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1999-12-11 03:00:00
2025-04-28 00:58:08
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A381115
Composite terms in A381019 in order of appearance.
[ "4", "9", "8", "6", "25", "12", "10", "49", "15", "16", "14", "27", "20", "21", "22", "18", "35", "24", "169", "28", "33", "26", "85", "32", "57", "77", "30", "34", "39", "55", "38", "51", "40", "91", "36", "121", "42", "65", "44", "45", "529", "48", "119", "46", "95", "81", "143", "50", "63", "52", "54", "115", "56", "841", "187", "69", "62", "125", "87", "64", "133", "75", "58", "221" ]
[ "nonn" ]
16
1
1
[ "A381019", "A381115", "A381116", "A381117" ]
null
N. J. A. Sloane, Feb 14 2025
2025-02-15T14:11:57
oeisdata/seq/A381/A381115.seq
28548a262b5ec6cf63b04464e9d81f40
A381116
Indices of composite terms in A381019.
[ "7", "13", "16", "23", "30", "36", "47", "55", "63", "64", "79", "91", "100", "113", "123", "142", "149", "167", "178", "196", "201", "223", "235", "256", "259", "279", "290", "325", "330", "346", "364", "382", "405", "422", "442", "468", "485", "488", "530", "534", "541", "583", "605", "630", "631", "665", "674", "682", "729", "735", "790", "798", "847", "854", "862" ]
[ "nonn" ]
15
1
1
[ "A381019", "A381115", "A381116", "A381117" ]
null
N. J. A. Sloane, Feb 14 2025
2025-02-15T13:58:39
oeisdata/seq/A381/A381116.seq
bd5c2dfe107b03f86b5eae0f954278ed
A381117
Lengths of runs of consecutive primes in A381019.
[ "5", "5", "2", "6", "6", "5", "10", "7", "7", "14", "11", "8", "12", "9", "18", "6", "17", "10", "17", "4", "21", "11", "20", "2", "19", "10", "34", "4", "15", "17", "17", "22", "16", "19", "25", "16", "2", "41", "3", "6", "41", "21", "24", "33", "8", "7", "46", "5", "54", "7", "48", "6", "7", "5", "41", "13", "31", "18", "5", "50", "1", "49", "10", "26", "41", "24", "45", "53", "20", "21", "44", "3" ]
[ "nonn" ]
10
1
1
[ "A381019", "A381115", "A381116", "A381117" ]
null
N. J. A. Sloane, Feb 14 2025
2025-02-14T10:19:53
oeisdata/seq/A381/A381117.seq
b4c46a2eddf9d7b8ca8d2bf0388fabbe
A381118
Index of 2^n in A381019.
[ "1", "2", "7", "16", "64", "256", "975", "3856", "16647", "65039", "260112", "1044504", "4177980", "16777224" ]
[ "nonn", "more" ]
14
0
2
[ "A381019", "A381115", "A381116", "A381118" ]
null
N. J. A. Sloane, Feb 14 2025
2025-02-16T05:40:43
oeisdata/seq/A381/A381118.seq
9300a943c45a64672e6fa7ed6fe3d1a7
A381119
Index of n in A381019.
[ "1", "2", "3", "7", "4", "23", "5", "16", "13", "47", "6", "36", "8", "79", "63", "64", "9", "142", "10", "100", "113", "123", "11", "167", "30", "223", "91", "196", "12", "290", "14", "256", "201", "325", "149", "442", "15", "364", "330", "405", "17", "485", "18", "530", "534", "630", "19", "583", "55", "682", "382", "735", "20", "790", "346", "847", "259", "1034", "21", "1095" ]
[ "nonn" ]
24
1
2
[ "A381019", "A381115", "A381116", "A381118", "A381119" ]
null
N. J. A. Sloane, Feb 14 2025
2025-02-24T02:07:02
oeisdata/seq/A381/A381119.seq
dfff77365a92293659bab5540007b92e
A381120
Numbers k such that both A381019(k) and A381019(k+1) are composite.
[ "63", "630", "2423", "5653", "9104", "26308", "36108", "41622", "64526", "85121", "108917", "143913", "148305", "176405", "316974", "399168", "399907", "406487", "536926", "621016", "830793", "937038", "937109", "970243", "1088629", "1480545", "1895503", "3961587", "4651102", "5171081", "5487450", "6219705", "7327856", "8118740" ]
[ "nonn" ]
21
1
1
[ "A379810", "A381019", "A381120" ]
null
N. J. A. Sloane, Feb 15 2025
2025-02-16T21:54:41
oeisdata/seq/A381/A381120.seq
51abc73bfd68ee6609133ba2fad12aba
A381121
Number of partially ordered sets ("posets") covering n unlabeled elements.
[ "1", "0", "1", "3", "11", "47", "255", "1727", "14954", "166232", "2384053", "44182143", "1058142319", "32718935706", "1304369332319", "66936884741385", "4414855587293931" ]
[ "nonn", "hard", "more" ]
10
0
4
[ "A000112", "A381121" ]
null
Peter Dolland, Feb 14 2025
2025-02-16T10:26:02
oeisdata/seq/A381/A381121.seq
391cc049ec484a8b9a963a9d42256d6f
A381122
Numbers k such that k^(k+1) == k (mod k+2).
[ "0", "1", "4", "8", "12", "20", "24", "28", "32", "36", "44", "56", "60", "72", "80", "84", "92", "104", "116", "120", "132", "140", "144", "156", "164", "168", "176", "180", "192", "200", "204", "212", "216", "224", "252", "260", "272", "276", "296", "300", "312", "324", "332", "344", "356", "360", "380", "384", "392", "396", "420", "444", "452", "456", "464", "476", "480", "500", "512", "524", "536", "540", "552", "560" ]
[ "nonn" ]
13
1
3
[ "A064935", "A115976", "A381122" ]
null
Robert Israel, Feb 14 2025
2025-02-15T12:28:19
oeisdata/seq/A381/A381122.seq
9c9c4b42c24aa800e97f6d8126af8a88
A381123
Number of unlabeled endofunctions on n points whose self-referencing elements are mapped from another element.
[ "1", "0", "2", "4", "12", "28", "83", "213", "608", "1664", "4703", "13173", "37412", "105995", "302301", "862794", "2470631", "7084425", "20357121", "58573788", "168789684", "486964114", "1406549550", "4066751083", "11769363663", "34090076148", "98820914068", "286672673725", "832183340955", "2417270306657", "7025657374736", "20430883575932", "59444386613999", "173039084438093" ]
[ "nonn" ]
18
0
3
[ "A001372", "A381123" ]
null
Peter Dolland, Feb 14 2025
2025-02-21T12:24:56
oeisdata/seq/A381/A381123.seq
e2d4bfd5d9b537d61e4d7226aa89b08a
A381124
Numerators of convergents to the supergolden ratio.
[ "1", "3", "19", "22", "85", "447", "1873", "41653", "43526", "85179", "384242", "469421", "1323084", "111608477", "112931561", "450403160", "563334721", "3830411486", "4393746207", "17011650107", "21405396314", "209660216933", "231065613247", "440725830180", "671791443427", "1112517273607", "21809619641960", "66541376199487" ]
[ "nonn", "frac", "easy" ]
12
0
2
[ "A092526", "A369346", "A381124", "A381125" ]
null
Eric W. Weisstein, Feb 14 2025
2025-02-14T23:11:34
oeisdata/seq/A381/A381124.seq
9296bc0ec66478428dd9cb493035e0a0
A381125
Denominators of the convergents to the supergolden ratio.
[ "1", "2", "13", "15", "58", "305", "1278", "28421", "29699", "58120", "262179", "320299", "902777", "76153567", "77056344", "307322599", "384378943", "2613596257", "2997975200", "11607521857", "14605497057", "143056995370", "157662492427", "300719487797", "458381980224", "759101468021", "14881309872623" ]
[ "nonn", "frac", "easy" ]
11
0
2
[ "A092526", "A369346", "A381124", "A381125" ]
null
Eric W. Weisstein, Feb 14 2025
2025-02-14T23:11:13
oeisdata/seq/A381/A381125.seq
10484718889320399c996f2f0ae7ec93
A381126
Primes that are the concatenation of prime(p) and p where p is a prime.
[ "53", "6719", "15737", "587107", "1297211", "1823281", "1913293", "3067439", "3593503", "3943547", "4397599", "5503727", "5651743", "6353827", "6361829", "6823877", "7109911", "7283929", "7523953", "85131061", "85271063", "87611093", "88071097", "104331277", "125031493", "128411531", "130031549", "133311583", "141071663" ]
[ "nonn", "base" ]
39
1
1
[ "A006450", "A084667", "A084669", "A229814", "A381126" ]
null
Maja Gwozdz, Feb 14 2025
2025-02-21T15:24:38
oeisdata/seq/A381/A381126.seq
4702af361801b51d5d55acfeefd6687c
A381127
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 Down-SpellUnder dealing is used, then the resulting cards will be dealt in increasing order.
[ "1", "1", "2", "1", "3", "2", "1", "2", "4", "3", "1", "3", "5", "4", "2", "1", "6", "4", "3", "2", "5", "1", "5", "3", "6", "2", "4", "7", "1", "3", "4", "5", "2", "7", "6", "8", "1", "6", "7", "9", "2", "8", "5", "4", "3", "1", "7", "6", "5", "2", "10", "4", "9", "3", "8", "1", "5", "10", "11", "2", "4", "7", "9", "3", "6", "8", "1", "7", "8", "4", "2", "12", "6", "9", "3", "11", "5", "10", "1", "11", "4", "6", "2", "12", "13", "8", "3", "5", "7", "9", "10", "1", "4", "9", "8", "2", "12", "7", "5", "3", "13", "14", "11", "10", "6" ]
[ "nonn", "word", "tabl" ]
9
1
3
[ "A005589", "A006257", "A225381", "A321298", "A378635", "A380201", "A380202", "A380204", "A380246", "A380247", "A380248", "A381114", "A381127", "A381128", "A381129" ]
null
Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Feb 14 2025
2025-03-02T22:55:22
oeisdata/seq/A381/A381127.seq
19449aa69e94d5d632b4d0bd9fc36388
A381128
The number of card moves required to deal n cards using Down-SpellUnder dealing.
