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1999-12-11 03:00:00
2025-04-25 01:21:50
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A359801
Number of 4-dimensional cubic lattice walks that start and end at origin after 2n steps, not touching origin at intermediate stages.
[ "1", "8", "104", "2944", "108136", "4525888", "204981888", "9792786432", "486323201640", "24874892400064", "1302278744460352", "69474942954714112", "3764568243058030208", "206675027529594291200", "11473858525271117889536", "643154944963894079717376", "36355546411928157876528744", "2070313613815122857027563200" ]
[ "nonn", "walk" ]
52
0
5
[ "A002420", "A039699", "A049037", "A054474", "A287317", "A359801", "A361397" ]
null
Shel Kaphan, Mar 08 2023
2024-11-15T19:18:02
oeisdata/seq/A359/A359801.seq
38e30c8652415855a24cb5cebbf84c6f
A359802
a(n) = product prime(d + 1), where d ranges over all the decimal digits of n.
[ "2", "3", "5", "7", "11", "13", "17", "19", "23", "29", "6", "9", "15", "21", "33", "39", "51", "57", "69", "87", "10", "15", "25", "35", "55", "65", "85", "95", "115", "145", "14", "21", "35", "49", "77", "91", "119", "133", "161", "203", "22", "33", "55", "77", "121", "143", "187", "209", "253", "319", "26", "39", "65", "91", "143", "169", "221", "247", "299", "377", "34", "51" ]
[ "nonn", "easy", "base" ]
41
0
5
[ "A113581", "A115078", "A359802" ]
null
Fabian I. Garcia, May 11 2023
2023-05-12T03:21:32
oeisdata/seq/A359/A359802.seq
da1e67068e953ee967366bf438dd3b34
A359803
a(1) = 1; for n > 1, a(n) = n-1 if a(n-1) = 1, otherwise, apply the '3x+1' function to a(n-1)
[ "1", "1", "2", "1", "4", "2", "1", "7", "22", "11", "34", "17", "52", "26", "13", "40", "20", "10", "5", "16", "8", "4", "2", "1", "24", "12", "6", "3", "10", "5", "16", "8", "4", "2", "1", "35", "106", "53", "160", "80", "40", "20", "10", "5", "16", "8", "4", "2", "1", "49", "148", "74", "37", "112", "56", "28", "14", "7", "22", "11", "34", "17", "52", "26", "13", "40", "20", "10", "5", "16", "8" ]
[ "nonn", "look", "easy" ]
92
0
5
[ "A014682", "A070165", "A359803" ]
null
Wagner Martins, Jul 17 2023
2023-08-06T17:49:03
oeisdata/seq/A359/A359803.seq
128ee179f282ed4294698c7ae9b556a0
A359804
a(1) = 1, a(2) = 2; thereafter let p be the smallest prime that does not divide a(n-2)*a(n-1), then a(n) is the smallest multiple of p that is not yet in the sequence.
[ "1", "2", "3", "5", "4", "6", "10", "7", "9", "8", "15", "14", "11", "12", "20", "21", "22", "25", "18", "28", "30", "33", "35", "16", "24", "40", "42", "44", "45", "49", "26", "27", "50", "56", "36", "55", "63", "32", "60", "70", "66", "13", "65", "34", "39", "75", "38", "77", "48", "80", "84", "88", "85", "51", "46", "90", "91", "99", "52", "95", "54", "98", "100", "57", "105", "58", "110", "69", "112", "115", "72", "119", "120", "121" ]
[ "nonn" ]
38
0
5
[ "A002110", "A007947", "A053669", "A351495", "A359804", "A361502", "A361503", "A361504", "A361505" ]
null
David James Sycamore, Mar 08 2023
2023-06-22T04:08:36
oeisdata/seq/A359/A359804.seq
54d20bb26d3f913aa3351aaafc235b97
A359805
Irregular triangle T(n, k), n > 0, k = 1..A056137(A009023(n)), read by rows: the n-th row contains the numbers m < A009023(n) such that A009023(n)^2 + m^2 is a square.
[ "3", "6", "5", "9", "8", "12", "15", "20", "7", "10", "18", "21", "16", "24", "12", "15", "27", "9", "30", "40", "33", "24", "28", "14", "20", "36", "39", "48", "33", "42", "11", "25", "32", "45", "16", "60", "48", "51", "24", "21", "30", "54", "65", "40", "57", "36", "18", "39", "60", "13", "35", "63", "80", "66", "48", "56", "60", "69", "28", "40", "72", "20", "75", "78", "36", "56", "88", "100" ]
[ "nonn", "look", "tabf" ]
16
0
5
[ "A009023", "A056137", "A359805", "A360020" ]
null
Rémy Sigrist, Mar 08 2023
2023-06-16T05:31:50
oeisdata/seq/A359/A359805.seq
8d62b5c6cbd4bb2817046bef16aa5809
A359806
Lexicographically earliest sequence of distinct positive terms such that for any n > 0 and any k > 0, floor((2^k) / n) AND floor((2^k) / a(n)) = 0 (where AND denotes the bitwise AND operator).
[ "2", "1", "6", "5", "4", "3", "14", "9", "8", "40", "32", "24", "60", "7", "20", "17", "16", "144", "128", "15", "72", "64", "512", "12", "256", "120", "13824", "39", "2048", "35", "62", "11", "1056", "544", "30", "288", "4096", "1008", "28", "10", "1024", "156", "5504", "1408", "112", "1424", "8192", "96", "1016", "51200", "102", "240", "32768", "27648", "248", "78" ]
[ "nonn", "base" ]
6
0
5
[ "A238757", "A306231", "A359806" ]
null
Rémy Sigrist, Jan 13 2023
2023-01-14T08:46:12
oeisdata/seq/A359/A359806.seq
49be668ff8f7646c617a80c5939ed70e
A359807
a(1) = 0; thereafter a(n) is the largest a(i) + i which is < n among i = 1..n-1.
