", "A228564", "A382252", "A382253", "A382257" ]
null
M. F. Hasler, Apr 15 2025
2025-04-16T10:25:15
oeisdata/seq/A382/A382252.seq
61f162698c66f5464c444583f3bbf6b9
A382253
Triangle T(n,k) = denominator of (n+k)/(1+n*k), 0 <= k <= n >= 0, read by rows.
[ "1", "1", "1", "1", "1", "5", "1", "1", "7", "5", "1", "1", "3", "13", "17", "1", "1", "11", "2", "7", "13", "1", "1", "13", "19", "5", "31", "37", "1", "1", "5", "11", "29", "3", "43", "25", "1", "1", "17", "25", "11", "41", "7", "19", "65", "1", "1", "19", "7", "37", "23", "11", "4", "73", "41", "1", "1", "7", "31", "41", "17", "61", "71", "9", "91", "101", "1" ]
[ "nonn", "tabl", "frac", "new" ]
7
0
6
[ "A000012", "A001477", "A228564", "A382252", "A382253", "A382257" ]
null
M. F. Hasler, Apr 15 2025
2025-04-16T10:25:24
oeisdata/seq/A382/A382253.seq
8b97d22b1a7df3a34e7b17e0ed5caa0c
A382254
Least prime p that has a decomposition into n distinct positive parts p(1) +...+ p(n) = p so that p + 6*p(k) is prime for each k.
[ "5", "7", "11", "23", "37", "41", "61", "83", "97", "127", "139", "167", "227", "227", "227", "307", "347", "383", "419", "443", "541", "571", "601", "727", "797", "797", "911", "991", "1091", "1151", "1181", "1277", "1381", "1423", "1531", "1741", "1811", "1871", "2063", "2207", "2207", "2267", "2333", "2531", "2657", "3001", "3019", "3109", "3163" ]
[ "nonn", "new" ]
11
2
1
null
null
M. F. Hasler, Apr 17 2025
2025-04-23T10:34:23
oeisdata/seq/A382/A382254.seq
68eece4efd737b5910c6deda8deec26e
A382255
Heinz number of the partition corresponding to run lengths in the bits of n.
[ "1", "2", "4", "3", "6", "8", "6", "5", "10", "12", "16", "12", "9", "12", "10", "7", "14", "20", "24", "18", "24", "32", "24", "20", "15", "18", "24", "18", "15", "20", "14", "11", "22", "28", "40", "30", "36", "48", "36", "30", "40", "48", "64", "48", "36", "48", "40", "28", "21", "30", "36", "27", "36", "48", "36", "30", "25", "30", "40", "30", "21", "28", "22", "13", "26", "44", "56", "42" ]
[ "nonn", "look", "base" ]
26
0
2
[ "A001747", "A001749", "A007088", "A008578", "A011782", "A030017", "A036036", "A080576", "A080577", "A112798", "A129129", "A185974", "A296150", "A334433", "A334434", "A334435", "A334436", "A334438", "A382255" ]
null
M. F. Hasler and Ali Sada, Mar 19 2025
2025-03-24T17:16:29
oeisdata/seq/A382/A382255.seq
1aea0a43248a25b89e960e50c9a974fb
A382256
Smallest binary number whose run lengths of bits correspond to a partition with Heinz number n.
[ "0", "1", "3", "2", "7", "4", "15", "5", "12", "8", "31", "11", "63", "16", "24", "10", "127", "19", "255", "23", "48", "32", "511", "22", "56", "64", "51", "47", "1023", "39", "2047", "21", "96", "128", "112", "44", "4095", "256", "192", "46", "8191", "79", "16383", "95", "103", "512", "32767", "45", "240", "71", "384", "191", "65535", "76", "224", "94", "768", "1024", "131071", "92", "262143", "2048", "207", "42", "448", "159" ]
[ "nonn" ]
12
1
3
[ "A036036", "A080576", "A080577", "A382255", "A382256" ]
null
M. F. Hasler, Mar 19 2025
2025-03-24T18:37:39
oeisdata/seq/A382/A382256.seq
974036c9540cb9e75fa62b500cd344d5
A382257
a(n) is the numerator of tanh(Sum_{k=1..n-1} artanh(k/n)), where artanh is the inverse hyperbolic tangent function.
[ "0", "1", "9", "17", "125", "461", "1715", "3217", "24309", "92377", "352715", "1352077", "5200299", "20058299", "77558759", "150270097", "1166803109", "4537567649", "17672631899", "68923264409", "269128937219", "1052049481859", "4116715363799", "16123801841549", "63205303218875", "247959266474051", "973469712824055", "3824345300380219", "15033633249770519" ]
[ "nonn", "frac", "new" ]
37
1
3
[ "A001700", "A010763", "A034602", "A382257", "A383431" ]
null
M. F. Hasler, Apr 15 2025
2025-04-27T14:55:15
oeisdata/seq/A382/A382257.seq
0e7a0a4a36a312204afdc1d8c978bf65
A382258
a(n) = last number placed on an infinite square grid at the n-th step, in order to surround the last number placed at the previous step, always using the next larger integer and going counter-clockwise, starting with a 1 at the origin.
[ "1", "9", "14", "18", "21", "25", "27", "30", "34", "36", "39", "42", "46", "48", "51", "54", "58", "60", "62", "65", "68", "72", "74", "76", "78", "81", "84", "88", "90", "92", "94", "97", "100", "103", "107", "109", "111", "113", "116", "119", "122", "126", "128", "130", "132", "134", "137", "140", "143", "147", "149", "151", "153", "155", "157", "160", "163", "166", "170", "172", "174", "176", "178", "180", "183", "186" ]
[ "nonn", "new" ]
27
0
2
[ "A382258", "A382259" ]
null
M. F. Hasler and Ali Sada, Apr 08 2025
2025-04-23T10:23:51
oeisdata/seq/A382/A382258.seq
f77b09291f7f2f372e6df2e449ec5501
A382259
a(n) = number of empty places to fill on an infinite square grid, at the n-th step, in order to completely surround the last square filled at the previous step n-1, starting with the origin at step 0.
[ "1", "8", "5", "4", "3", "4", "2", "3", "4", "2", "3", "3", "4", "2", "5", "4", "1", "4", "2", "2", "3", "3", "4", "2", "2", "2", "3", "3", "4", "2", "2", "2", "3", "3", "3", "4", "1", "4", "2", "5", "4", "1", "4", "1", "4", "2", "2", "2", "2", "3", "3", "3", "4", "2", "2", "2", "2", "2", "3", "3", "3", "4", "2", "2", "2", "2", "2", "3", "3", "3", "3", "4", "1", "4", "1", "4", "2", "5", "4", "1", "4", "1", "4", "1", "4", "2", "2", "2", "2", "2", "2", "3", "3", "3", "3", "4", "2", "2", "2", "2", "2" ]
[ "nonn" ]
6
0
2
[ "A382258", "A382259" ]
null
M. F. Hasler, Apr 08 2025
2025-04-13T16:36:41
oeisdata/seq/A382/A382259.seq
59a7080605e14f7eadedefd08dd9dce6
A382260
Decimal expansion of x, where x is the smallest number for which floor(x^(phi^k)) is prime for k > 0 where phi = (1+sqrt(5))/2, assuming that Oppermann's conjecture holds.
[ "1", "5", "8", "3", "1", "2", "0", "4", "0", "4", "8", "5", "8", "1", "0", "9", "2", "2", "1", "0", "3", "5", "9", "0", "5", "9", "7", "0", "7", "0", "0", "1", "3", "4", "5", "4", "0", "3", "1", "1", "0", "5", "4", "9", "6", "0", "6", "4", "1", "7", "9", "3", "7", "8", "6", "3", "7", "6", "2", "8", "2", "8", "8", "6", "1", "9", "2", "8", "9", "5", "8", "7", "1", "1", "5", "0", "0", "0", "8", "5", "2", "7", "4", "7", "4", "7", "2", "9", "7", "5", "7", "3", "7" ]
[ "nonn", "cons" ]
24
1
2
[ "A001622", "A051021", "A112597", "A382260", "A382261" ]
null
Thomas Scheuerle, Mar 19 2025
2025-03-28T15:27:26
oeisdata/seq/A382/A382260.seq
86309110e2ae5a9113a06ab9328e20c5
A382261
a(n) = floor(x^(phi^n)), where phi = (1+sqrt(5))/2 and x is the constant A382260.
[ "2", "3", "7", "23", "163", "3803", "620549", "2359981439", "1464484123012601", "3456155348019933976288373", "5061484633840283809323162088349619180781", "17493277186167814180104995425523045477935447066389138909089293633" ]
[ "nonn" ]
13
1
1
[ "A001622", "A051254", "A059784", "A090253", "A243358", "A382260", "A382261" ]
null
Thomas Scheuerle, Mar 19 2025
2025-03-27T18:37:49
oeisdata/seq/A382/A382261.seq
16d6c5f800b1c3eb81a454be23251593
A382262
Nonnegative numbers whose factorial base expansion, when read from right to left, corresponds to the ordinal transform of some finite sequence, with offset 0.
[ "0", "1", "3", "5", "9", "11", "15", "23", "33", "35", "39", "47", "57", "59", "63", "83", "87", "119", "153", "155", "159", "167", "177", "179", "183", "203", "207", "239", "273", "275", "279", "287", "297", "323", "327", "395", "399", "417", "419", "423", "527", "563", "567", "719", "873", "875", "879", "887", "897", "899", "903", "923", "927", "959", "993", "995" ]
[ "nonn", "base" ]
10
0
3
[ "A000085", "A120696", "A382262", "A382263" ]
null
Rémy Sigrist, Mar 19 2025
2025-03-21T14:39:18
oeisdata/seq/A382/A382262.seq
5dd9ca34f0885b50c18bcc61c91390b5
A382263
a(n) is the unique k such that the factorial base expansion of A382262(n) is, when read from right to left, the ordinal transform of that of A382262(k).
[ "0", "1", "3", "2", "7", "6", "5", "4", "17", "16", "15", "12", "11", "14", "13", "10", "9", "8", "43", "42", "41", "37", "40", "39", "38", "36", "35", "28", "27", "34", "33", "32", "31", "30", "29", "26", "25", "21", "24", "23", "22", "20", "19", "18", "119", "118", "117", "112", "116", "114", "113", "111", "110", "95", "115", "109", "108", "99", "107", "97", "96", "106", "105", "104" ]
[ "nonn", "base" ]
11
0
3
[ "A382262", "A382263", "A382269" ]
null
Rémy Sigrist, Mar 19 2025
2025-03-21T14:39:07
oeisdata/seq/A382/A382263.seq
198924ba25034019980607b418fca4a8
A382264
Semiprimes that are the sum of the m-th prime and the m-th semiprime for some m.