[ "1", "5", "9", "15", "20", "25", "29", "35", "41", "46", "50", "57", "64", "73", "82", "90", "98", "108", "117", "126", "133", "143", "153", "165", "176", "187", "197", "209", "221", "232", "239", "249", "259", "271", "282", "293", "303", "315", "327", "338", "344", "353", "362", "373", "383", "393", "402", "413", "424", "434", "440", "449", "458", "469", "479", "489", "498", "509", "520", "530", "536", "545", "554", "565", "575", "585", "594", "605" ]
[ "nonn", "word" ]
9
1
2
[ "A005589", "A006257", "A225381", "A321298", "A378635", "A380201", "A380202", "A380204", "A380246", "A380247", "A380248", "A381114", "A381127", "A381128", "A381129" ]
null
Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Feb 14 2025
2025-03-14T21:13:25
oeisdata/seq/A381/A381128.seq
fd11eea9a5eb5a06584eead306d6985f
A381129
A version of the Josephus problem: a(n) is the surviving integer under the spelling version of the elimination process, called Down-SpellUnder.
[ "1", "2", "2", "3", "3", "2", "7", "8", "4", "6", "4", "6", "7", "11", "10", "3", "14", "4", "17", "11", "3", "16", "7", "16", "7", "22", "2", "8", "24", "27", "7", "21", "13", "28", "30", "8", "3", "37", "12", "7", "8", "33", "7", "33", "44", "11", "32", "8", "6", "43", "2", "18", "49", "8", "32", "54", "26", "43", "44", "30", "40", "52", "26", "44", "8", "27", "60", "16", "11", "61", "70", "14", "58", "55" ]
[ "nonn", "word" ]
8
1
2
[ "A005589", "A006257", "A225381", "A321298", "A378635", "A380201", "A380202", "A380204", "A380246", "A380247", "A380248", "A381114", "A381127", "A381128", "A381129" ]
null
Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Feb 14 2025
2025-02-23T11:29:25
oeisdata/seq/A381/A381129.seq
34fed23a9b0e63c05a78423018cc5ba7
A381130
a(n) is the smallest prime not yet in the sequence that contains a substring of size 2 from a(n-1); a(1)=11.
[ "11", "113", "13", "131", "31", "311", "211", "421", "521", "523", "23", "223", "227", "127", "271", "71", "571", "157", "151", "251", "257", "457", "557", "577", "277", "677", "67", "167", "163", "263", "269", "569", "563", "463", "461", "61", "613", "137", "37", "337", "233", "239", "139", "313", "317", "17", "173", "73", "373", "379", "79", "179", "479", "47" ]
[ "nonn", "base", "changed" ]
9
1
1
[ "A107801", "A262323", "A381130" ]
null
Enrique Navarrete, Feb 14 2025
2025-04-16T05:31:32
oeisdata/seq/A381/A381130.seq
f8e582fca70d4144499bd77cf90da130
A381131
If n = (p_1^e_1)*(p_2^e_2)*(p_3^e_3)*... and min(p_1^e_1,p_2^e_2,...) = p_k^e_k then a(n) = p_k, a(1) = 1.
[ "1", "2", "3", "2", "5", "2", "7", "2", "3", "2", "11", "3", "13", "2", "3", "2", "17", "2", "19", "2", "3", "2", "23", "3", "5", "2", "3", "2", "29", "2", "31", "2", "3", "2", "5", "2", "37", "2", "3", "5", "41", "2", "43", "2", "5", "2", "47", "3", "7", "2", "3", "2", "53", "2", "5", "7", "3", "2", "59", "3", "61", "2", "7", "2", "5", "2", "67", "2", "3", "2", "71", "2", "73", "2", "3", "2", "7", "2", "79", "5" ]
[ "nonn" ]
8
1
2
[ "A020639", "A034684", "A088387", "A381131", "A381132", "A381133" ]
null
Ilya Gutkovskiy, Feb 14 2025
2025-03-04T23:20:20
oeisdata/seq/A381/A381131.seq
ec8f31dbf83f077dd5a9b3dfff00b46e
A381132
If n = (p_1^e_1)*(p_2^e_2)*(p_3^e_3)*... and min(p_1^e_1,p_2^e_2,...) = p_k^e_k then a(n) = pi(p_k), a(1) = 0.
[ "0", "1", "2", "1", "3", "1", "4", "1", "2", "1", "5", "2", "6", "1", "2", "1", "7", "1", "8", "1", "2", "1", "9", "2", "3", "1", "2", "1", "10", "1", "11", "1", "2", "1", "3", "1", "12", "1", "2", "3", "13", "1", "14", "1", "3", "1", "15", "2", "4", "1", "2", "1", "16", "1", "3", "4", "2", "1", "17", "2", "18", "1", "4", "1", "3", "1", "19", "1", "2", "1", "20", "1", "21", "1", "2", "1", "4", "1", "22", "3" ]
[ "nonn" ]
7
1
3
[ "A000720", "A034684", "A055396", "A108230", "A381131", "A381132", "A381133" ]
null
Ilya Gutkovskiy, Feb 14 2025
2025-03-04T23:20:54
oeisdata/seq/A381/A381132.seq
b1d5de18c9d33c6e5d39bbc1db9bb208
A381133
If n = (p_1^e_1)*(p_2^e_2)*(p_3^e_3)*... and min(p_1^e_1,p_2^e_2,...) = p_k^e_k then a(n) = e_k, a(1) = 0.
[ "0", "1", "1", "2", "1", "1", "1", "3", "2", "1", "1", "1", "1", "1", "1", "4", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "3", "2", "1", "1", "1", "5", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "6", "1", "1", "1", "2", "1", "1", "1", "3", "1", "1", "1", "2", "1", "1", "1", "1", "4", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "2", "2" ]
[ "nonn" ]
8
1
4
[ "A034684", "A051904", "A088388", "A381131", "A381132", "A381133" ]
null
Ilya Gutkovskiy, Feb 14 2025
2025-03-04T23:21:10
oeisdata/seq/A381/A381133.seq
c817fe8f333a99579e513a9e1f41891c
A381134
a(n) = 4*(-3)^n + 3*(-2)^n + 3*2^n - (-3)^n*2^(n + 1) + 2*3^n*(2^n - 2).
[ "0", "24", "648", "96", "29160", "384", "1102248", "1536", "40153320", "6144", "1449771048", "24576", "52230021480", "98304", "1880625147048", "393216", "67705604657640", "1572864", "2437429661950248", "6291456", "87747718878685800", "25165824", "3158920139068980648", "100663296", "113721145341409929960" ]
[ "nonn", "easy" ]
11
1
2
null
null
Eric W. Weisstein, Feb 21 2025
2025-02-21T11:49:34
oeisdata/seq/A381/A381134.seq
a6370f13cbe9b22af66eca3d38ae067f
A381135
Numbers of the form d_1 d_2 d_3 ... where the sum of their digits multiplied by their digit positions is equal to their number of digits.
[ "1", "20", "110", "300", "1010", "2100", "4000", "10010", "12000", "20100", "31000", "50000", "100010", "111000", "200100", "220000", "301000", "410000", "600000", "1000010", "1020000", "1101000", "1300000", "2000100", "2110000", "3001000", "3200000", "4010000", "5100000", "7000000", "10000010", "10110000", "11001000", "12100000" ]
[ "nonn", "base" ]
23
1
2
[ "A055642", "A156207", "A381135" ]
null
Leo Crabbe, Feb 14 2025
2025-03-04T23:22:06
oeisdata/seq/A381/A381135.seq
8634ee383aa394659f2ccf6353d9cf82
A381136
a(n) is the number of divisors d of n such that tau(d^(1 + n) + n) = 2^omega(d^(1 + n) + n), where tau = A000005 and omega = A001221.
[ "1", "2", "0", "1", "2", "4", "0", "0", "1", "3", "0", "2", "2", "3", "0", "1", "0", "2", "0", "2", "4", "2", "0", "1", "1", "2", "0", "2", "2", "8", "0", "1", "4", "4", "0", "1", "2", "3", "0", "2", "2", "7", "0", "1", "2", "4", "0", "1", "0", "2", "0", "2", "0", "2", "0", "2", "4", "2", "0", "3", "2", "2", "0", "1", "4", "8", "0", "2", "3", "5", "0", "1", "2", "3", "0", "2", "4", "8", "0", "1", "1", "3", "0", "4", "4", "4", "0" ]
[ "nonn" ]
22
1
2
[ "A000005", "A001221", "A049533", "A381136", "A381138" ]
null
Juri-Stepan Gerasimov, Feb 15 2025
2025-03-09T17:03:36
oeisdata/seq/A381/A381136.seq
3d89967993307fc295ad036760e0c7d3
A381137
Lexicographically earliest sequence of distinct positive integers such that no 3 terms are in harmonic progression.
[ "1", "2", "3", "4", "5", "7", "8", "9", "10", "11", "12", "13", "14", "16", "17", "19", "21", "22", "23", "25", "26", "27", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "41", "43", "44", "46", "47", "48", "49", "50", "51", "52", "53", "55", "57", "58", "59", "60", "61", "62", "63", "64", "65", "67", "68", "69", "70", "71", "73", "74", "76", "79", "81", "82", "83", "85", "86" ]
[ "nonn" ]
24
1
2
[ "A000452", "A003278", "A005279", "A174905", "A381137" ]
null
Neal Gersh Tolunsky, Feb 15 2025
2025-03-12T04:14:49
oeisdata/seq/A381/A381137.seq
9069933b422e0f4527de3d79960c8b29
A381138
a(n) is the number of divisors d of n such that tau(n^(1 + d) + d) = 2^omega(n^(1 + d) + d), where tau = A000005 and omega = A001221.