[ "0", "1", "1", "3", "4", "4", "4", "7", "7", "9", "10", "11", "11", "11", "11", "15", "16", "16", "16", "19", "19", "21", "21", "23", "24", "25", "26", "26", "26", "26", "26", "31", "31", "33", "34", "35", "35", "35", "35", "39", "40", "40", "40", "43", "44", "44", "44", "47", "47", "49", "49", "51", "51", "53", "54", "55", "56", "57", "57", "57", "57", "57", "57", "63", "64", "64", "64", "67", "67", "69", "69", "71", "72", "73", "74", "74", "74", "74", "74" ]
[ "nonn" ]
52
0
5
[ "A037988", "A094591", "A272727", "A272729", "A359807", "A367026", "A367039" ]
null
Neal Gersh Tolunsky, Jan 13 2023
2023-11-05T09:04:17
oeisdata/seq/A359/A359807.seq
2b4181b9c19ee7db45fa84650faae020
A359808
a(n) is the least prime factor of the alternating factorial n! - (n-1)! + (n-2)! - ... 1! for n > 2; a(1) = a(2) = 1.
[ "1", "1", "5", "19", "101", "619", "4421", "35899", "79", "3301819", "13", "29", "47", "23", "1226280710981", "53", "47", "2683", "115578717622022981", "8969", "113", "79", "85439", "12203", "59", "1657", "127", "61", "661", "47", "173183", "1117", "83", "4729", "37", "103", "2858548279", "59", "67", "431", "32656499591185747972776747396512425885838364422981" ]
[ "nonn" ]
16
0
5
[ "A001272", "A005165", "A020639", "A359808" ]
null
Jon E. Schoenfield, Jan 13 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359808.seq
b1e982519954067a490333ee87498e88
A359809
Decimal expansion of the positive solution to tanh(x) = x/2.
[ "1", "9", "1", "5", "0", "0", "8", "0", "4", "8", "1", "5", "4", "5", "3", "7", "4", "8", "1", "3", "5", "3", "0", "0", "3", "0", "6", "1", "0", "0", "4", "8", "1", "5", "6", "5", "0", "5", "7", "3", "3", "6", "2", "5", "6", "8", "7", "8", "5", "9", "2", "8", "9", "8", "6", "1", "1", "3", "7", "4", "7", "3", "4", "6", "6", "4", "1", "3", "5", "6", "2", "3", "7", "6", "2", "6", "3", "1", "7", "3", "0", "9", "7", "7", "9", "3", "7", "6", "6", "1", "1", "3", "6", "8" ]
[ "nonn", "cons" ]
15
0
5
[ "A309211", "A359809" ]
null
M. F. Hasler, Jan 13 2023
2023-01-28T14:00:13
oeisdata/seq/A359/A359809.seq
dca307251c9a2ea4611d0350eafd18da
A359810
Partial sums of A001035.
[ "1", "2", "5", "24", "243", "4474", "134497", "6264356", "437987735", "44949030246", "6656014279029", "1402937691384928", "416267888747238427", "172266996270334297778", "98656591253398541329961", "77665827611694086894379900", "83558195613101851900738636479", "122236099445908424714842019905630", "242061628696647085027612662167990653" ]
[ "nonn" ]
9
0
5
[ "A001035", "A354847", "A359810" ]
null
Firdous Ahmad Mala, Jan 13 2023
2023-02-07T12:44:16
oeisdata/seq/A359/A359810.seq
baa5ff6841ca61704bf54f346abd80e5
A359811
a(n) = Sum_{d|n} 2^(d-1) * d^(n/d-1).
[ "1", "3", "5", "13", "17", "53", "65", "177", "293", "625", "1025", "2541", "4097", "8769", "17109", "34561", "65537", "136013", "262145", "534481", "1054629", "2110465", "4194305", "8449325", "16787217", "33615873", "67155845", "134403521", "268435457", "537370845", "1073741825", "2148270081", "4295327397", "8591179777" ]
[ "nonn", "easy" ]
11
0
5
[ "A087909", "A359134", "A359730", "A359796", "A359811" ]
null
Seiichi Manyama, Jan 14 2023
2023-01-14T08:44:23
oeisdata/seq/A359/A359811.seq
6acbdcad61251350b2d40b48fed5f54e
A359812
a(n) = Sum_{d|n} (-1)^(d-1) * d^(n/d-1).
[ "1", "0", "2", "-2", "2", "-1", "2", "-12", "11", "-11", "2", "-27", "2", "-57", "108", "-200", "2", "-40", "2", "-653", "780", "-1013", "2", "-1177", "627", "-4083", "6644", "-11959", "2", "5043", "2", "-49680", "59172", "-65519", "18028", "-26670", "2", "-262125", "531612", "-713423", "2", "515723", "2", "-3144419", "5180382", "-4194281", "2" ]
[ "sign", "easy" ]
20
0
5
[ "A087909", "A359811", "A359812" ]
null
Seiichi Manyama, Jan 14 2023
2023-08-09T00:53:53
oeisdata/seq/A359/A359812.seq
57f48722248002e4cd3aa0b3d1868fba
A359813
Number of primes < 10^n with exactly one odd decimal digit.
[ "3", "12", "45", "171", "619", "2560", "10774", "46708", "202635", "904603", "4073767", "18604618", "85445767", "395944114", "1837763447", "8600149593" ]
[ "base", "nonn", "more" ]
14
0
5
[ "A030096", "A068690", "A154764", "A358685", "A358690", "A359813" ]
null
Zhining Yang, Jan 14 2023
2023-02-04T20:43:00
oeisdata/seq/A359/A359813.seq
42a6cb52dbdd65a063a83372fd4b1f9e
A359814
Dirichlet inverse of A359769, where A359769(n) = A353557(n) - A353556(n).