[ "6", "9", "14", "25", "38", "55", "86", "122", "141", "158", "178", "185", "218", "262", "301", "326", "446", "466", "537", "634", "695", "723", "758", "785", "866", "878", "886", "895", "898", "921", "993", "1006", "1041", "1047", "1077", "1099", "1126", "1138", "1154", "1198", "1214", "1219", "1234", "1262", "1366", "1466", "1535", "1679", "1706", "1751", "1774", "1779", "1822", "1977", "2026", "2173" ]
[ "nonn" ]
7
1
1
[ "A092021", "A133796", "A382186", "A382264" ]
null
Zak Seidov and Robert Israel, Mar 19 2025
2025-03-21T11:23:54
oeisdata/seq/A382/A382264.seq
16ca30eb5409b8d7895c96630ed9bc5d
A382265
In the prime factorization of n replace the k-th prime with the k-th nonprime number.
[ "1", "1", "4", "1", "6", "4", "8", "1", "16", "6", "9", "4", "10", "8", "24", "1", "12", "16", "14", "6", "32", "9", "15", "4", "36", "10", "64", "8", "16", "24", "18", "1", "36", "12", "48", "16", "20", "14", "40", "6", "21", "32", "22", "9", "96", "15", "24", "4", "64", "36", "48", "10", "25", "64", "54", "8", "56", "16", "26", "24", "27", "18", "128", "1", "60", "36", "28", "12", "60", "48", "30", "16", "32", "20", "144" ]
[ "nonn", "mult" ]
11
1
3
[ "A000720", "A003963", "A018252", "A066260", "A382265" ]
null
Ilya Gutkovskiy, Mar 19 2025
2025-03-22T13:04:46
oeisdata/seq/A382/A382265.seq
74a58473a836230b4fd322df6ea41388
A382266
Numerator of the harmonic mean of the exponents in the prime factorization of n.
[ "1", "1", "2", "1", "1", "1", "3", "2", "1", "1", "4", "1", "1", "1", "4", "1", "4", "1", "4", "1", "1", "1", "3", "2", "1", "3", "4", "1", "1", "1", "5", "1", "1", "1", "2", "1", "1", "1", "3", "1", "1", "1", "4", "4", "1", "1", "8", "2", "4", "1", "4", "1", "3", "1", "3", "1", "1", "1", "6", "1", "1", "4", "6", "1", "1", "1", "4", "1", "1", "1", "12", "1", "1", "4", "4", "1", "1", "1", "8", "4", "1", "1", "6", "1", "1", "1", "3", "1", "6", "1", "4", "1", "1", "1", "5", "1", "4", "4", "2" ]
[ "nonn", "frac" ]
10
2
3
[ "A070012", "A088529", "A250096", "A382266", "A382267" ]
null
Ilya Gutkovskiy, Mar 19 2025
2025-03-22T08:43:53
oeisdata/seq/A382/A382266.seq
cc6bd909c7f9a1e4e26db180fce1471c
A382267
Denominator of the harmonic mean of the exponents in the prime factorization of n.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "3", "1", "3", "1", "1", "1", "2", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "3", "3", "1", "1", "5", "1", "3", "1", "3", "1", "2", "1", "2", "1", "1", "1", "5", "1", "1", "3", "1", "1", "1", "1", "3", "1", "1", "1", "5", "1", "1", "3", "3", "1", "1", "1", "5", "1", "1", "1", "5", "1", "1", "1", "2", "1", "5", "1", "3", "1", "1", "1", "3", "1", "3", "3", "1" ]
[ "nonn", "frac" ]
9
2
11
[ "A070012", "A088530", "A250097", "A382266", "A382267" ]
null
Ilya Gutkovskiy, Mar 19 2025
2025-03-22T08:43:48
oeisdata/seq/A382/A382267.seq
b6421494df09640ad414a44c71cf0e42
A382268
Numbers k such that a right triangle can be formed from a chain of linked rods of lengths 1, 2, 3, ..., k, with the perimeter equal to the total length.
[ "15", "20", "24", "35", "39", "44", "48", "55", "56", "63", "75", "76", "80", "84", "91", "95", "99", "104", "111", "119", "120", "132", "135", "140", "143", "144", "152", "155", "168", "175", "176", "187", "188", "195", "203", "207", "215", "216", "219", "224", "252", "259", "260", "264", "272", "275", "279", "287", "288", "296", "299", "308", "315", "320", "324", "335", "351", "360" ]
[ "nonn" ]
20
1
1
[ "A000217", "A010814", "A380867", "A380868", "A380875", "A382268" ]
null
Ali Sada and Daniel Mondot, Mar 19 2025
2025-04-03T13:22:46
oeisdata/seq/A382/A382268.seq
3d19d1536e3cc194309308804ba3031a
A382269
The factorial base expansion of a(n) is, when read from right to left, the ordinal transform of that of n.
[ "0", "1", "3", "5", "3", "3", "11", "15", "15", "23", "9", "15", "11", "9", "9", "11", "15", "15", "11", "9", "9", "11", "9", "9", "47", "63", "63", "83", "39", "57", "59", "87", "87", "119", "57", "87", "35", "57", "57", "83", "39", "63", "35", "57", "57", "83", "33", "57", "47", "39", "39", "35", "63", "57", "35", "39", "39", "47", "57", "63", "59", "57", "57", "59", "87", "87", "35", "33" ]
[ "nonn", "base" ]
7
0
3
[ "A382262", "A382269" ]
null
Rémy Sigrist, Mar 20 2025
2025-03-21T14:38:47
oeisdata/seq/A382/A382269.seq
5b18c0c42f718ebbd8aec8100924ddfa
A382270
Maximum number of intercalates in a Brown's diagonal Latin square of order 2n.
[ "0", "12", "9", "112", "57" ]
[ "nonn", "more", "hard" ]
8
1
2
[ "A092237", "A307163", "A307164", "A339641", "A345760", "A368182", "A379665", "A382270" ]
null
Eduard I. Vatutin, Mar 20 2025
2025-04-01T21:43:01
oeisdata/seq/A382/A382270.seq
888aa5c4b94c9d803824920055e7f408
A382271
Smallest k such that A073734(k) = 2^n, where A073734 is the GCD of consecutive terms of the EKG sequence A064413.
[ "2", "3", "8", "17", "3070", "20143", "46660", "187759", "1339550", "2692614", "81281233", "61760615", "98845851" ]
[ "nonn", "more" ]
13
0
1
[ "A064413", "A064740", "A073734", "A073735", "A382222", "A382271" ]
null
Scott R. Shannon and Michael De Vlieger, Mar 20 2025
2025-03-23T13:54:09
oeisdata/seq/A382/A382271.seq
603b2366e772084c5c832ba1c4af0067
A382272
Maximum number of orthogonal diagonal Latin squares with the first row in ascending order that can be orthogonal to a given Brown's diagonal Latin square of order 2n.
[ "0", "1", "0", "824", "8" ]
[ "nonn", "more", "hard" ]
6
1
4
[ "A287695", "A339641", "A382272" ]
null
Eduard I. Vatutin, Mar 20 2025
2025-03-27T20:22:42
oeisdata/seq/A382/A382272.seq
cf0050aaa97a619f539fd3d1de7b7428
A382273
Number of minimum connected dominating sets in the n-Fibonacci cube graph.
[ "2", "1", "2", "3", "16", "7", "4", "2" ]
[ "nonn", "more" ]
10
1
1
null
null
Eric W. Weisstein, Mar 20 2025
2025-03-21T06:58:59
oeisdata/seq/A382/A382273.seq
30261d7ad6edd3bda91ad64b6b696916
A382274
Expansion of 1/(1 - 4*x/(1-x)^2)^(5/2).
[ "1", "10", "90", "730", "5570", "40762", "289370", "2007210", "13671170", "91750250", "608294490", "3991833210", "25968131010", "167664187290", "1075453670490", "6858654320970", "43517809896450", "274862176368330", "1728960219827290", "10835520927931930", "67679638209628098", "421442759107879930" ]
[ "nonn" ]
27
0
2
[ "A002802", "A110170", "A377198", "A377199", "A382274", "A382332" ]
null
Seiichi Manyama, Mar 29 2025
2025-04-13T03:10:22
oeisdata/seq/A382/A382274.seq
e2fb2ce0299831992dd025d65b8c53a8
A382275
Number of minimum connected dominating sets in the n-hypercube graph.
[ "1", "2", "4", "30", "192", "16320" ]
[ "nonn", "more" ]
4
0
2
null
null
Eric W. Weisstein, Mar 20 2025
2025-03-20T09:27:19
oeisdata/seq/A382/A382275.seq
4717976cee52c5c2f061dd4704f003a5
A382276
Number of minimum connected dominating sets in the n-odd graph.
[ "1", "3", "10", "8610" ]
[ "nonn", "more" ]
4
1
2
null
null
Eric W. Weisstein, Mar 20 2025
2025-03-20T09:27:14
oeisdata/seq/A382/A382276.seq
598e3b9718f8c50577bc08c2f37bfd60
A382277
a(n) is the least composite number obtained by inserting a nonempty string of 0's inside n.
[ "100", "1001", "102", "1003", "104", "105", "106", "1007", "108", "100009", "200", "201", "202", "203", "204", "205", "206", "207", "208", "209", "300", "301", "302", "303", "304", "305", "306", "3007", "308", "309", "400", "40001", "402", "403", "404", "405", "406", "407", "408", "4009", "500", "501", "502", "50003", "504", "505", "506", "507", "508", "50009", "600", "6001", "602", "603", "604", "605" ]
[ "nonn", "base", "look" ]
6
10
1
null
null
Robert Israel, Mar 20 2025
2025-03-21T11:24:03
oeisdata/seq/A382/A382277.seq
bc54f382714a72e10897b6a6bb3f8bf7
A382278
a(n) = least integer m >= 2 such that n is a sum of the form Sum_{k>=0} floor(h/m^k) for some integer h >= 1.