[ "1", "2", "1", "2", "2", "4", "0", "2", "1", "4", "1", "4", "2", "3", "2", "2", "1", "3", "1", "4", "2", "2", "1", "3", "2", "4", "1", "4", "2", "8", "1", "1", "2", "3", "2", "4", "2", "2", "2", "4", "1", "8", "0", "4", "2", "4", "1", "3", "1", "4", "2", "3", "1", "4", "2", "4", "1", "4", "1", "7", "2", "4", "2", "2", "4", "8", "1", "1", "1", "5", "1", "3", "2", "4", "2", "4", "2", "8", "1", "3", "1", "2", "1", "7", "3", "4", "2" ]
[ "nonn" ]
21
1
2
[ "A000005", "A001221", "A005117", "A381136", "A381138" ]
null
Juri-Stepan Gerasimov, Feb 15 2025
2025-03-10T11:11:37
oeisdata/seq/A381/A381138.seq
716967f4e24e4a96b3db4bd07e32b0a3
A381139
a(1) = 1, a(2) = 2. Let j = a(n-1) and let d = A160995(j) be the smallest non-divisor of j which shares a prime factor with j. Then for n > 2 a(n) is the smallest multiple of d which is not yet in the sequence.
[ "1", "2", "4", "6", "8", "12", "16", "18", "20", "24", "9", "30", "28", "36", "32", "42", "40", "48", "27", "54", "44", "60", "56", "66", "52", "72", "10", "64", "78", "68", "84", "80", "90", "76", "96", "45", "102", "88", "108", "104", "114", "92", "120", "63", "126", "100", "132", "112", "138", "116", "144", "50", "124", "150", "128", "156", "136", "162", "140", "168", "81", "174" ]
[ "nonn", "easy" ]
19
1
2
[ "A160995", "A337687", "A381139" ]
null
David James Sycamore and Michael De Vlieger, Feb 15 2025
2025-04-04T22:34:06
oeisdata/seq/A381/A381139.seq
718e0361795151fa8f0229b83daa1466
A381140
Expansion of e.g.f. exp( -LambertW(-x * cosh(x)) ).
[ "1", "1", "3", "19", "161", "1781", "24667", "409991", "7959233", "176920489", "4432942931", "123648692795", "3800647961761", "127654261471517", "4651982506605995", "182824074836850991", "7708128977570816129", "347059689259637711441", "16621016953663100702755", "843658152872351669816675" ]
[ "nonn" ]
15
0
3
[ "A003727", "A162649", "A185951", "A381140", "A381143" ]
null
Seiichi Manyama, Feb 15 2025
2025-02-16T08:34:07
oeisdata/seq/A381/A381140.seq
1d8782489b7d70d771e24068a72a5d03
A381141
Expansion of e.g.f. exp( -LambertW(-x * cos(x)) ).
[ "1", "1", "3", "13", "89", "821", "9667", "137817", "2306705", "44308009", "960645251", "23205700453", "618086944873", "17996847978461", "568729575572355", "19387150575025201", "709130794848586657", "27704208465508996945", "1151379111946617111043", "50721472225191792506301", "2360928161776701549045241" ]
[ "nonn" ]
13
0
3
[ "A009189", "A185951", "A381141", "A381144", "A381146" ]
null
Seiichi Manyama, Feb 15 2025
2025-02-16T08:34:07
oeisdata/seq/A381/A381141.seq
e474796d1523df420508b97c893272fc
A381142
Expansion of e.g.f. exp( -LambertW(-sin(x)) ).
[ "1", "1", "3", "15", "113", "1137", "14355", "218239", "3883585", "79218721", "1822842243", "46717337007", "1319891043569", "40759239427857", "1365932381706963", "49373610759452575", "1914856819983977473", "79316216447375396161", "3494800326874932467331", "163218136611270923087439" ]
[ "nonn" ]
11
0
3
[ "A002017", "A136630", "A185690", "A277498", "A381142", "A381145", "A381148" ]
null
Seiichi Manyama, Feb 15 2025
2025-02-16T08:34:07
oeisdata/seq/A381/A381142.seq
ac8ecddd6d147957ebf63533da49528f
A381143
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * cosh(x)) ).
[ "1", "1", "3", "19", "185", "2381", "38227", "739271", "16752465", "435437209", "12772234211", "417396070235", "15040805940745", "592531894182437", "25336144876513395", "1168670193628654351", "57845446906144852769", "3058248577410499021361", "172007282950136451003331", "10255035157348348977955619" ]
[ "nonn" ]
9
0
3
[ "A003727", "A162649", "A185951", "A381140", "A381143" ]
null
Seiichi Manyama, Feb 15 2025
2025-02-15T10:12:00
oeisdata/seq/A381/A381143.seq
e471a9895a35ceeb236f9ce79c4c3aef
A381144
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * cos(x)) ).
[ "1", "1", "3", "13", "65", "221", "-2933", "-120903", "-3104127", "-71637191", "-1562635789", "-31373685947", "-505087300991", "-1692007785259", "402032879446395", "28152810613025521", "1423083552938781697", "62552808878706976625", "2459148829654813484131", "82692880516086149155581" ]
[ "sign" ]
10
0
3
[ "A009189", "A185951", "A381141", "A381144", "A381146" ]
null
Seiichi Manyama, Feb 15 2025
2025-02-15T10:11:48
oeisdata/seq/A381/A381144.seq
e2a4b16110280309955881664a611559
A381145
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-sin(x)) ).
[ "1", "1", "3", "15", "105", "937", "10059", "124607", "1720593", "25578001", "391041299", "5628440015", "55397475705", "-847789025159", "-93469767131685", "-5040670692970753", "-236210967512228575", "-10629917015586704351", "-475183316832486106589", "-21394016956935371375601", "-975459739630268065696887" ]
[ "sign" ]
10
0
3
[ "A002017", "A136630", "A185690", "A334856", "A381142", "A381145", "A381148" ]
null
Seiichi Manyama, Feb 15 2025
2025-02-15T10:11:31
oeisdata/seq/A381/A381145.seq
3ef4f40e24f72eabad79fe029fca9bf5
A381146
E.g.f. A(x) satisfies A(x) = exp( x * cos(x * A(x)) ).
[ "1", "1", "1", "-2", "-35", "-264", "-1019", "9864", "302905", "4181824", "23080201", "-632195200", "-25239729899", "-478790195584", "-2682065360883", "188875659540736", "8843706554450033", "203538869514047488", "751681101659548177", "-169782541027003551744", "-8866196526809624969139" ]
[ "sign" ]
10
0
4
[ "A009189", "A185951", "A381141", "A381144", "A381146" ]
null
Seiichi Manyama, Feb 15 2025
2025-02-15T10:11:52
oeisdata/seq/A381/A381146.seq
9f6c2d7006f560161cc38054e4d70d68
A381147
E.g.f. A(x) satisfies A(x) = exp( sinh(x * A(x)) / A(x) ).
[ "1", "1", "1", "2", "13", "92", "621", "5112", "56057", "705168", "9480665", "141039648", "2366242693", "43609330624", "864164283269", "18414385180544", "422574196387953", "10374625080684800", "270563138370828465", "7472794772378583552", "218190569313134267517", "6714970997524417977344" ]
[ "nonn" ]
11
0
4
[ "A003724", "A136630", "A162650", "A219503", "A381147" ]
null
Seiichi Manyama, Feb 15 2025
2025-02-15T10:11:44
oeisdata/seq/A381/A381147.seq
7fef309c1bcff89748f610f3835a5a35
A381148
E.g.f. A(x) satisfies A(x) = exp( sin(x * A(x)) / A(x) ).
[ "1", "1", "1", "0", "-11", "-88", "-459", "-560", "27945", "502336", "5223945", "18968576", "-671465123", "-20909349888", "-345616002627", "-2437013715968", "65881260463697", "3252353828442112", "76987773739473809", "873339053357432832", "-17521718791602049595", "-1354633521318944473088" ]
[ "sign" ]
8
0
5
[ "A002017", "A136630", "A185690", "A381142", "A381145", "A381148" ]
null
Seiichi Manyama, Feb 15 2025
2025-02-15T10:11:26
oeisdata/seq/A381/A381148.seq
4770fb5b05a847079b87a86de6390289
A381149
a(1) = 2, a(2) = 3; thereafter, a(n) = a(n-1) + sum of prior prime terms.
[ "2", "3", "8", "13", "31", "80", "129", "178", "227", "503", "1282", "2061", "2840", "3619", "4398", "5177", "5956", "6735", "7514", "8293", "17365", "26437", "61946", "97455", "132964", "168473", "203982", "239491", "275000", "310509", "346018", "381527", "798563", "1215599", "1632635", "2049671", "2466707", "5350450", "8234193", "11117936" ]
[ "nonn" ]
21
1
1
[ "A101135", "A119746", "A131093", "A381149", "A381150" ]
null
James C. McMahon, Feb 15 2025
2025-02-25T14:54:42
oeisdata/seq/A381/A381149.seq
408a44939b70718f40f8f9a0ae626308
A381150
a(0) = 1, a(1) = 2, a(2) = 3; thereafter, a(n) = a(n-1) + (sum of prior prime terms or whose negatives are prime) - (sum of prior composite terms or whose negatives are composite).
[ "1", "2", "3", "8", "5", "7", "16", "9", "-7", "-30", "-23", "-39", "-16", "23", "85", "62", "-23", "-131", "-370", "-239", "-347", "-802", "-455", "347", "1496", "1149", "-347", "-2190", "-1843", "347", "2884", "2537", "-347", "-3578", "-3231", "347", "4272", "3925", "-347", "-4966", "-4619", "347", "5660", "5313", "-347", "-6354", "-6007", "-11667", "-5660" ]
[ "sign" ]
22
0
2
[ "A000040", "A002808", "A101135", "A119746", "A131093", "A381149", "A381150" ]
null
James C. McMahon, Feb 15 2025
2025-02-25T09:44:12
oeisdata/seq/A381/A381150.seq
3e28a44a4155ca73205a303cbc4192a4
A381151
The order of the 13 cards of one suit such that after Down-SpellUnder dealing the cards are in order; a(n) is the n-th card in the deck.