[ "1", "1", "0", "1", "0", "0", "0", "2", "-1", "0", "0", "1", "0", "0", "-1", "3", "0", "-1", "0", "1", "-1", "0", "0", "2", "-1", "0", "0", "1", "0", "-1", "0", "5", "-1", "0", "-1", "-1", "0", "0", "-1", "2", "0", "-1", "0", "1", "0", "0", "0", "4", "-1", "-1", "-1", "1", "0", "0", "-1", "2", "-1", "0", "0", "-1", "0", "0", "0", "8", "-1", "-1", "0", "1", "-1", "-1", "0", "-2", "0", "0", "0", "1", "-1", "-1", "0", "4", "0", "0", "0", "-1", "-1", "0", "-1", "2", "0", "0", "-1", "1", "-1", "0", "-1", "8" ]
[ "sign" ]
10
0
5
[ "A001222", "A003961", "A353556", "A353557", "A358777", "A359763", "A359769", "A359814", "A359815", "A359816" ]
null
Antti Karttunen, Jan 15 2023
2023-01-16T16:11:59
oeisdata/seq/A359/A359814.seq
95d9154eaf35c9f0caf180026922cb72
A359815
Dirichlet inverse of A359770, where A359770(n) = 1 if n and bigomega(n) are of different parity, otherwise 0.
[ "1", "-1", "0", "1", "0", "0", "0", "-2", "-1", "0", "0", "-1", "0", "0", "-1", "3", "0", "1", "0", "-1", "-1", "0", "0", "2", "-1", "0", "0", "-1", "0", "1", "0", "-5", "-1", "0", "-1", "-1", "0", "0", "-1", "2", "0", "1", "0", "-1", "0", "0", "0", "-4", "-1", "1", "-1", "-1", "0", "0", "-1", "2", "-1", "0", "0", "-1", "0", "0", "0", "8", "-1", "1", "0", "-1", "-1", "1", "0", "2", "0", "0", "0", "-1", "-1", "1", "0", "-4", "0", "0", "0", "-1", "-1", "0", "-1", "2", "0", "0", "-1", "-1", "-1", "0", "-1", "8" ]
[ "sign" ]
10
0
5
[ "A001222", "A003961", "A069345", "A353556", "A353557", "A358777", "A359763", "A359770", "A359814", "A359815", "A359816", "A359817" ]
null
Antti Karttunen, Jan 15 2023
2023-01-16T16:12:19
oeisdata/seq/A359/A359815.seq
e5e2c12f307cb558ec21dc250ac40171
A359816
Parity of A359815, where A359815 is the Dirichlet inverse of A359770, which is the characteristic function for numbers k such that k and bigomega(k) are of different parity.
[ "1", "1", "0", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "1", "0", "1", "0", "1", "1", "0", "0", "0", "1", "0", "0", "1", "0", "1", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "0", "1", "0", "1", "0", "0", "0", "0", "1", "1", "1", "1", "0", "0", "1", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "1", "1", "1", "0", "0", "0", "0", "0", "1", "1", "1", "0", "0", "0", "0", "0", "1", "1", "0", "1", "0", "0", "0", "1", "1", "1", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "0", "1" ]
[ "nonn" ]
11
0
5
[ "A001222", "A003961", "A353556", "A353557", "A359764", "A359770", "A359774", "A359781", "A359814", "A359815", "A359816", "A359817" ]
null
Antti Karttunen, Jan 15 2023
2023-01-16T15:44:11
oeisdata/seq/A359/A359816.seq
a27b022513a26940bd99bb17cbdc78ce
A359817
Positions of odd terms in A359815, where A359815 is the Dirichlet inverse of A359770, which is the characteristic function for numbers k such that k and bigomega(k) are of different parity.
[ "1", "2", "4", "9", "12", "15", "16", "18", "20", "21", "25", "28", "30", "32", "33", "35", "36", "39", "42", "44", "49", "50", "51", "52", "55", "57", "60", "65", "66", "68", "69", "70", "76", "77", "78", "84", "85", "87", "91", "92", "93", "95", "98", "100", "102", "108", "110", "111", "114", "115", "116", "119", "121", "123", "124", "128", "129", "130", "132", "133", "135", "138", "140", "141", "143", "145", "148", "154", "155", "156" ]
[ "nonn" ]
4
0
5
[ "A001222", "A359770", "A359815", "A359816", "A359817" ]
null
Antti Karttunen, Jan 15 2023
2023-01-15T19:51:24
oeisdata/seq/A359/A359817.seq
f4e69606a47289d7c0b62261689e65f9
A359818
Dirichlet inverse of A359549, where A359549 is the characteristic function for numbers that are either an odd squarefree number squared or twice such a number.
[ "1", "-1", "0", "1", "0", "0", "0", "-1", "-1", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "1", "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", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1" ]
[ "sign", "mult" ]
10
0
5
[ "A053866", "A143259", "A359549", "A359818" ]
null
Antti Karttunen, Jan 17 2023
2023-01-26T16:13:25
oeisdata/seq/A359/A359818.seq
3d3ee8156f78a7e4f21ef4cfd51ca0dc
A359819
Dirichlet inverse of A359590.