[ "2", "3", "2", "2", "3", "3", "2", "2", "3", "2", "2", "4", "3", "3", "2", "2", "3", "2", "2", "5", "3", "2", "2", "4", "2", "2", "3", "3", "4", "3", "2", "2", "4", "2", "2", "3", "4", "2", "2", "3", "2", "2", "4", "3", "3", "2", "2", "3", "2", "2", "5", "4", "2", "2", "3", "2", "2", "3", "3", "4", "3", "3", "2", "2", "4", "2", "2", "3", "4", "2", "2", "3", "2", "2", "3", "3", "5", "2", "2", "3", "2", "2", "5", "3", "2", "2" ]
[ "nonn" ]
15
1
1
[ "A005187", "A381897", "A382278", "A382324" ]
null
Clark Kimberling, Mar 21 2025
2025-03-31T21:21:04
oeisdata/seq/A382/A382278.seq
25d1c1760ef3ceb85b7e0e80e19961ac
A382279
a(n) is the integer whose bits encode subset sums of the first n arithmetic numbers (A003601).
[ "1", "3", "27", "891", "57339", "7340027", "15032385531", "123145302310907", "2017612633061982203", "66113130760175032991739", "8665580274997661924293869563", "4543259751217974174964184288067579", "4763953136893138488487244504044754960379", "9990733848941719167408001786146465954679226363" ]
[ "nonn", "base" ]
27
0
2
[ "A003601", "A368491", "A382279" ]
null
Yigit Oktar, Mar 20 2025
2025-04-03T11:40:05
oeisdata/seq/A382/A382279.seq
7f8344f091fc9d63b412fbfc14a2e930
A382280
Area of the Pythagoras Tree.
[ "1", "4", "6", "1", "3", "3", "6", "9", "4", "7", "8", "7", "0", "6", "7", "0", "3", "4", "8", "6", "8", "6", "5", "6", "9", "5", "1", "4", "0", "4", "5", "4", "2", "2", "5", "5", "7", "0", "6", "1", "5", "9", "3", "8", "4", "3", "6", "6", "9", "7", "0", "0", "1", "0", "3", "9", "2", "7", "1", "7", "0", "6", "8", "7", "4", "6", "2", "9", "5", "9", "3", "2", "6", "5", "2", "3", "4", "7", "7", "1", "1", "7", "4", "8", "4", "4", "5" ]
[ "nonn", "cons", "easy" ]
7
2
2
[ "A276647", "A276677", "A382280" ]
null
Charles R Greathouse IV, Mar 20 2025
2025-03-25T19:53:07
oeisdata/seq/A382/A382280.seq
9882b8d36254f62ea985fa1d4a62c2a7
A382281
Let n encode the edges of a graph by taking edges (u,v), with u < v, in colexicographic order ((0,1), (0,2), (1,2), (0,3), ...) and adding each edge to the graph if the corresponding binary digit of n (starting with the least significant digit) is 1. a(n) is the smallest nonnegative integer that encodes the same unlabeled graph as n (disregarding any isolated vertices), i.e., the code of the graph as defined in A076184.
[ "0", "1", "1", "3", "1", "3", "3", "7", "1", "3", "3", "11", "12", "13", "13", "15", "1", "3", "12", "13", "3", "11", "13", "15", "3", "7", "13", "15", "13", "15", "30", "31", "1", "12", "3", "13", "3", "13", "11", "15", "3", "13", "7", "15", "13", "30", "15", "31", "3", "13", "13", "30", "7", "15", "15", "31", "11", "15", "15", "31", "15", "31", "31", "63", "1", "3", "3", "11", "12", "13", "13", "15" ]
[ "nonn" ]
5
0
4
[ "A076184", "A382281" ]
null
Pontus von Brömssen, Mar 21 2025
2025-03-21T09:55:45
oeisdata/seq/A382/A382281.seq
2f3c3fb5a4eeaf9c009d545664c7cc6e
A382282
Code for the n-dimensional hypercube graph, encoded as in A076184.
[ "0", "1", "30", "15054720", "608598583690983931143264520896512" ]
[ "nonn", "more" ]
5
0
3
[ "A076184", "A382282" ]
null
Pontus von Brömssen, Mar 21 2025
2025-03-21T09:56:45
oeisdata/seq/A382/A382282.seq
3affb17b720abafe57d1a3f9eaacf271
A382283
Number of square roots of connected square graphs in the order listed in A382194.
[ "1", "1", "2", "1", "5", "1", "2", "3", "15", "1", "1", "2", "3", "4", "1", "3", "3", "15", "1", "1", "17", "60", "1", "2", "1", "2", "1", "1", "1", "1", "4", "2", "3", "2", "4", "11", "10", "11", "2", "1", "5", "3", "3", "6", "9", "8", "6", "1", "1", "19", "51", "3", "21", "1", "1", "3", "21", "2", "3", "113", "1", "11", "127", "374", "1", "1", "2", "3", "4", "1", "1", "2", "3", "4", "1", "1", "2", "1", "1", "1", "2" ]
[ "nonn", "tabf" ]
6
1
3
[ "A076184", "A241706", "A382180", "A382194", "A382283" ]
null
Pontus von Brömssen, Mar 22 2025
2025-03-22T18:50:37
oeisdata/seq/A382/A382283.seq
b2f1ad8c64fea9777334325f8c770c06
A382284
Number of unlabeled connected graphs with n vertices which are planar squares.
[ "1", "1", "1", "1", "2", "3", "7", "13", "31", "60", "146", "320", "787", "1864", "4654", "11526", "29318", "74632", "192868", "500487", "1310826" ]
[ "nonn", "more", "hard" ]
8
0
5
[ "A381961", "A382180", "A382284" ]
null
Brendan McKay and Sean A. Irvine, Mar 20 2025
2025-03-21T15:28:28
oeisdata/seq/A382/A382284.seq
031e2f2c473b2abc81e58675aa316283
A382285
Initial members of prime octuplets (p, p+4, p+12, p+24, p+28, p+40, p+48, p+52), where all primes are consecutive primes.
[ "241639", "44533249", "120833809", "245843149", "480454939", "547838359", "945331939", "1272712579", "1318911019", "1334157859", "1413122899", "1801178629", "1977960949", "2708995099", "3073533559", "3234255499", "3359304829", "3485412349", "3836960419", "4202567899", "4311168259", "4984840999", "5044981129" ]
[ "nonn" ]
17
1
1
[ "A022012", "A382285" ]
null
Federico Salas, Mar 20 2025
2025-03-28T15:59:28
oeisdata/seq/A382/A382285.seq
121a8f32b08808fa2b23cd16b3b2cc54
A382286
a(n) is the least k such that floor(sqrt(n*k/d(n*k))) = floor(sqrt(d(n*k))), where d(k) is the largest divisor of k which is <= sqrt(k).
[ "1", "1", "1", "1", "4", "1", "4", "2", "1", "2", "9", "2", "9", "2", "2", "1", "16", "2", "16", "1", "2", "5", "16", "1", "1", "5", "3", "1", "25", "1", "25", "1", "3", "8", "1", "1", "36", "8", "3", "1", "36", "1", "36", "3", "2", "8", "36", "1", "1", "2", "6", "3", "49", "2", "2", "1", "6", "13", "49", "2", "49", "13", "2", "1", "2", "2", "64", "4", "6", "2", "64", "2", "64", "18", "2", "4", "2", "2", "64", "4", "1", "18", "81", "2", "4", "18", "9", "4", "81" ]
[ "nonn", "new" ]
46
1
5
[ "A000196", "A033676", "A033677", "A048760", "A382286" ]
null
Hassan Baloui, Mar 20 2025
2025-04-14T18:15:25
oeisdata/seq/A382/A382286.seq
2840fee1a3eeaedf9cf4fbb9f53d48f7
A382287
Irregular triangle T(n,k), n >= 0, 0 <= k <= 2*n+1, read by rows, where T(n,k) = [x^k] (1-x)^(n+1) * Sum_{k=0..n} (k+1)^n * x^k.
[ "1", "-1", "1", "0", "-3", "2", "1", "1", "0", "-16", "23", "-9", "1", "4", "1", "0", "-125", "284", "-229", "64", "1", "11", "11", "1", "0", "-1296", "4079", "-5051", "2869", "-625", "1", "26", "66", "26", "1", "0", "-16807", "68074", "-114546", "98914", "-43531", "7776", "1", "57", "302", "302", "57", "1", "0", "-262144", "1303567", "-2784937", "3243218", "-2159662", "776887", "-117649" ]
[ "sign", "tabf", "easy" ]
16
0
5
[ "A000004", "A173018", "A382287", "A382289" ]
null
Seiichi Manyama, Mar 20 2025
2025-03-21T11:16:52
oeisdata/seq/A382/A382287.seq
193b65c44bcd406f2aec8a9ee7727333
A382288
Number of records in the n-th composition in standard order.
[ "0", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "2", "2", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "2", "2", "2", "2", "2", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "2", "1", "1", "1", "2", "2", "2", "2", "3", "2", "2", "2", "2", "2", "2", "2", "2", "2", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "1", "1" ]
[ "nonn", "easy" ]
8
0
7
[ "A066099", "A124762", "A124767", "A124768", "A164894", "A333381", "A333382", "A382288", "A382312" ]
null
John Tyler Rascoe, Mar 20 2025
2025-03-22T08:44:40
oeisdata/seq/A382/A382288.seq
9e202e3d8b6a91ccef72c7c1f671a07e
A382289
Irregular triangle T(n,k), n >= 0, 0 <= k <= 2*n+1, read by rows, where T(n,k) = [x^k] (1-x)^(n+1) * Sum_{k=0..n} (2*k+1)^n * x^k.
[ "1", "-1", "1", "1", "-5", "3", "1", "6", "1", "-49", "66", "-25", "1", "23", "23", "1", "-729", "1585", "-1247", "343", "1", "76", "230", "76", "1", "-14641", "44644", "-54230", "30404", "-6561", "1", "237", "1682", "1682", "237", "1", "-371293", "1468383", "-2433002", "2078278", "-907257", "161051", "1", "722", "10543", "23548", "10543", "722", "1", "-11390625", "55596806", "-117286023", "135337972", "-89493503", "32016102", "-4826809" ]
[ "sign", "tabf", "easy" ]
12
0
5
[ "A000004", "A060187", "A382287", "A382289" ]
null
Seiichi Manyama, Mar 21 2025
2025-03-21T11:17:00
oeisdata/seq/A382/A382289.seq
6e47237f845834bb3c0b9933a9d181fb
A382290
a(n) = A064547(n) - A001221(n).