[ "1", "11", "4", "6", "2", "12", "13", "8", "3", "5", "7", "9", "10" ]
[ "nonn", "fini", "full", "word" ]
16
1
2
[ "A005589", "A006257", "A225381", "A321298", "A378635", "A380201", "A380202", "A380204", "A380246", "A380247", "A380248", "A381151" ]
null
Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Feb 15 2025
2025-03-24T01:26:53
oeisdata/seq/A381/A381151.seq
d6e57dfa746879ed2412b995c3eb7b75
A381152
Decimal expansion of the isoperimetric quotient of a regular pentagon.
[ "8", "6", "4", "8", "0", "6", "2", "6", "5", "9", "7", "7", "2", "0", "9", "9", "6", "7", "2", "3", "1", "1", "8", "2", "0", "6", "5", "8", "5", "8", "6", "2", "3", "3", "3", "7", "0", "3", "8", "2", "8", "5", "5", "5", "6", "9", "0", "2", "2", "8", "3", "9", "9", "6", "2", "1", "3", "2", "0", "9", "5", "7", "3", "9", "8", "9", "3", "3", "2", "7", "0", "9", "3", "4", "1", "1", "8", "7", "1", "2", "9", "6", "4", "8", "0", "4", "0", "2", "3", "3" ]
[ "nonn", "cons", "easy" ]
12
0
1
[ "A003881", "A019952", "A073010", "A093766", "A102771", "A196522", "A381152", "A381153", "A381154", "A381155", "A381156", "A381157" ]
null
Paolo Xausa, Feb 15 2025
2025-02-15T16:49:09
oeisdata/seq/A381/A381152.seq
ac16ba7789b2f9817daed5b90bcc8fa1
A381153
Decimal expansion of the isoperimetric quotient of a regular heptagon.
[ "9", "3", "1", "9", "4", "0", "6", "2", "3", "4", "9", "9", "0", "9", "5", "7", "4", "5", "9", "5", "2", "2", "2", "6", "3", "0", "0", "8", "9", "4", "2", "2", "7", "5", "4", "5", "7", "4", "5", "2", "8", "5", "2", "5", "1", "5", "4", "7", "1", "5", "3", "1", "5", "6", "1", "2", "7", "3", "2", "0", "2", "2", "6", "8", "8", "6", "4", "5", "2", "5", "3", "9", "4", "8", "0", "5", "4", "7", "8", "5", "6", "9", "3", "7", "7", "2", "8", "6", "7", "1" ]
[ "nonn", "cons", "easy" ]
7
0
1
[ "A003881", "A073010", "A093766", "A178817", "A196522", "A343058", "A381152", "A381153", "A381154", "A381155", "A381156", "A381157" ]
null
Paolo Xausa, Feb 15 2025
2025-02-15T16:49:30
oeisdata/seq/A381/A381153.seq
7a2b58698dccb5e2e007734cb3f173f3
A381154
Decimal expansion of the isoperimetric quotient of a regular 9-gon.
[ "9", "5", "9", "0", "5", "0", "5", "4", "1", "8", "7", "3", "6", "0", "9", "3", "5", "8", "0", "7", "4", "5", "4", "3", "3", "0", "6", "7", "0", "8", "6", "4", "3", "4", "1", "3", "0", "2", "0", "1", "8", "1", "5", "8", "0", "9", "7", "5", "2", "8", "5", "8", "7", "3", "4", "3", "7", "2", "0", "7", "8", "9", "2", "8", "0", "3", "9", "1", "9", "4", "5", "1", "0", "3", "7", "5", "6", "4", "9", "7", "6", "1", "4", "4", "0", "5", "7", "7", "1", "2" ]
[ "nonn", "cons", "easy" ]
7
0
1
[ "A003881", "A019918", "A073010", "A093766", "A196522", "A256853", "A381152", "A381153", "A381154", "A381155", "A381156", "A381157" ]
null
Paolo Xausa, Feb 15 2025
2025-02-15T16:49:32
oeisdata/seq/A381/A381154.seq
3c35261dfbe97d8946764a626cfd7938
A381155
Decimal expansion of the isoperimetric quotient of a regular 10-gon.
[ "9", "6", "6", "8", "8", "2", "7", "9", "9", "0", "4", "6", "4", "0", "2", "5", "4", "0", "3", "2", "8", "1", "8", "3", "2", "1", "9", "1", "8", "2", "7", "5", "2", "9", "8", "8", "4", "6", "9", "8", "6", "8", "2", "4", "1", "0", "8", "4", "4", "0", "4", "2", "9", "1", "1", "0", "9", "9", "3", "6", "4", "1", "5", "1", "8", "4", "4", "7", "6", "9", "2", "9", "5", "1", "0", "1", "3", "1", "0", "2", "1", "4", "3", "7", "9", "2", "2", "0", "5", "5" ]
[ "nonn", "cons", "easy" ]
7
0
1
[ "A003881", "A019916", "A073010", "A093766", "A178816", "A196522", "A381152", "A381153", "A381154", "A381155", "A381156", "A381157" ]
null
Paolo Xausa, Feb 15 2025
2025-02-15T16:49:39
oeisdata/seq/A381/A381155.seq
779290708c856b945a5e3c20e2fbcc06
A381156
Decimal expansion of the isoperimetric quotient of a regular 11-gon.
[ "9", "7", "2", "6", "6", "2", "0", "0", "0", "9", "1", "9", "9", "0", "6", "8", "1", "9", "5", "3", "8", "2", "8", "8", "9", "7", "9", "3", "8", "5", "2", "6", "7", "6", "3", "1", "7", "1", "2", "9", "6", "5", "4", "1", "1", "1", "4", "2", "3", "4", "2", "8", "8", "2", "7", "3", "7", "9", "8", "9", "0", "4", "7", "0", "0", "5", "8", "7", "1", "2", "6", "7", "8", "3", "2", "5", "6", "9", "3", "0", "8", "0", "2", "3", "1", "7", "8", "7", "5", "0" ]
[ "nonn", "cons", "easy" ]
7
0
1
[ "A003881", "A073010", "A093766", "A196522", "A256854", "A381152", "A381153", "A381154", "A381155", "A381156", "A381157" ]
null
Paolo Xausa, Feb 15 2025
2025-02-15T16:49:48
oeisdata/seq/A381/A381156.seq
015e70b4c72eef6c4271c8bef0373d53
A381157
Decimal expansion of the isoperimetric quotient of a regular 12-gon.
[ "9", "7", "7", "0", "4", "8", "6", "1", "6", "6", "5", "6", "8", "5", "3", "3", "3", "5", "7", "2", "5", "6", "2", "6", "7", "9", "4", "9", "5", "7", "1", "2", "2", "7", "4", "7", "1", "0", "3", "8", "7", "8", "1", "2", "8", "5", "8", "5", "7", "0", "2", "7", "8", "0", "7", "2", "1", "6", "2", "8", "6", "6", "5", "8", "9", "8", "3", "3", "3", "5", "2", "9", "6", "6", "2", "6", "2", "3", "3", "0", "4", "0", "2", "5", "7", "0", "3", "7", "1", "7" ]
[ "nonn", "cons", "easy" ]
6
0
1
[ "A003881", "A019913", "A073010", "A093766", "A178809", "A196522", "A381152", "A381153", "A381154", "A381155", "A381156", "A381157" ]
null
Paolo Xausa, Feb 15 2025
2025-02-15T16:49:57
oeisdata/seq/A381/A381157.seq
b355aab39a1db173659844ea3c6af3cf
A381158
Prime numbers where digit values decrease while alternating parity.
[ "2", "3", "5", "7", "41", "43", "61", "83", "521", "541", "743", "761", "941", "983", "6521", "8521", "8543", "8741", "8761", "76541", "76543", "94321", "98321", "98543" ]
[ "nonn", "base", "fini", "full" ]
28
1
1
[ "A000040", "A028864", "A028867", "A052014", "A052015", "A381158", "A382027" ]
null
James S. DeArmon, Feb 15 2025
2025-03-20T10:32:04
oeisdata/seq/A381/A381158.seq
8764f5fbfb31261c94d1c7d66b939a17
A381159
Numbers whose prime divisors all end in the same digit.
[ "1", "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", "67", "69", "71", "73", "79", "81", "83", "89", "97", "101", "103", "107", "109", "113", "117", "119", "121", "125", "127", "128", "129", "131", "137", "139", "149", "151", "157", "159", "163", "167", "169", "173", "179" ]
[ "nonn", "base" ]
37
1
2
[ "A000079", "A000351", "A000961", "A004615", "A004618", "A090652", "A380758", "A381159" ]
null
Alexander M. Domashenko, Feb 15 2025
2025-02-21T07:19:45
oeisdata/seq/A381/A381159.seq
c3c257b36913da344e42fc0cfb64f77a
A381160
a(n) is the permanent of the n X n matrix whose element (i,j) is equal to A008277(i+3, j) with 1 <= i,j <= n.
[ "1", "1", "22", "3206", "1902936", "3504528354", "16660734321540", "179059038168086056", "3938830136216956996632", "164125096331945477980176920", "12173562237817299484378342192768", "1527294306324982018922212102518520032", "310564445230567070838152555220146533261496", "98712056006032672983172826864304778359411112064" ]
[ "nonn" ]
11
0
3
[ "A000442", "A008277", "A381160", "A381166" ]
null
Stefano Spezia, Feb 15 2025
2025-02-16T05:40:27
oeisdata/seq/A381/A381160.seq
b3df5b923481e54113e014013ff2cdda
A381161
a(n) = (10*n)!/((n!)^3*(2*n)!*(5*n)!).
[ "1", "15120", "3491888400", "1304290155168000", "601680868708529610000", "312696069714024464473125120", "175460887238127057573116837126400", "103865765423748548466734695459219968000", "63958974275578307119821712720619705931210000", "40596987692554701292235753375257230410967703200000" ]
[ "nonn" ]
9
0
2
[ "A000442", "A010050", "A100734", "A195394", "A381161", "A381162", "A381163", "A381164", "A381165" ]
null
Stefano Spezia, Feb 15 2025
2025-02-16T04:40:29
oeisdata/seq/A381/A381161.seq
02abcfa4443690d84991f1150b862821
A381162
a(n) = (8*n)!/((n!)^4*(4*n)!).