[ "1", "0", "-1", "-1", "-1", "0", "-1", "-1", "1", "0", "-1", "1", "-1", "0", "1", "1", "-1", "0", "-1", "1", "1", "0", "-1", "1", "1", "0", "-1", "1", "-1", "0", "-1", "1", "1", "0", "1", "-1", "-1", "0", "1", "1", "-1", "0", "-1", "1", "-1", "0", "-1", "-1", "1", "0", "1", "1", "-1", "0", "1", "1", "1", "0", "-1", "-1", "-1", "0", "-1", "-1", "1", "0", "-1", "1", "1", "0", "-1", "-1", "-1", "0", "-1", "1", "1", "0", "-1", "-1", "1", "0", "-1", "-1", "1", "0", "1", "1", "-1", "0", "1", "1", "1", "0", "1" ]
[ "sign", "mult" ]
11
0
5
[ "A152822", "A359590", "A359819" ]
null
Antti Karttunen, Jan 17 2023
2023-02-09T01:55:19
oeisdata/seq/A359/A359819.seq
39b5118be013198c5bd84a5894d74960
A359820
a(n) = 1 if n and n' are of different parity, otherwise 0. Here n' stands for the arithmetic derivative of n, A003415(n).
[ "0", "1", "1", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "1", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "0", "1" ]
[ "nonn" ]
13
0
5
[ "A000035", "A003415", "A129283", "A168036", "A347871", "A359820", "A359821", "A359822", "A359823", "A359824" ]
null
Antti Karttunen, Jan 14 2023
2023-01-14T18:36:39
oeisdata/seq/A359/A359820.seq
c453855c50a230d4c378e291d077c0a9
A359821
Numbers k whose arithmetic derivative, A003415(k), has the opposite parity to k.
[ "1", "2", "6", "9", "10", "14", "15", "18", "21", "22", "25", "26", "30", "33", "34", "35", "38", "39", "42", "46", "49", "50", "51", "54", "55", "57", "58", "62", "65", "66", "69", "70", "74", "77", "78", "81", "82", "85", "86", "87", "90", "91", "93", "94", "95", "98", "102", "106", "110", "111", "114", "115", "118", "119", "121", "122", "123", "126", "129", "130", "133", "134", "135", "138", "141", "142", "143", "145", "146", "150", "154" ]
[ "nonn", "easy" ]
8
0
5
[ "A003415", "A129283", "A168036", "A359820", "A359821", "A359822" ]
null
Antti Karttunen, Jan 14 2023
2023-01-14T17:19:20
oeisdata/seq/A359/A359821.seq
3d541ee3badca39f15a10281bda73405
A359822
Numbers k whose arithmetic derivative, A003415(k), has the same parity as k.
[ "0", "3", "4", "5", "7", "8", "11", "12", "13", "16", "17", "19", "20", "23", "24", "27", "28", "29", "31", "32", "36", "37", "40", "41", "43", "44", "45", "47", "48", "52", "53", "56", "59", "60", "61", "63", "64", "67", "68", "71", "72", "73", "75", "76", "79", "80", "83", "84", "88", "89", "92", "96", "97", "99", "100", "101", "103", "104", "105", "107", "108", "109", "112", "113", "116", "117", "120", "124", "125", "127", "128", "131", "132" ]
[ "nonn", "easy" ]
8
0
5
[ "A003415", "A129283", "A168036", "A359820", "A359821", "A359822" ]
null
Antti Karttunen, Jan 14 2023
2023-01-14T17:19:33
oeisdata/seq/A359/A359822.seq
2d4b7c0c274c57d979db6642d9c1b4de
A359823
Dirichlet inverse of A359820, where A359820 is the characteristic function of numbers whose parity differs from the parity of their arithmetic derivative (A003415).
[ "1", "-1", "0", "1", "0", "-1", "0", "-1", "-1", "-1", "0", "2", "0", "-1", "-1", "1", "0", "1", "0", "2", "-1", "-1", "0", "-3", "-1", "-1", "0", "2", "0", "1", "0", "-1", "-1", "-1", "-1", "0", "0", "-1", "-1", "-3", "0", "1", "0", "2", "0", "-1", "0", "4", "-1", "1", "-1", "2", "0", "1", "-1", "-3", "-1", "-1", "0", "1", "0", "-1", "0", "1", "-1", "1", "0", "2", "-1", "1", "0", "-2", "0", "-1", "0", "2", "-1", "1", "0", "4", "0", "-1", "0", "1", "-1", "-1", "-1", "-3", "0", "3", "-1", "2", "-1", "-1", "-1", "-5", "0" ]
[ "sign" ]
8
0
5
[ "A000035", "A003415", "A003961", "A359763", "A359780", "A359820", "A359823", "A359824" ]
null
Antti Karttunen, Jan 14 2023
2023-01-14T18:36:43
oeisdata/seq/A359/A359823.seq
177dc38ba61613c1c2c23244393cd510
A359824
Parity of A359823, where A359823 is the Dirichlet inverse of A359820.
[ "1", "1", "0", "1", "0", "1", "0", "1", "1", "1", "0", "0", "0", "1", "1", "1", "0", "1", "0", "0", "1", "1", "0", "1", "1", "1", "0", "0", "0", "1", "0", "1", "1", "1", "1", "0", "0", "1", "1", "1", "0", "1", "0", "0", "0", "1", "0", "0", "1", "1", "1", "0", "0", "1", "1", "1", "1", "1", "0", "1", "0", "1", "0", "1", "1", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "1", "1", "1" ]
[ "nonn" ]
8
0
5
[ "A003961", "A347082", "A347084", "A359764", "A359820", "A359823", "A359824", "A359825" ]
null
Antti Karttunen, Jan 14 2023
2023-01-14T18:36:46
oeisdata/seq/A359/A359824.seq
e93f2b5af26cf1fa8aa54145fba1abca
A359825
Positions of odd terms in A359823, where A359823 is the Dirichlet inverse of A359820.