[ "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0" ]
[ "nonn", "easy", "base" ]
11
1
null
[ "A000120", "A001221", "A034444", "A037445", "A046660", "A048881", "A064547", "A138302", "A295662", "A367512", "A382290", "A382291", "A382292", "A382293", "A382294" ]
null
Amiram Eldar, Mar 21 2025
2025-03-21T10:03:58
oeisdata/seq/A382/A382290.seq
f0c66bd10694208744889f17a8eccc43
A382291
a(n) = A037445(n)/A034444(n).
[ "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1" ]
[ "nonn", "easy", "mult" ]
11
1
8
[ "A000120", "A034444", "A037445", "A138302", "A243036", "A359411", "A367516", "A368168", "A368979", "A382290", "A382291", "A382292" ]
null
Amiram Eldar, Mar 21 2025
2025-03-21T10:04:12
oeisdata/seq/A382/A382291.seq
77af427c320dfb8b4d7f2e692577ae86
A382292
Numbers k such that A382290(k) = 1.
[ "8", "24", "27", "32", "40", "54", "56", "64", "72", "88", "96", "104", "108", "120", "125", "135", "136", "152", "160", "168", "184", "189", "192", "200", "224", "232", "243", "248", "250", "264", "270", "280", "288", "296", "297", "312", "320", "328", "343", "344", "351", "352", "360", "375", "376", "378", "392", "408", "416", "424", "432", "440", "448", "456", "459", "472", "480", "486", "488", "500" ]
[ "nonn", "easy" ]
10
1
1
[ "A018900", "A030078", "A030516", "A030629", "A030631", "A046660", "A048109", "A050997", "A060687", "A065036", "A143610", "A163569", "A178740", "A179646", "A179665", "A179666", "A179692", "A179702", "A189975", "A189987", "A189990", "A190115", "A190464", "A271727", "A374590", "A375432", "A381315", "A382290", "A382291", "A382292" ]
null
Amiram Eldar, Mar 21 2025
2025-03-21T10:04:21
oeisdata/seq/A382/A382292.seq
d26aaa31ac1708dd6ed0979188189213
A382293
a(n) is the least number k such that A382290(k) = n.
[ "1", "8", "128", "3456", "279936", "34992000", "8957952000", "3072577536000", "1920360960000000", "2556000437760000000", "5615532961758720000000", "13482894641182686720000000", "66241461372130539855360000000", "434610228062548471991016960000000", "2980991554281019969386385328640000000" ]
[ "nonn" ]
7
0
2
[ "A025487", "A037992", "A050376", "A382290", "A382291", "A382293" ]
null
Amiram Eldar, Mar 21 2025
2025-03-21T10:04:33
oeisdata/seq/A382/A382293.seq
f86009c8fb0c7c8d14302130c9af74aa
A382294
Decimal expansion of the asymptotic mean of the excess of the number of Fermi-Dirac factors of k over the number of distinct prime factors of k when k runs over the positive integers.
[ "1", "3", "6", "0", "5", "4", "4", "7", "0", "4", "9", "6", "2", "2", "8", "3", "6", "5", "2", "2", "9", "9", "8", "9", "2", "6", "3", "8", "3", "7", "6", "8", "9", "9", "7", "6", "1", "6", "5", "8", "2", "4", "6", "9", "0", "8", "3", "7", "8", "3", "9", "7", "1", "0", "3", "6", "8", "9", "3", "4", "2", "7", "8", "7", "1", "5", "6", "1", "4", "9", "7", "6", "6", "7", "4", "9", "7", "7", "1", "7", "9", "1", "4", "6", "0", "6", "5", "2", "2", "8", "2", "9", "7", "5", "0", "8", "5", "4", "1", "4", "8", "7", "3", "5", "9" ]
[ "nonn", "cons" ]
7
0
2
[ "A001221", "A046660", "A064547", "A088705", "A136141", "A382290", "A382294" ]
null
Amiram Eldar, Mar 21 2025
2025-03-21T10:04:41
oeisdata/seq/A382/A382294.seq
36362a697e03ea4a0c95b316c9b944f3
A382295
Decimal expansion of the asymptotic mean of the number of ways to factor k into "Fermi-Dirac primes" when k runs over the positive integers.
[ "1", "7", "8", "7", "6", "3", "6", "8", "0", "0", "1", "6", "9", "4", "4", "5", "6", "6", "6", "9", "8", "8", "6", "3", "2", "9", "3", "9", "4", "8", "9", "4", "5", "9", "8", "8", "1", "4", "6", "5", "9", "0", "0", "4", "6", "1", "3", "7", "0", "0", "2", "2", "6", "4", "1", "1", "6", "7", "3", "2", "9", "5", "4", "5", "6", "6", "6", "3", "7", "5", "1", "3", "9", "5", "4", "3", "4", "0", "2", "5", "1", "5", "5", "1", "5", "5", "0", "8", "8", "3", "3", "3", "5", "8", "7", "1", "3", "7", "5", "6", "1", "5", "6", "0", "4" ]
[ "nonn", "cons" ]
5
1
2
[ "A005117", "A050377", "A082293", "A330687", "A382295" ]
null
Amiram Eldar, Mar 21 2025
2025-03-21T10:04:52
oeisdata/seq/A382/A382295.seq
bcb0484065de50536c1897cc3bcda6f2
A382296
Number of states in smallest DFAO computing t(i+n) on input n in base 2, msd-first, where t(n) = A010060(n), the Thue-Morse sequence.
[ "2", "4", "6", "10", "10", "16", "18", "20", "16", "26", "28", "34", "32", "38", "34", "36", "26", "42", "44", "50", "48", "62", "60", "66", "58", "70", "66", "68", "60", "70", "62", "62", "42", "68", "70", "76", "74", "88", "86", "94", "84", "110", "108", "114", "106", "124", "120", "124", "106", "128", "124", "126", "116", "124", "120", "128", "110", "130", "122", "128", "112" ]
[ "nonn" ]
7
0
1
[ "A000045", "A010060", "A382296", "A382298" ]
null
Jeffrey Shallit, Mar 21 2025
2025-03-21T10:03:21
oeisdata/seq/A382/A382296.seq
9b79ab412289116d83c450d8055e4195
A382297
Indices of right triangles in A381337.
[ "1", "2", "3", "4", "6", "7", "12", "14", "17", "23", "28", "31", "34", "35", "49", "51", "62", "69", "71", "73", "77", "85", "93", "97", "98", "102", "119", "127", "142", "161", "170", "194", "196", "199", "223", "233", "238", "241", "245", "279", "281", "287", "291", "337", "357", "381", "388", "391", "398", "439", "446", "449", "476", "482", "483", "511", "521", "527", "562" ]
[ "nonn" ]
7
1
2
[ "A381336", "A381337", "A382297" ]
null
Felix Huber, Mar 26 2025
2025-03-29T18:37:44
oeisdata/seq/A382/A382297.seq
c24cf0e149a61ca1c47684b6370de8d8
A382298
Number of states in smallest DFAO computing t(i+n) on input n in base 2, lsd-first, where t(n) = A010060(n), the Thue-Morse sequence.
[ "2", "3", "5", "6", "7", "8", "9", "9", "9", "10", "11", "11", "11", "12", "13", "12", "11", "13", "15", "14", "13", "14", "15", "14", "13", "15", "17", "16", "15", "16", "17", "15", "13", "16", "19", "18", "17", "18", "19", "17", "15", "17", "19", "18", "17", "18", "19", "17", "15", "18", "21", "20", "19", "20", "21", "19", "17", "19", "21", "20", "19", "20", "21", "18", "15", "19", "23" ]
[ "nonn" ]
4
0
1
[ "A010060", "A382296", "A382298" ]
null
Jeffrey Shallit, Mar 21 2025
2025-03-21T10:03:29
oeisdata/seq/A382/A382298.seq
e395d7391d1d9fbba81ea47c71d5df4b
A382299
Number of minimum connected dominating sets in the n-folded cube graph.
[ "2", "4", "16", "40", "1520" ]
[ "nonn", "more" ]
11
2
1
null
null
Eric W. Weisstein, Mar 29 2025
2025-03-29T09:15:30
oeisdata/seq/A382/A382299.seq
b9dda700f16adf575f0f9d41bf25611a
A382300
a(n) = Sum_{k=0..floor(n/2)} (k+1) * binomial(2*k,2*n-4*k).
[ "1", "0", "2", "2", "3", "18", "7", "60", "65", "144", "356", "410", "1272", "1722", "3743", "7202", "11482", "25566", "40421", "81610", "147169", "259810", "507267", "867792", "1659112", "2961860", "5362592", "9940420", "17583485", "32564548", "58228386", "105606458", "191831767", "343313042", "625086891", "1119760040", "2023087045" ]
[ "nonn", "easy" ]
18
0
3
[ "A034839", "A375218", "A376729", "A381421", "A382300", "A382494", "A382495", "A382496" ]
null
Seiichi Manyama, Mar 29 2025
2025-03-29T14:01:36
oeisdata/seq/A382/A382300.seq
b2d43ffb810fa2edda50fd7b95c0c3e4
A382301
Number of integer partitions of n having a unique multiset partition into constant blocks with distinct sums.
[ "1", "1", "2", "2", "3", "6", "8", "9", "14", "16", "25", "30", "41", "52", "69", "83", "105", "129", "164", "208", "263", "315", "388", "449", "573", "694" ]
[ "nonn", "more" ]
9
0
3
[ "A000009", "A000041", "A000688", "A000726", "A001055", "A004709", "A006171", "A045778", "A047966", "A050361", "A265947", "A279784", "A279786", "A293511", "A295935", "A300383", "A317141", "A326535", "A353864", "A355743", "A381453", "A381455", "A381633", "A381635", "A381636", "A381716", "A381717", "A381870", "A381990", "A381991", "A381992", "A381993", "A382079", "A382203", "A382301", "A382427", "A382460" ]
null
Gus Wiseman, Mar 26 2025
2025-03-28T22:54:32
oeisdata/seq/A382/A382301.seq
60d0534ccbb82cc94b39e7797004499d
A382302
Number of integer partitions of n with greatest part, greatest multiplicity, and number of distinct parts all equal.