[ "1", "1680", "32432400", "999456057600", "37905932634570000", "1617318175088527591680", "74451445170005824874553600", "3614146643656788883257309696000", "182458061523203642337177421198794000", "9493111901274733909567003010522405280000", "505860213332178847817809654781948251947782400" ]
[ "nonn" ]
10
0
2
[ "A100733", "A134375", "A195392", "A381161", "A381162", "A381163", "A381164", "A381165" ]
null
Stefano Spezia, Feb 15 2025
2025-02-19T13:00:14
oeisdata/seq/A381/A381162.seq
29cfc3b5c9550df75f04a27f91fe5959
A381163
a(n) = Sum_{k=0..n} binomial(n,k)*(4*k)!*(2*k)!/(k!)^6.
[ "1", "49", "15217", "7437505", "4444068913", "2978797867489", "2151085262277121", "1636678166183569873", "1294384621280668799665", "1054623536679756097536097", "879831837105310233485202337", "748258333337818719124808979313", "646586399881218539235007860940609", "566284969531710881501724274920081265" ]
[ "nonn" ]
16
0
2
[ "A007318", "A010050", "A100733", "A307618", "A381161", "A381162", "A381163", "A381164", "A381165" ]
null
Stefano Spezia, Feb 15 2025
2025-04-01T03:29:06
oeisdata/seq/A381/A381163.seq
fb8fab125c5b37ad77a166bc0f681687
A381164
a(n) = Sum_{k=0..n} binomial(n,k)*(5*k)!/(k!)^5.
[ "1", "121", "113641", "168508561", "306213587881", "624890127114721", "1374618918516663841", "3187068298971939367561", "7682172545187676630759081", "19079663136489248380982551201", "48525227073661262262248690661841", "125818607409307965748858681991235961", "331488456546076036761442657285875590881" ]
[ "nonn" ]
17
0
2
[ "A007318", "A008978", "A100734", "A381161", "A381162", "A381163", "A381164", "A381165" ]
null
Stefano Spezia, Feb 15 2025
2025-04-01T03:29:11
oeisdata/seq/A381/A381164.seq
760da5392f72c5d8e91f4d621e210ec6
A381165
a(n) = Sum_{k=0..n} binomial(2*n,n)*binomial(n, k)*(5*k)!/((k!)^3*(2*k)!).
[ "1", "122", "114126", "169305620", "307902541870", "628881704226972", "1384648756554128604", "3213280613371692112392", "7752574653184355259506670", "19272593072633780827550508620", "49062146831202726778631520779476", "127331178560917294198014376933764792", "335791906923524740189894975371277920796" ]
[ "nonn" ]
12
0
2
[ "A000442", "A000984", "A007318", "A010050", "A100734", "A381161", "A381162", "A381163", "A381164", "A381165" ]
null
Stefano Spezia, Feb 15 2025
2025-04-01T05:29:53
oeisdata/seq/A381/A381165.seq
bd37c67b1cdd8dd94d948005b2bebf51
A381166
a(n) is the permanent of the n X n matrix whose element (i,j) is equal to A008277(i+4, j) with 1 <= i,j <= n.
[ "1", "1", "46", "23216", "70437736", "911400637082", "39931366088759328", "5015203546888139970264", "1592320463242701429692077472", "1158339311156769223634640734447744", "1783702957209729441902140461938160455424", "5447268928199100257603373050876725987854119216", "31237114830378466799129128930824084710690680271414364" ]
[ "nonn" ]
10
0
3
[ "A008277", "A134375", "A381160", "A381166" ]
null
Stefano Spezia, Feb 15 2025
2025-02-16T05:40:23
oeisdata/seq/A381/A381166.seq
0881174c1939d369ca089e9bd9fb4199
A381167
Each term is the least positive integer not appearing earlier such that gcd(a(m),a(n)) = 1 or |m-n| > max(a(m),a(n)) for all m <> n.
[ "1", "2", "3", "5", "7", "11", "4", "13", "17", "19", "23", "29", "9", "31", "37", "8", "41", "43", "47", "53", "59", "61", "67", "71", "6", "73", "79", "83", "89", "25", "97", "101", "103", "107", "109", "113", "127", "12", "131", "137", "139", "149", "151", "157", "163", "167", "173", "179", "181", "191", "193", "197", "14", "199", "211", "15", "223", "227", "229", "233", "239", "241", "251", "257", "263", "269", "271", "277" ]
[ "nonn" ]
16
1
2
[ "A381019", "A381167" ]
null
M. F. Hasler and Ali Sada, Feb 15 2025
2025-02-15T23:43:35
oeisdata/seq/A381/A381167.seq
934086853b4c99d3cb51cc42a789e56c
A381168
Number of minimal dominating sets in the n-Hanoi graph.
[ "3", "27", "16940" ]
[ "nonn", "bref", "more" ]
4
1
1
null
null
Eric W. Weisstein, Feb 15 2025
2025-02-15T20:41:53
oeisdata/seq/A381/A381168.seq
6fba0b0b6453c54971ddb5a704fafc05
A381169
List of twin prime averages (A014574) is partitioned by including as many elements as possible in the n-th partition, L_n, such that any gap in L_n is smaller than the gap between L_n and L_(n-1) but not bigger than the first gap in L_n. a(n) is the number of elements in L_n.
[ "1", "1", "1", "1", "1", "1", "2", "2", "2", "3", "2", "2", "1", "1", "2", "1", "6", "3", "2", "2", "2", "1", "1", "5", "2", "2", "2", "3", "1", "2", "2", "2", "2", "3", "2", "2", "1", "2", "4", "2", "2", "2", "2", "5", "2", "2", "1", "1", "1", "3", "2", "2", "1", "3", "3", "2", "1", "4", "2", "3", "2", "2", "1", "2", "2", "3", "3", "1", "3", "2", "1", "2", "1", "1", "2", "3", "3", "1", "1", "2", "2", "3", "2", "2", "1", "5", "2" ]
[ "nonn" ]
11
1
7
[ "A001097", "A014574", "A348168", "A381169" ]
null
Ya-Ping Lu, Feb 15 2025
2025-03-02T23:54:20
oeisdata/seq/A381/A381169.seq
31856c6ede97febcab6718b687ce7567
A381170
Euler transform of n^2 * A065959(n).
[ "1", "1", "37", "289", "2107", "14329", "105187", "693579", "4512054", "28468770", "176428599", "1065826203", "6323626404", "36816785552", "210944620532", "1189766311028", "6615412814561", "36287015790029", "196547683500294", "1051919158699442", "5566679104757415", "29144209704259923", "151039019038054896" ]
[ "nonn" ]
29
0
3
[ "A065959", "A156733", "A381170", "A381709" ]
null
Seiichi Manyama, Mar 04 2025
2025-04-01T03:28:25
oeisdata/seq/A381/A381170.seq
6624a5bf0c8bc629d0646529c1d859f7
A381171
Expansion of e.g.f. (1/x) * Series_Reversion( x / (1 + x*cosh(x)) ).
[ "1", "1", "2", "9", "72", "725", "8640", "124117", "2117248", "41477193", "913305600", "22371549761", "604476094464", "17858943664861", "572524035586048", "19793963392789965", "734249332747960320", "29090332675789113617", "1225991945551031304192", "54765451909152748484857", "2584803582762012599910400" ]
[ "nonn" ]
13
0
3
[ "A162653", "A162654", "A185951", "A215364", "A381171", "A381172", "A381173", "A381181" ]
null
Seiichi Manyama, Feb 16 2025
2025-02-16T09:41:01
oeisdata/seq/A381/A381171.seq
091dd606a3f795ec155c0883ddc8b922
A381172
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x)^2 * cosh(x * A(x)) ).
[ "1", "1", "6", "75", "1416", "36065", "1160400", "45182347", "2066343552", "108594342369", "6449557524480", "427226389872491", "31230489190382592", "2497416890105693569", "216875134620623990784", "20324880119519860657515", "2044641793664946681446400", "219762483007148574205773377", "25134006030221243013604835328" ]
[ "nonn" ]
10
0
3
[ "A162654", "A185951", "A215364", "A364984", "A381171", "A381172", "A381175" ]
null
Seiichi Manyama, Feb 16 2025
2025-02-16T09:41:04
oeisdata/seq/A381/A381172.seq
943db2456698894eedc036e4ea550e8e
A381173
Expansion of e.g.f. (1/x) * Series_Reversion( x / (1 + x*cos(x)) ).
[ "1", "1", "2", "3", "-24", "-475", "-5760", "-52297", "-155008", "8781705", "313344000", "6966991339", "102864807936", "18664712365", "-71473582229504", "-3387816787568865", "-103478592573112320", "-1899945146589964783", "18941335827815596032", "3808766537454425974739", "215681241589289359769600" ]
[ "sign" ]
12
0
3
[ "A162653", "A185951", "A381171", "A381173", "A381174", "A381175", "A381176", "A381181" ]
null
Seiichi Manyama, Feb 16 2025
2025-02-16T09:41:08
oeisdata/seq/A381/A381173.seq
269a8a2abd4bce9e64aaeb64dd26aff9
A381174
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x*cos(x)) ).
[ "1", "1", "4", "27", "264", "3365", "52800", "980903", "20984320", "506078505", "13525493760", "394758794419", "12414039171072", "414990179398093", "14523823020621824", "521523225315049215", "18594912994237808640", "613842569215361446097", "14735570097970682265600", "-228398321523777856462261" ]
[ "sign" ]
11
0
3
[ "A185951", "A381173", "A381174", "A381175", "A381176" ]
null
Seiichi Manyama, Feb 16 2025
2025-02-16T09:41:12
oeisdata/seq/A381/A381174.seq
7484752264d3e1eec346be4e7012d8cc
A381175
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x)^2 * cos(x * A(x)) ).