[ "1", "2", "4", "6", "8", "9", "10", "14", "15", "16", "18", "21", "22", "24", "25", "26", "30", "32", "33", "34", "35", "38", "39", "40", "42", "46", "49", "50", "51", "54", "55", "56", "57", "58", "60", "62", "64", "65", "66", "69", "70", "74", "77", "78", "82", "84", "85", "86", "87", "88", "90", "91", "93", "94", "95", "96", "98", "102", "104", "106", "110", "111", "114", "115", "118", "119", "120", "121", "122", "123", "126", "128", "129" ]
[ "nonn" ]
5
0
5
[ "A003415", "A347082", "A347084", "A359765", "A359783", "A359820", "A359823", "A359824", "A359825" ]
null
Antti Karttunen, Jan 14 2023
2023-01-14T12:40:17
oeisdata/seq/A359/A359825.seq
0eb72c1dafde24c19eebde7d106a5455
A359826
Parity of A353348, where A353348 is Dirichlet inverse of the characteristic function for numbers k such that A048675(k) is a multiple of 3.
[ "1", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "1", "0", "1", "1" ]
[ "nonn" ]
16
0
5
[ "A003961", "A048675", "A332820", "A353348", "A353350", "A359826", "A359827", "A359836" ]
null
Antti Karttunen, Jan 17 2023
2023-01-24T12:34:57
oeisdata/seq/A359/A359826.seq
5291ef120eddcb263f820c1da0280186
A359827
Positions of odd terms in A353348, where A353348 is Dirichlet inverse of the characteristic function for numbers k where A048675(k) is a multiple of 3.
[ "1", "6", "8", "14", "15", "20", "26", "27", "33", "35", "38", "44", "48", "50", "51", "58", "63", "65", "68", "69", "74", "77", "84", "86", "90", "92", "93", "95", "106", "110", "112", "117", "119", "120", "122", "123", "124", "125", "141", "142", "143", "145", "147", "156", "158", "160", "161", "162", "164", "170", "171", "177", "178", "185", "188", "198", "201", "202", "208", "209", "210", "214", "215", "217", "219", "221", "226" ]
[ "nonn" ]
5
0
5
[ "A048675", "A332820", "A353348", "A353350", "A359826", "A359827" ]
null
Antti Karttunen, Jan 17 2023
2023-01-17T16:32:28
oeisdata/seq/A359/A359827.seq
5ce85d9058db8267cd90cf953c8a8f92
A359828
Characteristic function for primitive elements of A235992.
[ "1", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "1", "0", "0", "0", "1", "0", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "1", "0", "0", "1", "0", "1" ]
[ "nonn" ]
14
0
5
[ "A003415", "A235992", "A358680", "A359828", "A359829", "A359831" ]
null
Antti Karttunen, Jan 17 2023
2025-01-17T09:11:34
oeisdata/seq/A359/A359828.seq
a9fc415a48a676df5d762ceffe654ac5
A359829
Primitive elements of A235992: numbers k with an even arithmetic derivative that cannot be represented as a product of two smaller such numbers.
[ "1", "4", "8", "9", "12", "15", "20", "21", "24", "25", "28", "33", "35", "39", "40", "44", "49", "51", "52", "55", "56", "57", "65", "68", "69", "76", "77", "85", "87", "88", "91", "92", "93", "95", "104", "111", "115", "116", "119", "121", "123", "124", "129", "133", "136", "141", "143", "145", "148", "152", "155", "159", "161", "164", "169", "172", "177", "183", "184", "185", "187", "188", "201", "203", "205", "209", "212", "213" ]
[ "nonn" ]
28
0
5
[ "A003415", "A046315", "A235992", "A358680", "A359828", "A359829", "A359831" ]
null
Antti Karttunen, Jan 17 2023
2023-01-19T09:35:53
oeisdata/seq/A359/A359829.seq
eaaf6a70f05e8b70e60b3e021be22c2e
A359830
Numbers k such that A048675(k) is not a multiple of 3.
[ "2", "3", "4", "5", "7", "9", "10", "11", "12", "13", "16", "17", "18", "19", "21", "22", "23", "24", "25", "28", "29", "30", "31", "32", "34", "37", "39", "40", "41", "42", "43", "45", "46", "47", "49", "52", "53", "54", "55", "56", "57", "59", "60", "61", "62", "66", "67", "70", "71", "72", "73", "75", "76", "78", "79", "80", "81", "82", "83", "85", "87", "88", "89", "91", "94", "96", "97", "98", "99", "100", "101", "102", "103", "104", "105", "107", "108" ]
[ "nonn" ]
9
0
5
[ "A000040", "A003961", "A048675", "A332820", "A332821", "A332822", "A348717", "A353348", "A353350", "A359830" ]
null
Antti Karttunen, Jan 17 2023
2023-01-18T02:21:37
oeisdata/seq/A359/A359830.seq
171393952e2555f9a229c20c88f58ba8
A359831
Nonprimitive elements of A235992: numbers k such that their arithmetic derivative (A003415) is even, and also for some divisor d|k, 1<d<k, both d and k/d have even derivative.
[ "16", "32", "36", "48", "60", "64", "72", "80", "81", "84", "96", "100", "108", "112", "120", "128", "132", "135", "140", "144", "156", "160", "168", "176", "180", "189", "192", "196", "200", "204", "208", "216", "220", "224", "225", "228", "240", "252", "256", "260", "264", "272", "276", "280", "288", "297", "300", "304", "308", "312", "315", "320", "324", "336", "340", "348", "351", "352", "360", "364", "368", "372", "375" ]
[ "nonn" ]
7
0
5
[ "A003415", "A235992", "A358680", "A359828", "A359829", "A359831" ]
null
Antti Karttunen, Jan 17 2023
2023-01-17T16:32:42
oeisdata/seq/A359/A359831.seq
31cc678643f872e9b70db4f16b803d14
A359832
a(n) = 1 if the 2-adic valuation of n is either 0 or odd, otherwise 0.