[ "0", "1", "0", "0", "1", "1", "1", "0", "1", "0", "2", "2", "2", "4", "3", "3", "4", "4", "3", "6", "5", "8", "8", "13", "13", "16", "17", "21", "22", "25", "26", "32", "34", "37", "44", "47", "55", "62", "72", "78", "94", "103", "118", "132", "151", "163", "189", "205", "230", "251", "284", "307", "346", "377", "420", "462", "515", "562", "629", "690", "763" ]
[ "nonn" ]
14
0
11
[ "A000009", "A000041", "A001221", "A007814", "A008284", "A008289", "A047966", "A047993", "A051903", "A055932", "A061395", "A091602", "A106529", "A116598", "A116608", "A130091", "A212166", "A237984", "A239455", "A239964", "A240312", "A241131", "A351293", "A362608", "A363719", "A365676", "A381079", "A381438", "A381542", "A381543", "A381544", "A382302", "A382303" ]
null
Gus Wiseman, Mar 24 2025
2025-03-26T08:30:52
oeisdata/seq/A382/A382302.seq
df2cebc3a92642fb8f85012c37427dc2
A382303
Number of integer partitions of n with exactly as many ones as the next greatest multiplicity.
[ "0", "0", "0", "1", "1", "1", "3", "2", "4", "5", "8", "6", "15", "13", "19", "25", "33", "36", "54", "58", "80", "96", "122", "141", "188", "217", "274", "326", "408", "474", "600", "695", "859", "1012", "1233", "1440", "1763", "2050", "2475", "2899", "3476", "4045", "4850", "5630", "6695", "7797", "9216", "10689", "12628", "14611", "17162", "19875", "23253" ]
[ "nonn" ]
6
0
7
[ "A000009", "A000041", "A007814", "A008284", "A008289", "A047966", "A047993", "A051903", "A051904", "A091602", "A091605", "A106529", "A116598", "A116861", "A212166", "A237984", "A239455", "A239964", "A240312", "A241131", "A360013", "A360014", "A360015", "A362608", "A363724", "A381079", "A381437", "A381438", "A381439", "A381542", "A381543", "A381544", "A382302", "A382303" ]
null
Gus Wiseman, Mar 24 2025
2025-03-25T08:57:46
oeisdata/seq/A382/A382303.seq
4a7c4980b82f79fd4db4f24c2aee5ab1
A382304
MM-numbers of multiset partitions into sets with a common sum.
[ "1", "2", "3", "4", "5", "8", "9", "11", "13", "16", "17", "25", "27", "29", "31", "32", "41", "43", "47", "59", "64", "67", "73", "79", "81", "83", "101", "109", "113", "121", "125", "127", "128", "137", "139", "143", "149", "157", "163", "167", "169", "179", "181", "191", "199", "211", "233", "241", "243", "256", "257", "269", "271", "277", "283", "289", "293", "313", "317" ]
[ "nonn" ]
8
1
2
[ "A000720", "A003465", "A005117", "A035470", "A050320", "A050326", "A055396", "A056239", "A058891", "A061395", "A112798", "A279788", "A293511", "A302242", "A302478", "A302494", "A323818", "A326534", "A326535", "A381635", "A381636", "A381995", "A382080", "A382201", "A382215", "A382304", "A382429" ]
null
Gus Wiseman, Apr 01 2025
2025-04-03T14:57:57
oeisdata/seq/A382/A382304.seq
8fcfd4700a3bf6f4b9c3693defabfb54
A382306
a(n) is the number of values m that satisfy floor(sqrt(m))=n and A382286(m)=1.
[ "3", "2", "1", "3", "5", "4", "2", "1", "3", "5", "7", "6", "4", "2", "1", "3", "5", "7", "9", "8", "6", "4", "2", "1", "3", "5", "7", "9", "11", "10", "8", "6", "4", "2", "1", "3", "5", "7", "9", "11", "13", "12", "10", "8", "6", "4", "2", "1", "3", "5", "7", "9", "11", "13", "15", "14", "12", "10", "8", "6", "4", "2", "1", "3", "5", "7", "9", "11", "13", "15", "17", "16", "14", "12", "10", "8", "6", "4", "2", "1" ]
[ "nonn", "new" ]
32
1
1
[ "A033676", "A033677", "A382286", "A382306" ]
null
Hassan Baloui, Mar 21 2025
2025-04-14T18:15:30
oeisdata/seq/A382/A382306.seq
7fc7633842a9000f7f2abf09233e295a
A382307
Position of start of first run of alternating bit values in the base-2 representation of Pi, or -1 if no such run exists.
[ "1", "2", "2", "19", "19", "19", "19", "19", "1195", "1697", "1890", "1890", "1890", "1890", "15081", "63795", "206825", "206825", "206825", "470577", "470577", "557265", "557265", "557265", "557265", "557265", "447666572", "447666572", "699793337", "699793337", "2049646803", "2250772991" ]
[ "nonn", "base", "more" ]
25
1
2
[ "A004601", "A175945", "A178708", "A233836", "A378472", "A382307" ]
null
James S. DeArmon, Mar 21 2025
2025-04-07T10:37:35
oeisdata/seq/A382/A382307.seq
aae8268896368bc1d3234f2cdbb2d7cc
A382308
Sum of the legs of the unique primitive Pythagorean triple whose inradius is A000045(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
[ "1", "7", "7", "17", "31", "71", "161", "391", "967", "2449", "6271", "16199", "42049", "109511", "285767", "746641", "1952287", "5107207", "13364449", "34978247", "91557511", "239673617", "627429887", "1642561927", "4300168321", "11257801351", "29473006471", "77160847121", "202008934687", "528864985799", "1384584451361" ]
[ "nonn", "easy", "new" ]
34
0
2
[ "A000045", "A382308", "A382608", "A382609", "A382610" ]
null
Miguel-Ángel Pérez García-Ortega, Apr 13 2025
2025-04-19T16:56:58
oeisdata/seq/A382/A382308.seq
6b196cb32ad0a4960b06bbe220d66d2e
A382309
Number of permutations of [2n] with exactly n ascents and an even number of inversions.
[ "1", "1", "5", "147", "7819", "655315", "81255642", "13985577438", "3191399514435", "932692830330915", "339781108888268398", "150979116192562395562", "80377829037419610855326", "50509994170589416909171726", "36995186973806250851237265812", "31240798437883511927927569474140" ]
[ "nonn" ]
14
0
3
[ "A128612", "A180056", "A382309" ]
null
Alois P. Heinz, Mar 21 2025
2025-04-02T07:04:46
oeisdata/seq/A382/A382309.seq
bc6d41750d45fbe21fa40ba6e8ae014c
A382310
Array read by ascending antidiagonals: A(n,m) is the squared distance between the roots of the 2nd degree equations z^2 +- n*z + m = 0 on the complex plane.
[ "0", "1", "4", "4", "3", "8", "9", "0", "7", "12", "16", "5", "4", "11", "16", "25", "12", "1", "8", "15", "20", "36", "21", "8", "3", "12", "19", "24", "49", "32", "17", "4", "7", "16", "23", "28", "64", "45", "28", "13", "0", "11", "20", "27", "32", "81", "60", "41", "24", "9", "4", "15", "24", "31", "36", "100", "77", "56", "37", "20", "5", "8", "19", "28", "35", "40", "121", "96", "73", "52", "33", "16", "1", "12", "23", "32", "39", "44" ]
[ "nonn", "easy", "tabl" ]
16
0
3
[ "A000290", "A008586", "A028347", "A028566", "A028884", "A131098", "A134594", "A145917", "A382310", "A382311" ]
null
Stefano Spezia, Mar 21 2025
2025-03-22T19:22:03
oeisdata/seq/A382/A382310.seq
98366ee1d5c8b8d92c6e19987d1bb9e2
A382311
Antidiagonal sums of A382310.
[ "0", "5", "15", "28", "52", "81", "123", "176", "240", "325", "425", "542", "684", "849", "1037", "1250", "1498", "1775", "2083", "2424", "2806", "3227", "3687", "4188", "4732", "5329", "5973", "6666", "7410", "8207", "9065", "9982", "10958", "11995", "13095", "14260", "15500", "16809", "18189", "19642", "21170", "22775", "24465", "26238", "28094", "30035" ]
[ "nonn" ]
5
0
2
[ "A382310", "A382311" ]
null
Stefano Spezia, Mar 21 2025
2025-03-22T08:43:44
oeisdata/seq/A382/A382311.seq
0af20249ac3ae8ddf8f924b9fd2b55f6
A382312
Irregular triangle read by rows: T(n,k) is the number of compositions of n with k records.
[ "1", "0", "1", "0", "2", "0", "3", "1", "0", "5", "3", "0", "8", "8", "0", "14", "17", "1", "0", "24", "36", "4", "0", "43", "72", "13", "0", "77", "143", "36", "0", "140", "281", "90", "1", "0", "256", "550", "213", "5", "0", "472", "1073", "484", "19", "0", "874", "2093", "1068", "61", "0", "1628", "4079", "2308", "177", "0", "3045", "7950", "4912", "476", "1", "0", "5719", "15498", "10328", "1217", "6" ]
[ "nonn", "tabf", "easy" ]
16
0
5
[ "A002024", "A011782", "A079500", "A336482", "A352525", "A382312" ]
null
John Tyler Rascoe, Mar 21 2025
2025-03-28T15:42:38
oeisdata/seq/A382/A382312.seq
332202699abf014408243e81dcdc3de1
A382313
The factorial base expansion of a(n) corresponds to the restricted growth sequence of that of n (when read from right to left).
[ "0", "1", "5", "3", "5", "5", "15", "11", "17", "9", "23", "11", "15", "23", "23", "15", "17", "17", "15", "23", "23", "15", "23", "23", "57", "41", "59", "39", "83", "47", "63", "35", "65", "33", "95", "35", "87", "47", "71", "39", "89", "41", "87", "47", "71", "39", "119", "47", "57", "89", "83", "87", "59", "71", "87", "83", "89", "57", "71", "59", "63", "95", "95", "63", "65", "65", "87" ]
[ "nonn", "base", "easy" ]
6
0
3
[ "A120696", "A382269", "A382313" ]
null
Rémy Sigrist, Mar 21 2025
2025-03-22T08:44:35
oeisdata/seq/A382/A382313.seq
5dd96a4967e58ac8751c93d64e981b3a
A382314
G.f. satisfies A(x) = 1/(1-x) + 2*x*A(x^2) + 3*x^2*A(x^3).
[ "1", "3", "4", "7", "1", "18", "1", "15", "13", "3", "1", "58", "1", "3", "4", "31", "1", "81", "1", "7", "4", "3", "1", "162", "1", "3", "40", "7", "1", "18", "1", "63", "4", "3", "1", "337", "1", "3", "4", "15", "1", "18", "1", "7", "13", "3", "1", "418", "1", "3", "4", "7", "1", "324", "1", "15", "4", "3", "1", "58", "1", "3", "13", "127", "1", "18", "1", "7", "4", "3", "1", "1161", "1", "3", "4", "7", "1", "18", "1", "31", "121", "3", "1", "58", "1", "3", "4", "15", "1", "81", "1", "7", "4", "3", "1", "1026" ]
[ "nonn", "new" ]
14
0
2
[ "A003586", "A007814", "A007949", "A072079", "A382126", "A382314" ]
null
Paul D. Hanna, Apr 14 2025
2025-04-15T18:46:03
oeisdata/seq/A382/A382314.seq
243f3ee0ea216380fe4e08f3bd03b3c8
A382315
G.f. satisfies A(x) = x + Sum_{n>=1} A(x^n)^2.