[ "1", "1", "6", "69", "1224", "29465", "898320", "33187133", "1441200768", "71956238769", "4061414246400", "255737764687669", "17773804761259008", "1351494159065894857", "111608708333568036864", "9947544079380663728685", "951770403836914402099200", "97301151510219112917218657", "10585077723403580668983902208" ]
[ "nonn" ]
10
0
3
[ "A185951", "A364984", "A381172", "A381173", "A381174", "A381175", "A381176" ]
null
Seiichi Manyama, Feb 16 2025
2025-02-16T10:05:51
oeisdata/seq/A381/A381175.seq
d54fda792f6fea9f2bcc0c13e31ba6ac
A381176
E.g.f. A(x) satisfies A(x) = 1 + x*cos(x*A(x)).
[ "1", "1", "0", "-3", "-24", "-55", "480", "8813", "61824", "-264591", "-13662720", "-185252771", "-117427200", "52162650553", "1214778679296", "7998339208845", "-370278535495680", "-14623177924271263", "-202753399336206336", "3863010744775239101", "286065782789626920960", "6603193175290504771881" ]
[ "sign" ]
10
0
4
[ "A185951", "A381173", "A381174", "A381175", "A381176" ]
null
Seiichi Manyama, Feb 16 2025
2025-02-16T10:05:55
oeisdata/seq/A381/A381176.seq
bdecf2c3dbb6c008deb79cad4d4d4c2a
A381177
E.g.f. A(x) satisfies A(x) = 1/( 1 - A(x) * sinh(x * A(x)) ).
[ "1", "1", "6", "73", "1352", "33861", "1072000", "41083477", "1849680768", "95708731945", "5597075177984", "365091888890433", "26281788308598784", "2069729710424907181", "177006820644852031488", "16337090667286093559821", "1618592591411194127089664", "171337824188415839421148881", "19299478529228162963028508672" ]
[ "nonn" ]
10
0
3
[ "A136630", "A162653", "A196776", "A201628", "A381177", "A381179" ]
null
Seiichi Manyama, Feb 16 2025
2025-02-16T10:05:59
oeisdata/seq/A381/A381177.seq
cae4e34ef45305fa0aa842eaf0ad9a8b
A381178
Irregular triangle read by rows, where row n lists the elements of the multiset of bases and exponents (including exponents = 1) in the prime factorization of n.
[ "1", "2", "1", "3", "2", "2", "1", "5", "1", "1", "2", "3", "1", "7", "2", "3", "2", "3", "1", "1", "2", "5", "1", "11", "1", "2", "2", "3", "1", "13", "1", "1", "2", "7", "1", "1", "3", "5", "2", "4", "1", "17", "1", "2", "2", "3", "1", "19", "1", "2", "2", "5", "1", "1", "3", "7", "1", "1", "2", "11", "1", "23", "1", "2", "3", "3", "2", "5", "1", "1", "2", "13", "3", "3", "1", "2", "2", "7", "1", "29", "1", "1", "1", "2", "3", "5", "1", "31" ]
[ "nonn", "tabf", "easy" ]
31
2
2
[ "A000026", "A001221", "A008474", "A035306", "A081812", "A381178", "A381203", "A381204", "A381212", "A381398", "A381401", "A381403", "A381404", "A381576" ]
null
Paolo Xausa, Feb 27 2025
2025-03-01T12:19:05
oeisdata/seq/A381/A381178.seq
30f237b82ec19302d699956cd3f6071a
A381179
E.g.f. A(x) satisfies A(x) = 1 + sinh(x*A(x)) / A(x).
[ "1", "1", "0", "1", "8", "21", "64", "1093", "8448", "47785", "654848", "9402537", "94222336", "1264390141", "23392960512", "363389219053", "5722054885376", "117602664867921", "2434091053613056", "47867013812467921", "1080303165427679232", "26716998341391367141", "645003218568158904320", "16403742152044108508181" ]
[ "nonn" ]
8
0
5
[ "A136630", "A162653", "A196776", "A201628", "A381177", "A381179" ]
null
Seiichi Manyama, Feb 16 2025
2025-02-16T10:06:03
oeisdata/seq/A381/A381179.seq
3520f30cb98e7a73c03b2a345f1ce4f0
A381180
E.g.f. A(x) satisfies A(x) = 1 + sin(x*A(x)) / A(x).
[ "1", "1", "0", "-1", "-8", "-19", "64", "1091", "7680", "-1415", "-650752", "-8575865", "-35559424", "857890021", "21380186112", "203548592651", "-1615715926016", "-95486152906639", "-1599622990659584", "-1397194164399601", "657963431581974528", "18168041375501245021", "157453907927886725120", "-6059840564222790027821" ]
[ "sign" ]
7
0
5
[ "A136630", "A196776", "A201627", "A381180", "A381181", "A381182" ]
null
Seiichi Manyama, Feb 16 2025
2025-02-16T10:06:14
oeisdata/seq/A381/A381180.seq
392e5266f4cc4366e178e79ef28eac96
A381181
Expansion of e.g.f. (1/x) * Series_Reversion( x / (1 + sin(x)) ).
[ "1", "1", "2", "5", "8", "-79", "-1584", "-20539", "-223616", "-1855295", "-1736960", "435730789", "14511117312", "338965239601", "6202042886144", "71638247035109", "-714560796196864", "-84697775518956799", "-3650903032332091392", "-115829159202293866939", "-2739961030150105333760", "-29414406825401517785039" ]
[ "sign" ]
12
0
3
[ "A136630", "A162653", "A196776", "A201627", "A381171", "A381173", "A381180", "A381181", "A381182" ]
null
Seiichi Manyama, Feb 16 2025
2025-02-16T10:06:41
oeisdata/seq/A381/A381181.seq
6c5fb9d1d38eb252be741a8cb7aeebbb
A381182
E.g.f. A(x) satisfies A(x) = 1/( 1 - A(x) * sin(x * A(x)) ).
[ "1", "1", "6", "71", "1288", "31661", "984640", "37085075", "1641305472", "83497838425", "4801347029504", "307975150996831", "21802395720298496", "1688562016007776261", "142023935786330431488", "12892154760586821775019", "1256251152910271399624704", "130793914073764385411654321", "14490427167940362294881615872" ]
[ "nonn" ]
9
0
3
[ "A136630", "A196776", "A201627", "A381180", "A381181", "A381182" ]
null
Seiichi Manyama, Feb 16 2025
2025-02-16T10:06:36
oeisdata/seq/A381/A381182.seq
f2f924cf785e61bbfac4b148f90de50f
A381183
a(n) = the smallest positive integer that produces a product that contains the digit 2 when multiplied by 2 at most n times, and where a further multiplication by 2 produces a number that does not contain the digit 2. Set a(n) = -1 if no such number exists.
[ "2", "1", "6", "31", "128", "64", "516", "331", "814", "1607", "4107", "10158", "10258", "5129", "10283", "12819", "25633", "28141", "16163", "51404", "80134", "80864", "40633", "80216", "40108", "128129", "250627", "160626", "80313", "125641", "208141", "383814", "391628", "195814", "156766", "196314", "391563", "490641", "806166", "785313", "628222", "314111", "625322", "312661", "1563305", "2630104", "1315052", "657526", "328763", "1643815" ]
[ "nonn", "base" ]
24
0
1
[ "A011532", "A378138", "A381087", "A381183" ]
null
Michael De Vlieger and Scott R. Shannon, Feb 16 2025
2025-02-23T09:32:00
oeisdata/seq/A381/A381183.seq
3f2cacb9ac52abb9c3455e91e570641d
A381184
a(n) = [(x*y*z*u)^n] 1/((1-(x+y+z+u))*(1-x*y-z*u)).
[ "1", "30", "2958", "428652", "72819090", "13516242348", "2655799814220", "543000625464600", "114327634610709630", "24620695529789323140", "5397810728037535659852", "1200730183508291762472120", "270334385874587473289188884", "61483631908884909800347922616", "14105087055649813954756928131800" ]
[ "nonn" ]
9
0
2
[ "A006134", "A381184" ]
null
Stefano Spezia, Feb 16 2025
2025-02-19T13:38:38
oeisdata/seq/A381/A381184.seq
9f0c1f7e0f24be63748582e7e22af116
A381185
a(n) = numerator( [x^n] hypergeom([1/4, 3/4], [1], 2^6*x/3^2)/sqrt(1 - 4*x) ).
[ "1", "10", "374", "15484", "230210", "10919020", "1635492740", "9461595400", "169793701330", "253354748427220", "4762913165558548", "272892459138645320", "15830057357705343116", "309116222832740182552", "18252959497023816606200", "3254657058859020013332688", "7203918574814465440160390", "1297593844520826560448239324" ]
[ "nonn", "frac" ]
14
0
2
[ "A381185", "A381186" ]
null
Stefano Spezia, Feb 16 2025
2025-02-19T13:38:31
oeisdata/seq/A381/A381185.seq
9359b9194be9dd45acc36d28ae172788
A381186
a(n) = denominator( [x^n] hypergeom([1/4, 3/4], [1], 2^6*x/3^2)/sqrt(1 - 4*x) ).
[ "1", "3", "27", "243", "729", "6561", "177147", "177147", "531441", "129140163", "387420489", "3486784401", "31381059609", "94143178827", "847288609443", "22876792454961", "7625597484987", "205891132094649", "50031545098999707", "150094635296999121", "1350851717672992089", "1350851717672992089", "4052555153018976267" ]
[ "nonn", "frac" ]
11
0
2
[ "A381185", "A381186" ]
null
Stefano Spezia, Feb 16 2025
2025-02-19T13:38:21
oeisdata/seq/A381/A381186.seq
fa85d9f7eebb2b4fda8253fcd1dd64a8
A381187
Triangle T(n,k) read by rows whose n-th row is the lexicographically first n-tuple of ordered positive integers with sum A380887(n) and product A380887(n) * 100^(n-1).
[ "1", "200", "200", "150", "175", "200", "125", "160", "175", "184", "125", "125", "160", "165", "184", "125", "125", "144", "150", "160", "160", "125", "125", "128", "144", "150", "150", "150", "110", "125", "125", "125", "128", "150", "150", "176", "125", "125", "125", "125", "128", "128", "132", "150", "150", "120", "120", "125", "125", "125", "125", "128", "128", "150", "150" ]
[ "tabl", "nonn" ]
26
1
2
[ "A380887", "A381187" ]
null
Markus Sigg, Feb 16 2025
2025-03-28T14:13:09
oeisdata/seq/A381/A381187.seq
3f434a6dcff98a2a07f98b5b092f08ea
A381188
Number of connected minimal dominating sets in the n X n queen graph.