[ "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1" ]
[ "nonn", "mult" ]
18
0
5
[ "A000035", "A007814", "A048675", "A328981", "A359794", "A359832", "A359833" ]
null
Antti Karttunen, Jan 24 2023
2023-01-25T22:23:08
oeisdata/seq/A359/A359832.seq
a1d5e3d2944b2f2ddde978b2a16355f5
A359833
Dirichlet inverse of A359832, where A359832(n) = 1 if the 2-adic valuation of n is either 0 or odd, otherwise 0.
[ "1", "-1", "-1", "1", "-1", "1", "-1", "-2", "0", "1", "-1", "-1", "-1", "1", "1", "3", "-1", "0", "-1", "-1", "1", "1", "-1", "2", "0", "1", "0", "-1", "-1", "-1", "-1", "-5", "1", "1", "1", "0", "-1", "1", "1", "2", "-1", "-1", "-1", "-1", "0", "1", "-1", "-3", "0", "0", "1", "-1", "-1", "0", "1", "2", "1", "1", "-1", "1", "-1", "1", "0", "8", "1", "-1", "-1", "-1", "1", "-1", "-1", "0", "-1", "1", "0", "-1", "1", "-1", "-1", "-3", "0", "1", "-1", "1", "1", "1", "1", "2", "-1", "0", "1", "-1", "1", "1", "1", "5", "-1", "0", "0", "0", "-1", "-1", "-1", "2", "-1" ]
[ "sign", "mult" ]
12
0
5
[ "A000045", "A007814", "A359832", "A359833", "A359834" ]
null
Antti Karttunen, Jan 24 2023
2023-01-25T22:23:13
oeisdata/seq/A359/A359833.seq
2e723ed1862a4daee1d5f84a26f6a3e5
A359834
Parity of Dirichlet inverse of A359832, where A359832(n) = 1 if the 2-adic valuation of n is either 0 or odd, otherwise 0.
[ "1", "1", "1", "1", "1", "1", "1", "0", "0", "1", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "0", "1", "0", "1", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "1", "0", "0", "1", "1", "1", "0", "1", "0", "1", "1", "1", "1", "1", "1", "0", "0", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "0", "1", "0", "1", "1", "1", "1", "1", "1", "1", "0", "0", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "0", "0" ]
[ "nonn", "mult" ]
11
0
5
[ "A359590", "A359831", "A359832", "A359834" ]
null
Antti Karttunen, Jan 25 2023
2023-01-26T12:17:25
oeisdata/seq/A359/A359834.seq
54ae1b0a420daffb7df240e6c07cd324
A359835
a(n) = 0 if A353418(n) = 0, otherwise 1. Here A353418 is Dirichlet inverse of the characteristic function for numbers k at which points A156552(k) is a multiple of 3.
[ "1", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1", "0", "1", "1" ]
[ "nonn" ]
8
0
5
[ "A156552", "A353269", "A353418", "A359835", "A359836" ]
null
Antti Karttunen, Jan 21 2023
2023-01-25T17:29:30
oeisdata/seq/A359/A359835.seq
f2dc884c94a6ce4ce91fdef73897fae6
A359836
Parity of A353418, where A353418 is Dirichlet inverse of the characteristic function for numbers k where A156552(k) is a multiple of 3.
[ "1", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "1", "0", "1", "1" ]
[ "nonn" ]
13
0
5
[ "A003961", "A156552", "A348717", "A353269", "A353348", "A353418", "A359826", "A359835", "A359836" ]
null
Antti Karttunen, Jan 17 2023
2023-01-26T12:17:29
oeisdata/seq/A359/A359836.seq
c0b8da9624aec1c78d437b7c6727860e
A359837
Decimal expansion of the unsigned ratio of similitude between an equilateral reference triangle and its first Morley triangle.
[ "1", "8", "4", "7", "9", "2", "5", "3", "0", "9", "0", "4", "0", "9", "5", "3", "7", "2", "7", "0", "1", "3", "5", "2", "0", "4", "7", "5", "7", "2", "2", "0", "3", "7", "5", "5", "8", "7", "0", "9", "1", "3", "5", "5", "9", "7", "9", "2", "6", "5", "1", "7", "1", "7", "2", "3", "5", "6", "0", "7", "8", "1", "3", "0", "2", "0", "1", "7", "9", "1", "3", "3", "4", "3", "5", "7", "1", "9", "9", "7", "6", "2", "1", "3", "4", "2", "5", "3", "2", "7" ]
[ "easy", "nonn", "cons" ]
30
0
5
[ "A019819", "A019829", "A019879", "A020760", "A359837" ]
null
Frank M Jackson, Jan 14 2023
2025-02-05T10:03:36
oeisdata/seq/A359/A359837.seq
9bcbc8e3d0bb0d47d9497ccca2985ea4
A359838
Continued fraction for binary expansion of A359456 interpreted in base 2.
[ "0", "1", "3", "3", "1", "2", "1", "262143", "3", "1", "3", "3", "1", "1532495540865888858358347027150309183618739122183602175", "4", "3", "1", "3", "262143", "1", "2", "1", "3", "3", "1" ]
[ "nonn", "base", "cofr" ]
20
0
5
[ "A014710", "A317538", "A317539", "A359456", "A359457", "A359458", "A359838" ]
null
A.H.M. Smeets, Jan 14 2023
2023-02-16T05:37:47
oeisdata/seq/A359/A359838.seq
50f007da431f40837e13defc3bc742d5
A359839
Numbers k such that k, k + 1 and k + 2 are 3 consecutive Niven (Harshad) numbers that are also divisible by a square.