[ "1", "1", "2", "6", "16", "51", "158", "524", "1762", "6089", "21326", "75879", "272794", "990673", "3626536", "13371544", "49606460", "185046037", "693621174", "2611275523", "9869097706", "37431498607", "142426706634", "543524937780", "2079768883112", "7977836453011", "30672352831760", "118175566117561", "456206491221514", "1764370233131135" ]
[ "nonn", "new" ]
13
1
3
[ "A382315", "A382321" ]
null
Paul D. Hanna, Apr 17 2025
2025-04-26T04:26:15
oeisdata/seq/A382/A382315.seq
3d1eeaabba6ac9417bd5a80efc8ce9f2
A382318
G.f. satisfies A(x) = x + ( Sum_{n>=1} A(x^n) )^3.
[ "1", "0", "1", "3", "9", "25", "72", "213", "635", "1950", "6036", "19021", "60429", "194172", "628384", "2049225", "6722658", "22178631", "73523028", "244805574", "818317630", "2745167418", "9238878207", "31185404902", "105550046640", "358134472293", "1217955671785", "4150882760334", "14174481594375", "48492262770919", "166181651660136", "570415046251962" ]
[ "nonn", "changed" ]
12
1
4
[ "A008683", "A382318", "A382319", "A382320" ]
null
Paul D. Hanna, Apr 10 2025
2025-04-15T06:36:52
oeisdata/seq/A382/A382318.seq
9145220316a4795d95b13b8f44a61958
A382319
G.f. satisfies A(x) = x/(1-x) + Sum_{n>=1} A(x^n)^3.
[ "1", "1", "2", "4", "10", "27", "73", "217", "637", "1960", "6037", "19051", "60430", "194245", "628395", "2049442", "6722659", "22179293", "73523029", "244807537", "818317704", "2745173455", "9238878208", "31185424166", "105550046650", "358134532723", "1217955672422", "4150882954582", "14174481594376", "48492263401289", "166181651660137", "570415048301404" ]
[ "nonn" ]
7
1
3
[ "A382318", "A382319", "A382321" ]
null
Paul D. Hanna, Apr 10 2025
2025-04-11T01:28:06
oeisdata/seq/A382/A382319.seq
103b0f46adaef37434d76ecbf0aa8559
A382320
G.f. satisfies A(x) = x + ( Sum_{n>=1} A(x^n) )^2.
[ "1", "1", "4", "14", "52", "195", "774", "3140", "13118", "55861", "241988", "1062411", "4718380", "21156811", "95652842", "435553638", "1995707806", "9194770161", "42570402238", "197957907525", "924157498638", "4329762257151", "20351029400480", "95938011359954", "453492517932696", "2148971058064469", "10206782449568402", "48581518322215785" ]
[ "nonn" ]
6
1
3
[ "A008683", "A382320", "A382321" ]
null
Paul D. Hanna, Apr 09 2025
2025-04-09T22:55:43
oeisdata/seq/A382/A382320.seq
4a7ac3816da19b4f248b34c586db4889
A382321
G.f. satisfies A(x) = x/(1-x) + Sum_{n>=1} A(x^n)^2.
[ "1", "2", "5", "16", "53", "201", "775", "3156", "13123", "55915", "241989", "1062626", "4718381", "21157587", "95652899", "435556794", "1995707807", "9194783480", "42570402239", "197957963454", "924157499417", "4329762499141", "20351029400481", "95938012425720", "453492517932749", "2148971062782851", "10206782449581525", "48581518343373386" ]
[ "nonn", "changed" ]
18
1
2
[ "A382320", "A382321" ]
null
Paul D. Hanna, Apr 09 2025
2025-04-15T06:43:06
oeisdata/seq/A382/A382321.seq
e87c26201e744adb8296758fba5a089b
A382322
G.f. A(x) satisfies -2 = Sum_{n=-oo..+oo} (-1)^n * x^(2*n+1) * (1 + x^n)^(n+1) * A(x)^n.
[ "1", "2", "8", "50", "308", "2044", "14072", "100172", "730328", "5428498", "40978780", "313322910", "2421454020", "18884988540", "148443853936", "1174814738082", "9353539487160", "74865615299260", "602057472027484", "4862177553583604", "39416710563473400", "320650120976612168", "2616673301770051376", "21414973020645504142" ]
[ "nonn" ]
13
0
2
[ "A356783", "A380557", "A382322", "A382323" ]
null
Paul D. Hanna, Mar 21 2025
2025-03-22T18:50:12
oeisdata/seq/A382/A382322.seq
ee6e0b2bf15d79d87e8cf453a9563425
A382323
G.f. A(x) satisfies -3 = Sum_{n=-oo..+oo} (-1)^n * x^(2*n+1) * (1 + x^n)^(n+1) * A(x)^n.
[ "1", "3", "18", "150", "1323", "12486", "123069", "1253595", "13089576", "139367370", "1507353966", "16515098985", "182913374493", "2044565139303", "23035036108755", "261312501113193", "2982280058702499", "34217698991867058", "394470188685557271", "4566935001939261414", "53076293916648500439", "618991948535588040078" ]
[ "nonn" ]
13
0
2
[ "A356783", "A380557", "A382322", "A382323" ]
null
Paul D. Hanna, Mar 21 2025
2025-03-22T18:50:20
oeisdata/seq/A382/A382323.seq
d23835df86a31ddd71484e9907c23e57
A382324
a(n) = least integer h >= 1 such that n is a sum of the form Sum_{k>=0} floor(h/m^k) for some integer m >= 2.
[ "1", "2", "2", "3", "4", "5", "4", "5", "7", "6", "7", "10", "9", "10", "8", "9", "12", "10", "11", "17", "15", "12", "13", "19", "14", "15", "19", "20", "23", "21", "16", "17", "26", "18", "19", "26", "29", "20", "21", "27", "22", "23", "33", "30", "31", "24", "25", "33", "26", "27", "42", "40", "28", "29", "38", "30", "31", "40", "41", "47", "42", "43", "32", "33", "50", "34", "35", "47" ]
[ "nonn" ]
6
1
2
[ "A382278", "A382324" ]
null
Clark Kimberling, Apr 01 2025
2025-04-07T17:52:50
oeisdata/seq/A382/A382324.seq
5ca0e1e995b3758d8f5657430e20ff68
A382325
Numbers with a record ratio of proper factorizations to nontrivial divisors.
[ "4", "16", "32", "64", "128", "192", "256", "384", "512", "576", "768", "864", "1024", "1152", "1536", "1728", "2304", "3456", "4608", "5184", "5760", "6912", "8640", "9216", "10368", "11520", "13824", "17280", "20736", "23040", "25920", "27648", "34560", "41472", "51840", "62208", "69120", "82944", "103680", "138240", "165888", "172800" ]
[ "nonn" ]
14
1
1
[ "A002182", "A025487", "A028422", "A033833", "A070824", "A382325", "A382326", "A382327" ]
null
Charles L. Hohn, Mar 21 2025
2025-04-02T20:36:56
oeisdata/seq/A382/A382325.seq
68296716afad019fcab113d928bbb6ad
A382326
Numbers with a record ratio of nontrivial divisors to prime factors (counted with multiplicity).
[ "4", "6", "12", "24", "30", "60", "120", "180", "210", "360", "420", "840", "1260", "2310", "2520", "4620", "7560", "9240", "13860", "27720", "55440", "60060", "83160", "110880", "120120", "138600", "166320", "180180", "277200", "360360", "720720", "1081080", "1441440", "1801800", "2162160", "3063060", "3603600", "5405400", "6126120" ]
[ "nonn" ]
14
1
1
[ "A001222", "A002182", "A025487", "A070824", "A382325", "A382326", "A382327" ]
null
Charles L. Hohn, Mar 21 2025
2025-04-02T20:37:06
oeisdata/seq/A382/A382326.seq
e637d6c40ba0202cb88a1feee23aacb3
A382327
Numbers with a record ratio of proper factorizations to prime factors (counted with multiplicity).
[ "4", "8", "12", "24", "36", "48", "60", "72", "120", "144", "180", "240", "288", "360", "480", "576", "720", "1080", "1440", "2160", "2520", "2880", "3600", "4320", "5040", "7200", "7560", "8640", "10080", "14400", "15120", "20160", "25200", "30240", "40320", "50400", "60480", "80640", "90720", "100800", "120960", "151200", "181440", "201600" ]
[ "nonn" ]
16
1
1
[ "A001222", "A025487", "A028422", "A033833", "A382325", "A382326", "A382327" ]
null
Charles L. Hohn, Mar 21 2025
2025-04-02T20:36:51
oeisdata/seq/A382/A382327.seq
2f08d00136343d2a20635e1446a268e4
A382328
Maximum possible product of differences of every pair in a set of nonnegative integers with sum n.
[ "1", "1", "2", "3", "6", "12", "20", "48", "120", "240", "540", "1440", "4320", "11520", "30240", "64512", "207360", "725760", "2419200", "7257600", "17418240", "39191040", "174182400", "696729600", "2786918400", "9405849600", "25082265600", "65840947200", "182891520000", "1003290624000", "4514807808000", "21069103104000" ]
[ "nonn" ]
18
0
3
[ "A002620", "A382328" ]
null
Zhao Hui Du, Mar 21 2025
2025-04-05T18:32:58
oeisdata/seq/A382/A382328.seq
acb577c5ff562900c50b76e174d5d492
A382329
Least positive integer that gives a square of an integer when multiplied by the n-th harmonic number.
[ "1", "6", "66", "12", "8220", "20", "420", "213080", "17965080", "153720", "2320468920", "14109480", "412970037480", "422245703880", "430902992520", "6076390320", "516336630329520", "161488607280", "21362271268818480", "866533600973040", "97555876321904", "186715152624", "52866073370045936" ]
[ "nonn" ]
34
1
2
[ "A001008", "A002805", "A007913", "A382329" ]
null
Ali Sada, Mar 21 2025
2025-03-23T13:32:54
oeisdata/seq/A382/A382329.seq
e7a4fe9505ad4950924fdde38085e77f
A382330
a(n) is the number of positive integers k for which Sum_{i=1..j} (p_i+e_i) = n, where p_1^e_1*...*p_j^e_j is the prime factorization of k.