[ "1", "4", "13", "92", "1359" ]
[ "nonn", "more" ]
5
1
2
null
null
Eric W. Weisstein, Feb 16 2025
2025-02-16T10:06:51
oeisdata/seq/A381/A381188.seq
4b30570fa0ca981de679acfe6e6fc171
A381189
Ulam numbers that are squarefree semiprimes.
[ "6", "26", "38", "57", "62", "69", "77", "82", "87", "106", "145", "155", "177", "206", "209", "219", "221", "253", "309", "319", "339", "341", "358", "382", "451", "485", "497", "502", "566", "685", "695", "734", "781", "849", "866", "893", "905", "949", "1018", "1037", "1079", "1081", "1101", "1157", "1167", "1169", "1186", "1191", "1257", "1313", "1355", "1387", "1389" ]
[ "nonn" ]
10
1
1
[ "A002858", "A006881", "A068820", "A378795", "A379162", "A379532", "A381189" ]
null
Massimo Kofler, Feb 16 2025
2025-03-02T23:54:43
oeisdata/seq/A381/A381189.seq
cccb5174fe1e3a0cb58de18284fafa81
A381190
Number of connected minimal dominating sets in the n-trapezohedral graph.
[ "6", "16", "30", "36", "70", "96", "144", "220", "308", "456", "650" ]
[ "nonn", "more" ]
4
3
1
null
null
Eric W. Weisstein, Feb 16 2025
2025-02-16T10:06:46
oeisdata/seq/A381/A381190.seq
e9dc952644272281c9ad93f69566a05a
A381191
Order of the minimal polynomial for the n-th smallest Pisot number.
[ "3", "4", "5", "3", "6", "5", "7", "6", "5", "8" ]
[ "nonn", "more" ]
6
1
1
null
null
Eric W. Weisstein, Feb 16 2025
2025-02-16T17:53:20
oeisdata/seq/A381/A381191.seq
fff7584d2ff3ba4637b87d5426e0d666
A381192
Irregular triangle read by rows. Properly color the vertices of a simple labeled graph on [n] using exactly n colors c_1<c_2<...<c_n (in other words, use each color exactly once). Orient the edges according to the strict order on the colors. T(n,k) is the number of such graphs with exactly k descents, n>=0, 0<=k<=binomial(n,2).
[ "1", "1", "3", "1", "21", "19", "7", "1", "315", "516", "419", "208", "65", "12", "1", "9765", "24186", "31445", "27488", "17538", "8420", "3050", "816", "153", "18", "1", "615195", "2080323", "3769767", "4754751", "4592847", "3555479", "2257723", "1188595", "519745", "187705", "55237", "12941", "2325", "301", "25", "1" ]
[ "nonn", "tabf" ]
14
0
3
[ "A005329", "A011266", "A381058", "A381102", "A381192" ]
null
Geoffrey Critzer, Feb 16 2025
2025-02-24T19:41:40
oeisdata/seq/A381/A381192.seq
89ecf3fa35bd791ede35ce52f45e4387
A381193
a(n) = (3*n-1)*(n^4-18*n^3+179*n^2-582*n+720)/120.
[ "5", "6", "12", "33", "77", "153", "274", "460", "741", "1160", "1776", "2667", "3933", "5699", "8118", "11374", "15685", "21306", "28532", "37701", "49197", "63453", "80954", "102240", "127909", "158620", "195096", "238127", "288573", "347367", "415518", "494114", "584325", "687406", "804700", "937641", "1087757", "1256673", "1446114" ]
[ "nonn", "easy" ]
19
1
1
null
null
Eric W. Weisstein, Feb 16 2025
2025-03-03T05:18:07
oeisdata/seq/A381/A381193.seq
a99ba0710096c45ee775eb08dfc2974d
A381194
Number of equal-length matchings of 2n uniformly spaced points on a circle.
[ "1", "3", "3", "9", "5", "17", "7", "33", "15", "49", "11", "113", "13", "153", "57", "321", "17", "617", "19", "1153", "165", "2089", "23", "4577", "85", "8241", "555", "16737", "29", "34049", "31", "66177", "2109", "131137", "377", "267521", "37", "524361", "8265", "1051393", "41", "2114081", "43", "4198561", "33945", "8388697", "47", "16851905", "427", "33556689" ]
[ "nonn" ]
20
1
2
null
null
Jerrold Grossman, Feb 16 2025
2025-04-13T01:47:26
oeisdata/seq/A381/A381194.seq
a7ad88224b508e8aa71ee3e852385c41
A381195
Expansion of g.f. (1 - sqrt(1 - 1728*x))/(864*x).
[ "1", "432", "373248", "403107840", "487599243264", "631928619270144", "857978513934778368", "1204601833564428828672", "1734626640332777513287680", "2547819609320783611516944384", "3802273336964543978787469000704", "5749037285490390495926653129064448", "8788066841328079995004188536982208512" ]
[ "nonn" ]
11
0
2
[ "A009971", "A277757", "A381195" ]
null
Stefano Spezia, Feb 16 2025
2025-02-19T13:38:13
oeisdata/seq/A381/A381195.seq
cf19b3d136993d20388af1dcb57267e9
A381196
Stellated octagon numbers: a(n) = 20*n^2 + 8*n + 1.
[ "1", "29", "97", "205", "353", "541", "769", "1037", "1345", "1693", "2081", "2509", "2977", "3485", "4033", "4621", "5249", "5917", "6625", "7373", "8161", "8989", "9857", "10765", "11713", "12701", "13729", "14797", "15905", "17053", "18241", "19469", "20737", "22045", "23393", "24781", "26209", "27677", "29185", "30733", "32321", "33949" ]
[ "nonn", "easy" ]
36
0
2
[ "A000217", "A001844", "A016742", "A016814", "A168668", "A195162", "A381196" ]
null
Aaron David Fairbanks, Feb 16 2025
2025-03-05T20:44:00
oeisdata/seq/A381/A381196.seq
af3d26df6d4fab6ecb1fcfb50eb4e4a8
A381197
a(n) = numerator( [(x*y*z*u)^n] 1/sqrt(1 - (x + y + z + u*(x*y + x*z + y*z))) ).
[ "1", "9", "1575", "107415", "143918775", "13539797271", "5492167201521", "586937023583625", "4173054453859037175", "477630312182609961375", "223908157536370130248425", "26751307348701533866638825", "51959852697049291288154030625", "6393039919009116988875533492625", "3182668486503393355366954041669375" ]
[ "nonn", "frac" ]
10
0
2
[ "A268554", "A381197", "A381198" ]
null
Stefano Spezia, Feb 16 2025
2025-02-19T13:38:04
oeisdata/seq/A381/A381197.seq
37f612d8ec6b54d3d588edf581507320
A381198
a(n) = denominator( [(x*y*z*u)^n] 1/sqrt(1 - (x + y + z + u*(x*y + x*z + y*z))) ).
[ "1", "4", "64", "256", "16384", "65536", "1048576", "4194304", "1073741824", "4294967296", "68719476736", "274877906944", "17592186044416", "70368744177664", "1125899906842624", "4503599627370496", "4611686018427387904", "18446744073709551616", "295147905179352825856", "1180591620717411303424", "75557863725914323419136" ]
[ "nonn", "frac" ]
13
0
2
[ "A268554", "A381197", "A381198" ]
null
Stefano Spezia, Feb 16 2025
2025-02-19T13:37:59
oeisdata/seq/A381/A381198.seq
442889491fd973108566f3f6544f74d7
A381199
a(n) = (4*n)!/((n!)^2*(2*n)!)*Sum_{k=0..n} binomial(n,k)^2*binomial(2*k,k).
[ "1", "36", "6300", "1718640", "575675100", "216636756336", "87874675224336", "37563969509352000", "16692217815436148700", "7642084994921759382000", "3582530520581922083974800", "1712083670316898167464884800", "831357643152788660610464490000", "409154554816583487288034143528000", "203690783136217174743485058666840000" ]
[ "nonn" ]
12
0
2
[ "A000897", "A000984", "A001044", "A002893", "A007318", "A008459", "A010050", "A100733", "A381199" ]
null
Stefano Spezia, Feb 16 2025
2025-02-19T13:37:51
oeisdata/seq/A381/A381199.seq
66ad963126c263201f20edaf2cd17e27
A381200
Numbers k such that (49^k - 2^k)/47 is prime.
[ "3", "5", "29", "89", "35279" ]
[ "nonn", "hard", "more" ]
6
1
1
[ "A062587", "A062589", "A127996", "A127997", "A128344", "A204940", "A217320", "A225807", "A229542", "A375161", "A375236", "A377031", "A381200" ]
null
Robert Price, Feb 16 2025
2025-02-16T22:38:23
oeisdata/seq/A381/A381200.seq
d2cb74f5f3812386432dd2aed4a0c6ed
A381201
a(n) is the product of the elements of the set of bases and exponents in the prime factorization of n.
[ "1", "2", "3", "2", "5", "6", "7", "6", "6", "10", "11", "6", "13", "14", "15", "8", "17", "6", "19", "10", "21", "22", "23", "6", "10", "26", "3", "14", "29", "30", "31", "10", "33", "34", "35", "6", "37", "38", "39", "30", "41", "42", "43", "22", "30", "46", "47", "24", "14", "10", "51", "26", "53", "6", "55", "42", "57", "58", "59", "30", "61", "62", "42", "12", "65", "66", "67", "34", "69", "70" ]
[ "nonn", "easy" ]
14
1
2
[ "A000026", "A336965", "A381201", "A381202", "A381203", "A381204", "A381205" ]
null
Paolo Xausa, Feb 16 2025
2025-02-18T18:57:06
oeisdata/seq/A381/A381201.seq
c8a21e4ecf02a27413c6baafbefdf202
A381202
a(n) is the sum of the elements of the set of bases and exponents (including exponents = 1) in the prime factorization of n.