[ "2023", "4912", "12103", "17575", "23273", "51424", "52675", "60399", "78650", "80800", "87723", "93624", "100303", "112624", "117962", "121224", "122875", "182182", "193075", "200752", "228175", "235024", "245725", "245726", "249500", "263275", "306963", "320704", "333475", "373490", "403675", "416583", "421072", "444624", "448000" ]
[ "nonn", "base" ]
13
0
5
[ "A005349", "A013929", "A060159", "A068781", "A070258", "A141769", "A154701", "A235578", "A330927", "A330928", "A330929", "A330930", "A359839" ]
null
Bernard Schott, Jan 15 2023
2025-01-05T19:51:42
oeisdata/seq/A359/A359839.seq
bd36459801c94fbc81ba98ce5d8c64d2
A359840
Numbers k that are the representation of primes in base 4 and in base 5.
[ "2", "3", "23", "131", "133", "221", "1211", "1231", "2023", "2111", "2113", "2311", "3013", "3211", "3233", "3323", "10031", "10033", "10121", "12011", "12121", "13223", "13331", "20131", "20203", "22111", "23233", "31313", "32033", "32303", "33133", "33331", "100123", "100211", "100231", "101003", "101333", "103333", "110021", "111211" ]
[ "nonn", "base" ]
29
0
5
[ "A004678", "A004679", "A007090", "A007091", "A235474", "A235615", "A340290", "A359840" ]
null
Bernard Schott, Jan 15 2023
2023-01-20T09:02:53
oeisdata/seq/A359/A359840.seq
c48024f636fbe3e90bc6ae1e73786996
A359841
Integers Xd which are divisible by X, where d is the last decimal digit.
[ "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "22", "24", "26", "28", "30", "33", "36", "39", "40", "44", "48", "50", "55", "60", "66", "70", "77", "80", "88", "90", "99", "100", "110", "120", "130", "140", "150", "160", "170", "180", "190", "200", "210", "220", "230", "240", "250", "260", "270", "280", "290", "300", "310", "320", "330", "340", "350", "360", "370", "380", "390", "400", "410", "420" ]
[ "nonn", "base", "easy" ]
36
0
5
[ "A008592", "A034837", "A059995", "A178157", "A292683", "A359841" ]
null
Bernard Schott, Jan 15 2023
2023-01-20T15:39:11
oeisdata/seq/A359/A359841.seq
a97aed9a827b52f0c5a12b4ee779cea9
A359842
a(n) = Sum_{k=0..n} binomial(n*k,n+k).
[ "1", "0", "1", "90", "13690", "3443275", "1308315371", "701623884514", "505274768721332", "470638793249281593", "550707386335951810915", "790898932162231992184327", "1367864138835420575101044139", "2804370191530797723173615407860", "6725366044028696102055907486691290" ]
[ "nonn" ]
13
0
5
[ "A096131", "A099237", "A226391", "A359842" ]
null
Vaclav Kotesovec, Jan 15 2023
2023-01-19T09:33:58
oeisdata/seq/A359/A359842.seq
c93db2b7411a0a5f102d24203db801e3
A359843
Array listed by antidiagonals: row m is the numbers k such that prime(i)+k is prime for i from m to j where prime(j+1) = A360228(m).
[ "0", "1", "0", "3", "2", "0", "5", "8", "6", "0", "9", "14", "96", "90", "0", "11", "26", "1476", "16050" ]
[ "nonn", "more", "hard" ]
32
0
5
[ "A001359", "A022006", "A022008", "A040976", "A359843" ]
null
Robert Israel, Jan 30 2023
2023-02-01T08:17:00
oeisdata/seq/A359/A359843.seq
4bd7fcdd4c474d36bc5eecb364a6b0d0
A359844
a(n) = ((2*n+1)^8 + 1)/2.
[ "1", "3281", "195313", "2882401", "21523361", "107179441", "407865361", "1281445313", "3487878721", "8491781521", "18911429681", "39155492641", "76293945313", "141214768241", "250123206481", "426445518721", "703204309121", "1125937695313", "1756239726961", "2676004630241", "3992462614561", "5844100138801" ]
[ "nonn", "easy" ]
16
0
5
[ "A000012", "A001477", "A050492", "A175110", "A175113", "A219086", "A359844" ]
null
Jianing Song, Jan 15 2023
2025-01-23T03:36:44
oeisdata/seq/A359/A359844.seq
0809d3d770b1694f5000f390ad0c6452
A359845
Centered triangular numbers which are products of four distinct primes.
[ "9010", "20710", "39610", "67735", "91885", "108946", "163846", "191710", "197110", "237010", "243010", "293710", "307135", "342010", "349210", "409510", "461206", "466210", "474610", "488206", "526585", "544510", "619210", "625006", "640594", "656374", "678385", "688510", "698710", "708985", "789526", "890506", "934966", "985366", "992674", "1039585" ]
[ "nonn" ]
9
0
5
[ "A005448", "A046386", "A359845" ]
null
Massimo Kofler, Jan 15 2023
2023-01-28T18:25:59
oeisdata/seq/A359/A359845.seq
de9b57b15d02417090133606d4c4eb51
A359846
a(n) = (((5 - (n mod 2))*10^(3 + n*(9/2) - (n mod 2)*(5/2)))^2 + 2)/81.