[ "0", "0", "1", "2", "2", "3", "4", "6", "8", "11", "15", "21", "27", "36", "47", "61", "79", "104", "133", "170", "215", "272", "343", "433", "542", "678", "845", "1050", "1300", "1608", "1981", "2437", "2988", "3655", "4460", "5433", "6603", "8014", "9705", "11731", "14155", "17055", "20509", "24624", "29512", "35313", "42184", "50315", "59916", "71248", "84598" ]
[ "nonn" ]
11
1
4
[ "A008474", "A219180", "A377505", "A377537", "A382330" ]
null
Felix Huber, Mar 23 2025
2025-03-29T18:38:18
oeisdata/seq/A382/A382330.seq
6d92da4718e8e4c8efdc2e1cffac6d27
A382331
If n = Product (p_j^k_j) then a(n) = -Sum ((-1)^k_j * p_j).
[ "0", "2", "3", "-2", "5", "5", "7", "2", "-3", "7", "11", "1", "13", "9", "8", "-2", "17", "-1", "19", "3", "10", "13", "23", "5", "-5", "15", "3", "5", "29", "10", "31", "2", "14", "19", "12", "-5", "37", "21", "16", "7", "41", "12", "43", "9", "2", "25", "47", "1", "-7", "-3", "20", "11", "53", "5", "16", "9", "22", "31", "59", "6", "61", "33", "4", "-2", "18", "16", "67", "15", "26", "14", "71", "-1", "73", "39", "-2" ]
[ "sign", "easy" ]
13
1
2
[ "A001414", "A008472", "A316523", "A332422", "A332423", "A332424", "A340901", "A366749", "A382331" ]
null
Ilya Gutkovskiy, Mar 22 2025
2025-03-29T18:55:10
oeisdata/seq/A382/A382331.seq
493ddb1a7980954dc50b1869fedd219e
A382332
Expansion of 1/(1 - 4*x/(1-x)^2)^(7/2).
[ "1", "14", "154", "1470", "12866", "106078", "837018", "6385262", "47420674", "344553902", "2458367898", "17272647966", "119770278978", "821068784382", "5572735854234", "37490757508302", "250247764120578", "1658681038111566", "10924592141535898", "71541334475749502", "466060971286552642" ]
[ "nonn" ]
21
0
2
[ "A020918", "A110170", "A377198", "A377200", "A382274", "A382332" ]
null
Seiichi Manyama, Mar 30 2025
2025-03-30T09:49:20
oeisdata/seq/A382/A382332.seq
afe2181e6a413b41591f133ec6fb1b18
A382333
Expansion of ( 1 + 4 * Sum_{k>=0} x^(2^k)/(1 - x^(2^k)) )^(1/2).
[ "1", "2", "2", "-2", "8", "-10", "6", "26", "-108", "258", "-342", "-194", "2700", "-8994", "17830", "-12878", "-61910", "322110", "-860106", "1284546", "571880", "-10749654", "38883554", "-82867578", "68869212", "286234558", "-1619591538", "4559780610", "-7250287740", "-2206074398", "59250601986", "-225063455922" ]
[ "sign", "easy" ]
8
0
2
[ "A001511", "A223142", "A382333", "A382334", "A382335" ]
null
Seiichi Manyama, Mar 22 2025
2025-03-22T08:41:26
oeisdata/seq/A382/A382333.seq
c5579440f2d09b308113ced682d9253e
A382334
Expansion of ( 1 + 9 * Sum_{k>=0} x^(2^k)/(1 - x^(2^k)) )^(1/3).
[ "1", "3", "-3", "12", "-45", "210", "-1038", "5331", "-28068", "150645", "-820713", "4526157", "-25217451", "141722985", "-802455807", "4573197111", "-26211368118", "150988107936", "-873651133218", "5075417681184", "-29591720994384", "173094835970280", "-1015510421231184", "5973910500301608", "-35229684687254898" ]
[ "sign", "easy" ]
9
0
2
[ "A001511", "A223143", "A382333", "A382334", "A382336" ]
null
Seiichi Manyama, Mar 22 2025
2025-03-22T08:41:30
oeisdata/seq/A382/A382334.seq
2f1815e86f33e5d7b6ddf9b8e606d4a8
A382335
Expansion of ( 1 + 4 * Sum_{k>=0} x^(2^k)/(1 - x^(2^k))^2 )^(1/2).
[ "1", "2", "4", "-2", "10", "-2", "-20", "82", "-108", "-114", "1052", "-2702", "2054", "11394", "-52636", "99534", "32938", "-831698", "2649676", "-3119694", "-8779530", "54334130", "-125649628", "31877726", "849214460", "-3274210670", "5129552132", "7097067566", "-65583106070", "180299051838", "-133300439300" ]
[ "sign", "easy" ]
8
0
2
[ "A129527", "A223142", "A382333", "A382335", "A382336" ]
null
Seiichi Manyama, Mar 22 2025
2025-03-22T08:41:49
oeisdata/seq/A382/A382335.seq
092966a733fa54eec82119b5d1a398dc
A382336
Expansion of ( 1 + 9 * Sum_{k>=0} x^(2^k)/(1 - x^(2^k))^2 )^(1/3).
[ "1", "3", "0", "0", "21", "-111", "504", "-2004", "7092", "-21150", "43614", "24288", "-949878", "7022118", "-38308320", "175670820", "-691787607", "2250673143", "-4994247456", "-2841846468", "120496073523", "-931900270923", "5282041372722", "-25033533979260", "101401747872534", "-337523450786736", "757180705527738" ]
[ "sign", "easy" ]
9
0
2
[ "A129527", "A223143", "A382334", "A382335", "A382336" ]
null
Seiichi Manyama, Mar 22 2025
2025-03-22T08:41:44
oeisdata/seq/A382/A382336.seq
f4a529989eae9ca417f4db7585c707f2
A382337
Palindromes in base 10 in which the difference between the sums of the digits in the even and odd positions is zero.
[ "0", "11", "22", "33", "44", "55", "66", "77", "88", "99", "121", "242", "363", "484", "1001", "1111", "1221", "1331", "1441", "1551", "1661", "1771", "1881", "1991", "2002", "2112", "2222", "2332", "2442", "2552", "2662", "2772", "2882", "2992", "3003", "3113", "3223", "3333", "3443", "3553", "3663", "3773", "3883", "3993", "4004", "4114", "4224", "4334", "4444", "4554", "4664", "4774", "4884", "4994" ]
[ "nonn", "easy", "base" ]
28
1
2
[ "A002113", "A135499", "A382337" ]
null
Alexander Yutkin, Mar 22 2025
2025-03-30T15:23:01
oeisdata/seq/A382/A382337.seq
d2f32f5ef49a1e508bb053604ef7caef
A382338
Positive integers k such that there are at least 3 positive integer solutions (x,y) to the equation x^3 + y^2 = k^2.
[ "105", "120", "210", "260", "405", "440", "504", "510", "561", "665", "840", "897", "960", "1155", "1173", "1485", "1610", "1680", "1947", "2001", "2052", "2080", "2145", "2233", "2415", "2457", "2465", "2628", "2835", "2850", "3045", "3135", "3240", "3300", "3315", "3395", "3520", "4004", "4032", "4080", "4095", "4290", "4488", "4600", "4760", "4950", "5145", "5265", "5320", "5580", "5670", "5795" ]
[ "nonn" ]
21
1
1
null
null
Robert Israel, Mar 23 2025
2025-04-06T14:54:14
oeisdata/seq/A382/A382338.seq
6866d222e1c7cbd97772cef1e9c8dffe
A382339
Triangle read by rows: T(n,k) is the number of partitions of a 2-colored set of n objects into exactly k parts with 0 <= k <= n.
[ "1", "0", "2", "0", "3", "3", "0", "4", "6", "4", "0", "5", "14", "9", "5", "0", "6", "22", "24", "12", "6", "0", "7", "37", "49", "34", "15", "7", "0", "8", "52", "92", "76", "44", "18", "8", "0", "9", "76", "157", "162", "103", "54", "21", "9", "0", "10", "100", "260", "302", "232", "130", "64", "24", "10", "0", "11", "135", "400", "554", "468", "302", "157", "74", "27", "11" ]
[ "nonn", "tabl", "changed" ]
20
0
3
[ "A005380", "A008284", "A381891", "A382339" ]
null
Peter Dolland, Mar 22 2025
2025-04-17T07:03:42
oeisdata/seq/A382/A382339.seq
3ef370466a135fa63ee7870993cf9c70
A382340
Triangle read by rows: T(n,k) is the number of partitions of a 3-colored set of n objects into exactly k parts with 0 <= k <= n.
[ "1", "0", "3", "0", "6", "6", "0", "10", "18", "10", "0", "15", "51", "36", "15", "0", "21", "105", "123", "60", "21", "0", "28", "208", "326", "226", "90", "28", "0", "36", "360", "771", "678", "360", "126", "36", "0", "45", "606", "1641", "1836", "1161", "525", "168", "45", "0", "55", "946", "3271", "4431", "3403", "1775", "721", "216", "55", "0", "66", "1446", "6096", "10026", "8982", "5472", "2520", "948", "270", "66" ]
[ "nonn", "tabl", "changed" ]
10
0
3
[ "A008284", "A217093", "A382045", "A382339", "A382340" ]
null
Peter Dolland, Mar 22 2025
2025-04-17T07:04:31
oeisdata/seq/A382/A382340.seq
36c61dabad1fcd170c015a9185d4868c
A382341
Triangle read by rows: T(n,k) is the number of partitions of a 4-colored set of n objects into exactly k parts with 0 <= k <= n.
[ "1", "0", "4", "0", "10", "10", "0", "20", "40", "20", "0", "35", "135", "100", "35", "0", "56", "340", "420", "200", "56", "0", "84", "784", "1370", "950", "350", "84", "0", "120", "1596", "3900", "3580", "1800", "560", "120", "0", "165", "3070", "9905", "11835", "7425", "3045", "840", "165", "0", "220", "5500", "23180", "34780", "27020", "13360", "4760", "1200", "220" ]
[ "nonn", "tabl", "changed" ]
12
0
3
[ "A008284", "A255050", "A382241", "A382339", "A382340", "A382341" ]
null
Peter Dolland, Mar 22 2025
2025-04-17T07:04:54
oeisdata/seq/A382/A382341.seq
f479866df69866817053f80082faefee
A382342
Triangle read by rows: T(n, k) is the number of partitions of n into k parts where 0 <= k <= n, and each part is one of two kinds.