[ "0", "3", "4", "2", "6", "6", "8", "5", "5", "8", "12", "6", "14", "10", "9", "6", "18", "6", "20", "8", "11", "14", "24", "6", "7", "16", "3", "10", "30", "11", "32", "7", "15", "20", "13", "5", "38", "22", "17", "11", "42", "13", "44", "14", "11", "26", "48", "10", "9", "8", "21", "16", "54", "6", "17", "13", "23", "32", "60", "11", "62", "34", "13", "8", "19", "17", "68", "20", "27", "15", "72", "5" ]
[ "nonn", "easy" ]
12
1
2
[ "A008474", "A338038", "A381201", "A381202", "A381203", "A381204", "A381205" ]
null
Paolo Xausa, Feb 16 2025
2025-02-18T18:57:15
oeisdata/seq/A381/A381202.seq
8a8392dc3d714b794ae842cc9e648fda
A381203
a(n) is the lcm of the elements of the set of bases and exponents in the prime factorization of n.
[ "2", "3", "2", "5", "6", "7", "6", "6", "10", "11", "6", "13", "14", "15", "4", "17", "6", "19", "10", "21", "22", "23", "6", "10", "26", "3", "14", "29", "30", "31", "10", "33", "34", "35", "6", "37", "38", "39", "30", "41", "42", "43", "22", "30", "46", "47", "12", "14", "10", "51", "26", "53", "6", "55", "42", "57", "58", "59", "30", "61", "62", "42", "6", "65", "66", "67", "34", "69", "70", "71" ]
[ "nonn", "easy" ]
10
2
1
[ "A381201", "A381202", "A381203", "A381204", "A381205", "A381213" ]
null
Paolo Xausa, Feb 17 2025
2025-02-18T18:57:34
oeisdata/seq/A381/A381203.seq
ae4f2ef509fc9c23df95d505f68069a1
A381204
a(n) is the gcd of the elements of the set of bases and exponents in the prime factorization of n.
[ "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn", "easy" ]
13
2
3
[ "A368107", "A381201", "A381202", "A381203", "A381204", "A381205" ]
null
Paolo Xausa, Feb 17 2025
2025-02-21T16:46:51
oeisdata/seq/A381/A381204.seq
6e22eceefc623c12fb50cfda0dec3c0b
A381205
a(n) is the cardinality of the set of bases and exponents (including exponents = 1) in the prime factorization of n.
[ "0", "2", "2", "1", "2", "3", "2", "2", "2", "3", "2", "3", "2", "3", "3", "2", "2", "3", "2", "3", "3", "3", "2", "3", "2", "3", "1", "3", "2", "4", "2", "2", "3", "3", "3", "2", "2", "3", "3", "4", "2", "4", "2", "3", "4", "3", "2", "4", "2", "3", "3", "3", "2", "3", "3", "4", "3", "3", "2", "4", "2", "3", "4", "2", "3", "4", "2", "3", "3", "4", "2", "2", "2", "3", "4", "3", "3", "4", "2", "4", "2", "3", "2", "4", "3", "3", "3", "4", "2", "4" ]
[ "nonn", "easy" ]
18
1
2
[ "A051674", "A381201", "A381202", "A381203", "A381204", "A381205", "A381212" ]
null
Paolo Xausa, Feb 17 2025
2025-02-22T09:57:14
oeisdata/seq/A381/A381205.seq
dfe3c70f0106bf1a56d6716325c86690
A381206
Expansion of e.g.f. 1/(1 - x*cosh(x))^2.
[ "1", "2", "6", "30", "192", "1450", "12960", "133574", "1550976", "20055186", "285903360", "4452231982", "75186726912", "1368588922298", "26709799753728", "556339845854550", "12318065768693760", "288894650033594914", "7154212267816648704", "186545064693433665854", "5108590743587243950080" ]
[ "nonn" ]
10
0
2
[ "A185951", "A205571", "A381206", "A381207" ]
null
Seiichi Manyama, Feb 17 2025
2025-02-17T08:18:12
oeisdata/seq/A381/A381206.seq
27955d79a28a586caa4a072b304b4c22
A381207
Expansion of e.g.f. 1/(1 - x*cosh(x))^3.
[ "1", "3", "12", "69", "504", "4335", "43200", "490161", "6220032", "87242427", "1340305920", "22375475133", "403237638144", "7801208775399", "161245892161536", "3545854432602345", "82653484859228160", "2035605515838402291", "52814589875313573888", "1439814136866851346357", "41145786213980645621760" ]
[ "nonn" ]
12
0
2
[ "A185951", "A205571", "A377530", "A381206", "A381207", "A381209", "A381210", "A381211" ]
null
Seiichi Manyama, Feb 17 2025
2025-02-17T08:18:15
oeisdata/seq/A381/A381207.seq
012cbef07ca6700ddfa81052305977a4
A381208
Expansion of e.g.f. 1/(1 - x*cos(x))^2.
[ "1", "2", "6", "18", "48", "10", "-1440", "-17654", "-153216", "-1003950", "-2787840", "58057538", "1483941888", "22381115354", "245730121728", "1455189928890", "-18135147970560", "-856283065534046", "-19218870434267136", "-306007541260257422", "-2933654664287354880", "20552099782407258282", "1938717354581701951488" ]
[ "sign" ]
10
0
2
[ "A185951", "A352252", "A381208", "A381209" ]
null
Seiichi Manyama, Feb 17 2025
2025-02-17T08:18:19
oeisdata/seq/A381/A381208.seq
cf5cc6df1ad8fe215fcf13810931c469
A381209
Expansion of e.g.f. 1/(1 - x*cos(x))^3.
[ "1", "3", "12", "51", "216", "735", "0", "-39081", "-575232", "-6047973", "-48314880", "-189159333", "3046957056", "99745485879", "1789140627456", "23433663134655", "185580069027840", "-1250544374605389", "-94781673979379712", "-2543434372808424957", "-47763303489939701760", "-586864592847636893937" ]
[ "sign" ]
12
0
2
[ "A185951", "A352252", "A377530", "A381207", "A381208", "A381209", "A381210", "A381211" ]
null
Seiichi Manyama, Feb 17 2025
2025-02-17T08:18:26
oeisdata/seq/A381/A381209.seq
c188bb59c0ee2c394e3113eb4e4d160e
A381210
Expansion of e.g.f. 1/(1 - sinh(x))^3.
[ "1", "3", "12", "63", "408", "3123", "27552", "275103", "3065088", "37682883", "506606592", "7392091743", "116329479168", "1963781841843", "35395627487232", "678401549017983", "13776623985819648", "295481239628640003", "6674320861079273472", "158364407589097613823", "3937958237874411798528" ]
[ "nonn" ]
10
0
2
[ "A136630", "A377530", "A381207", "A381209", "A381210", "A381211" ]
null
Seiichi Manyama, Feb 17 2025
2025-02-17T08:18:22
oeisdata/seq/A381/A381210.seq
cb036015b561e5ceb6d03d5b13afb21f
A381211
Expansion of e.g.f. 1/(1 - sin(x))^3.
[ "1", "3", "12", "57", "312", "1923", "13152", "98697", "805632", "7102563", "67233792", "679970937", "7315786752", "83421156003", "1004860895232", "12749105088777", "169926064668672", "2373678328434243", "34676591077097472", "528758667342524217", "8400613520498491392", "138830752520282729283" ]
[ "nonn" ]
11
0
2
[ "A136630", "A185690", "A377530", "A381207", "A381209", "A381210", "A381211" ]
null
Seiichi Manyama, Feb 17 2025
2025-02-17T08:18:31
oeisdata/seq/A381/A381211.seq
0661966fef3496d839059d94db61951d
A381212
a(n) is the smallest element of the set of bases and exponents (including exponents = 1) in the prime factorization of n.
[ "1", "1", "2", "1", "1", "1", "2", "2", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "3", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "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", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn", "easy" ]
12
2
3
[ "A001694", "A081812", "A288636", "A331048", "A381201", "A381202", "A381203", "A381204", "A381205", "A381212", "A381214" ]
null
Paolo Xausa, Feb 19 2025
2025-03-05T05:36:43
oeisdata/seq/A381/A381212.seq
ee53d9b2439bd601f713ad183f74fb6d
A381213
Numbers k such that A381201(k) != A381203(k).
[ "16", "48", "64", "80", "112", "144", "162", "176", "192", "208", "240", "256", "272", "304", "320", "324", "336", "368", "400", "432", "448", "464", "496", "528", "560", "576", "592", "624", "648", "656", "688", "704", "720", "729", "752", "768", "784", "810", "816", "832", "848", "880", "912", "944", "960", "976", "1008", "1024", "1040", "1072", "1088", "1104" ]
[ "nonn", "easy" ]
6
1
1
[ "A381201", "A381203", "A381213" ]
null
Paolo Xausa, Feb 17 2025
2025-02-18T18:58:47
oeisdata/seq/A381/A381213.seq
7c403e448de7d5b12a4ae6ecc86fe016
A381214
a(n) is the difference between the largest and smallest element of the set of bases and exponents (including exponents = 1) in the prime factorization of n.
[ "1", "2", "0", "4", "2", "6", "1", "1", "4", "10", "2", "12", "6", "4", "2", "16", "2", "18", "4", "6", "10", "22", "2", "3", "12", "0", "6", "28", "4", "30", "3", "10", "16", "6", "1", "36", "18", "12", "4", "40", "6", "42", "10", "4", "22", "46", "3", "5", "4", "16", "12", "52", "2", "10", "6", "18", "28", "58", "4", "60", "30", "6", "4", "12", "10", "66", "16", "22", "6", "70", "1", "72", "36", "4", "18" ]
[ "nonn", "easy" ]
13
2
2
[ "A046665", "A051674", "A081812", "A381212", "A381214", "A381215" ]
null
Paolo Xausa, Feb 19 2025
2025-02-21T09:31:16
oeisdata/seq/A381/A381214.seq
da5693f8794654501e2f4923b579839a