[ "1", "0", "2", "0", "2", "3", "0", "2", "4", "4", "0", "2", "7", "6", "5", "0", "2", "8", "12", "8", "6", "0", "2", "11", "18", "17", "10", "7", "0", "2", "12", "26", "28", "22", "12", "8", "0", "2", "15", "34", "46", "38", "27", "14", "9", "0", "2", "16", "46", "64", "66", "48", "32", "16", "10", "0", "2", "19", "56", "94", "100", "86", "58", "37", "18", "11", "0", "2", "20", "70", "124", "152", "136", "106", "68", "42", "20", "12" ]
[ "nonn", "tabl", "changed" ]
22
0
3
[ "A000712", "A008284", "A022597", "A381895", "A382342", "A382345" ]
null
Peter Dolland, Mar 27 2025
2025-04-19T03:53:53
oeisdata/seq/A382/A382342.seq
1198ee320f85fc1b6ad1332438049803
A382343
Triangle read by rows: T(n, k) is the number of partitions of n into k parts where 0 <= k <= n, and each part is one of 3 kinds.
[ "1", "0", "3", "0", "3", "6", "0", "3", "9", "10", "0", "3", "15", "18", "15", "0", "3", "18", "36", "30", "21", "0", "3", "24", "55", "66", "45", "28", "0", "3", "27", "81", "114", "105", "63", "36", "0", "3", "33", "108", "189", "195", "153", "84", "45", "0", "3", "36", "145", "276", "348", "298", "210", "108", "55", "0", "3", "42", "180", "405", "552", "558", "423", "276", "135", "66" ]
[ "nonn", "tabl" ]
12
0
3
[ "A000217", "A000716", "A008284", "A022598", "A382025", "A382342", "A382343" ]
null
Peter Dolland, Mar 27 2025
2025-03-28T08:00:03
oeisdata/seq/A382/A382343.seq
1e3cd3f1d98b2f54c1ed504f984bd0ab
A382344
Triangle read by rows: T(n, k) is the number of partitions of n into k parts where 0 <= k <= n, and each part is one of 4 kinds.
[ "1", "0", "4", "0", "4", "10", "0", "4", "16", "20", "0", "4", "26", "40", "35", "0", "4", "32", "80", "80", "56", "0", "4", "42", "124", "180", "140", "84", "0", "4", "48", "184", "320", "340", "224", "120", "0", "4", "58", "248", "535", "660", "574", "336", "165", "0", "4", "64", "332", "800", "1200", "1184", "896", "480", "220", "0", "4", "74", "416", "1176", "1956", "2284", "1932", "1320", "660", "286" ]
[ "nonn", "tabl" ]
8
0
3
[ "A000292", "A008284", "A022599", "A023003", "A382041", "A382342", "A382343", "A382344" ]
null
Peter Dolland, Mar 28 2025
2025-03-29T04:21:10
oeisdata/seq/A382/A382344.seq
0b3ac3a1755af58d758b94eb93491e21
A382345
Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where n unlabeled objects are distributed into k containers of two kinds. Containers may be left empty.
[ "1", "2", "0", "3", "2", "0", "4", "4", "2", "0", "5", "6", "7", "2", "0", "6", "8", "12", "8", "2", "0", "7", "10", "17", "18", "11", "2", "0", "8", "12", "22", "28", "26", "12", "2", "0", "9", "14", "27", "38", "46", "34", "15", "2", "0", "10", "16", "32", "48", "66", "64", "46", "16", "2", "0", "11", "18", "37", "58", "86", "100", "94", "56", "19", "2", "0", "12", "20", "42", "68", "106", "136", "152", "124", "70", "20", "2", "0" ]
[ "nonn", "tabl" ]
33
0
2
[ "A000712", "A073252", "A381895", "A382342", "A382345" ]
null
Peter Dolland, Mar 29 2025
2025-04-07T09:26:11
oeisdata/seq/A382/A382345.seq
fbd4bcda01bb4db634dd08f9fc06f07c
A382351
Numbers with an integer harmonic mean of the indices of distinct prime factors.
[ "2", "3", "4", "5", "7", "8", "9", "11", "13", "16", "17", "19", "23", "25", "27", "29", "31", "32", "37", "39", "41", "43", "47", "49", "53", "59", "61", "64", "65", "67", "71", "73", "79", "81", "83", "89", "97", "101", "103", "107", "109", "113", "117", "121", "125", "127", "128", "130", "131", "137", "139", "149", "151", "157", "163", "167", "169", "173", "179", "181", "191", "193", "195", "197", "199", "211" ]
[ "nonn" ]
6
1
1
[ "A067340", "A078174", "A326621", "A382351" ]
null
Ilya Gutkovskiy, Mar 22 2025
2025-03-29T18:55:21
oeisdata/seq/A382/A382351.seq
76b1d97ab34f7468ac5ff05652371b70
A382352
Numbers k such that the sum of the reciprocals of the indices of distinct prime factors of k is an integer.
[ "1", "2", "4", "8", "16", "32", "64", "128", "195", "256", "390", "512", "585", "780", "975", "1024", "1170", "1560", "1755", "1950", "2048", "2340", "2535", "2925", "3120", "3510", "3900", "4096", "4680", "4875", "5070", "5265", "5850", "6240", "7020", "7605", "7800", "8192", "8775", "9360", "9750", "10101", "10140", "10530", "11700", "12480", "12675", "14040", "14625" ]
[ "nonn" ]
9
1
2
[ "A072873", "A316856", "A382352" ]
null
Ilya Gutkovskiy, Mar 22 2025
2025-03-29T18:56:54
oeisdata/seq/A382/A382352.seq
1bbecb7696df201a3567ef3d650b7fa1
A382353
Numbers k > 0 such that A006218(k) / A018804(k) is an integer.
[ "1", "2", "3", "4", "8", "10", "15", "43", "63", "6934", "316563", "2428132", "56264126" ]
[ "nonn", "more" ]
13
1
2
[ "A006218", "A018804", "A382353" ]
null
Ctibor O. Zizka, Mar 22 2025
2025-03-23T08:39:47
oeisdata/seq/A382/A382353.seq
02cee63178aec626b44889048650b8e2
A382354
Triangle T(n,k) read by rows, where row n is a permutation of the numbers 1 through n, such that if a deck of n cards is prepared in this order, and under-down-under dealing is used, then the resulting cards will be dealt in increasing order.
[ "1", "2", "1", "3", "1", "2", "2", "1", "3", "4", "4", "1", "5", "3", "2", "4", "1", "3", "5", "2", "6", "3", "1", "7", "5", "2", "4", "6", "5", "1", "7", "4", "2", "8", "6", "3", "7", "1", "4", "6", "2", "8", "5", "3", "9", "4", "1", "10", "8", "2", "5", "7", "3", "9", "6", "10", "1", "7", "5", "2", "11", "9", "3", "6", "8", "4", "9", "1", "5", "11", "2", "8", "6", "3", "12", "10", "4", "7", "5", "1", "8", "10", "2", "6", "12", "3", "9", "7", "4", "13", "11" ]
[ "nonn", "tabl" ]
10
1
2
[ "A006257", "A225381", "A321298", "A378635", "A382354", "A382355", "A382356", "A382358" ]
null
Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Mar 22 2025
2025-04-13T23:20:36
oeisdata/seq/A382/A382354.seq
14356108451fa34f0d50c5d086ab40f7
A382355
A version of the Josephus problem: a(n) is the surviving integer under the skip-eliminate-skip version of the elimination process.
[ "1", "1", "1", "4", "3", "6", "3", "6", "9", "3", "6", "9", "12", "1", "4", "7", "10", "13", "16", "19", "1", "4", "7", "10", "13", "16", "19", "22", "25", "28", "31", "3", "6", "9", "12", "15", "18", "21", "24", "27", "30", "33", "36", "39", "42", "45", "1", "4", "7", "10", "13", "16", "19", "22", "25", "28", "31", "34", "37", "40", "43", "46", "49", "52", "55", "58", "61", "64", "67", "70", "3", "6" ]
[ "nonn" ]
10
1
4
[ "A006257", "A225381", "A321298", "A378635", "A382354", "A382355", "A382356", "A382358" ]
null
Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Mar 22 2025
2025-04-05T23:25:37
oeisdata/seq/A382/A382355.seq
f17ed0a983a808644186fef5ab480ac2
A382356
Elimination order of the first person in a variation of the Josephus problem, where there are n people total. During each round the first person is skipped, the second is eliminated and the third person is skipped. Then the process repeats.
[ "1", "2", "3", "2", "4", "4", "3", "5", "7", "4", "10", "9", "5", "14", "9", "6", "10", "15", "7", "18", "21", "8", "19", "14", "9", "15", "24", "10", "21", "28", "11", "23", "19", "12", "20", "26", "13", "31", "28", "14", "36", "24", "15", "25", "43", "16", "47", "39", "17", "44", "29", "18", "30", "44", "19", "40", "50", "20", "42", "34", "21", "35", "45", "22", "57", "47", "23", "55", "39", "24" ]
[ "nonn" ]
9
1
2
[ "A006257", "A225381", "A321298", "A378635", "A382354", "A382355", "A382356", "A382358" ]
null
Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Mar 22 2025
2025-04-05T23:41:53
oeisdata/seq/A382/A382356.seq
361a803cf3cb131606ed0459a16ac6e2
A382357
Lexicographically earliest sequence of distinct positive integers such that the 2-adic valuations of adjacent terms differ exactly by one.
[ "1", "2", "3", "6", "4", "8", "12", "10", "5", "14", "7", "18", "9", "22", "11", "26", "13", "30", "15", "34", "17", "38", "19", "42", "20", "24", "16", "32", "48", "40", "28", "46", "21", "50", "23", "54", "25", "58", "27", "62", "29", "66", "31", "70", "33", "74", "35", "78", "36", "56", "44", "72", "52", "82", "37", "86", "39", "90", "41", "94", "43", "98", "45", "102", "47", "106", "49" ]
[ "nonn", "base" ]
11
1
2
[ "A003602", "A007814", "A073675", "A266089", "A382357", "A382360" ]
null
Rémy Sigrist, Mar 22 2025
2025-03-26T16:17:03
oeisdata/seq/A382/A382357.seq
a8a224cb8301445092c030ae3a7e39fd