[ "308642", "1975308642", "308641975308641975308642", "1975308641975308641975308642", "308641975308641975308641975308641975308642", "1975308641975308641975308641975308641975308642", "308641975308641975308641975308641975308641975308641975308642" ]
[ "nonn", "easy", "base" ]
49
0
5
[ "A014824", "A359846" ]
null
Thomas Scheuerle, Jan 15 2023
2025-01-23T12:37:59
oeisdata/seq/A359/A359846.seq
da5cd14a6faa87df0d89fbe5e2baa8d2
A359847
Oblong numbers k for which phi(k) is also an oblong number.
[ "6", "42", "182", "650", "930", "4830", "7482", "9506", "12882", "13572", "16770", "79242", "167690", "181902", "228006", "289982", "380072", "3480090", "5209806", "6872262", "10102862", "16068072", "56002772", "56648202", "59174556", "70299840", "74831150", "123287712", "261517412", "342601590", "356322252", "455459622", "536223492", "1057452842" ]
[ "nonn" ]
33
0
5
[ "A000010", "A002378", "A236386", "A287472", "A359847" ]
null
Alexandru Petrescu, Jan 15 2023
2023-02-17T02:06:08
oeisdata/seq/A359/A359847.seq
c6487fefafb3e99709e50fa0ccf5d0dc
A359848
a(n) is the smallest tribonacci number (A000073) with exactly n distinct prime factors.
[ "1", "2", "24", "504", "35890", "8646064", "1697490356184", "120879712950776", "98079530178586034536500564", "748829299860308729347600", "119816209721856219780831547518850", "15418262617564622254988364568360573618470100684551892712710640455037970" ]
[ "nonn" ]
11
0
5
[ "A000073", "A001221", "A060319", "A359848", "A359849", "A359850" ]
null
Ilya Gutkovskiy, Jan 15 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359848.seq
a75ac4c7d36a1252cd8e3474ab82d148
A359849
a(n) is the smallest tetranacci number (A000078) with exactly n distinct prime factors.
[ "1", "2", "15", "1490", "39648", "28074040", "100808458960497", "9966792788887776", "4997150614173857218560", "1835682610171974487231869", "889487735339682550112673527109223032", "52499930084496170026238596234557616056408988199026780675759699719704592" ]
[ "nonn" ]
11
0
5
[ "A000078", "A001221", "A060319", "A359848", "A359849", "A359851" ]
null
Ilya Gutkovskiy, Jan 15 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359849.seq
8a08cce8e1bd6f30e962755fa11f5934
A359850
a(n) is the index of the smallest tribonacci number (A000073) with exactly n distinct prime factors.
[ "2", "4", "8", "13", "20", "29", "49", "56", "101", "93", "124", "268", "221" ]
[ "nonn", "more" ]
11
0
5
[ "A000073", "A001221", "A060320", "A359848", "A359850", "A359851" ]
null
Ilya Gutkovskiy, Jan 15 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359850.seq
16f9e8b6ab9edebb1bfdd8384061b17b
A359851
a(n) is the index of the smallest tetranacci number (A000078) with exactly n distinct prime factors.
[ "3", "5", "8", "15", "20", "30", "53", "60", "80", "89", "130", "252" ]
[ "nonn", "more" ]
11
0
5
[ "A000078", "A001221", "A060320", "A359849", "A359850", "A359851" ]
null
Ilya Gutkovskiy, Jan 15 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359851.seq
5d323c8de9ffb3b387aed68699b9e459
A359852
a(n) is the smallest Fibonacci n-step number with exactly n distinct prime factors.
[ "21", "504", "39648", "6930", "12669125245488", "471771076278370", "32818036405994618064", "71577732779401085355729600", "204945946670840805166309694624676331385919836360545974559162291811394735721440" ]
[ "nonn" ]
12
0
5
[ "A001221", "A060319", "A359848", "A359849", "A359852", "A359853" ]
null
Ilya Gutkovskiy, Jan 15 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359852.seq
a50a0f67dda9dd500d0d7fe1047a0e67
A359853
a(n) is the index of the smallest Fibonacci n-step number with exactly n distinct prime factors.
[ "8", "13", "20", "18", "50", "56", "73", "95", "267" ]
[ "nonn", "more" ]
11
0
5
[ "A001221", "A060320", "A359850", "A359851", "A359852", "A359853" ]
null
Ilya Gutkovskiy, Jan 15 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359853.seq
f88b461979d7150faced9496048e65e8
A359854
a(n) is the least n-gonal number that is the product of n distinct primes, or 0 if there are none.
[ "6", "66", "0", "11310", "303810", "28962934", "557221665", "15529888374", "1219300152070", "23900058257790", "1231931106828345", "500402553453949510", "14990069451769732194", "610385355391371697410" ]
[ "nonn", "more" ]
18
0
5
[ "A057145", "A358862", "A358863", "A359854" ]
null
Robert Israel, Jan 15 2023
2023-01-24T12:34:17
oeisdata/seq/A359/A359854.seq
5964693b07ee7f6ebf78c3516c1e91fd
A359855
Array read by antidiagonals: T(n,k) is the number of Hamiltonian cycles in the stacked prism graph P_n X C_k, n >= 1, k >= 2.
[ "1", "1", "4", "1", "3", "4", "1", "6", "6", "4", "1", "5", "22", "12", "4", "1", "8", "30", "82", "24", "4", "1", "7", "86", "160", "306", "48", "4", "1", "10", "126", "776", "850", "1142", "96", "4", "1", "9", "318", "1484", "7010", "4520", "4262", "192", "4", "1", "12", "510", "6114", "18452", "63674", "24040", "15906", "384", "4", "1", "11", "1182", "12348", "126426", "229698", "578090", "127860", "59362", "768", "4" ]
[ "nonn", "tabl" ]
32
0
5
[ "A000012", "A003699", "A003731", "A003945", "A103889", "A123932", "A180582", "A180583", "A180584", "A180585", "A180586", "A180587", "A180588", "A222196", "A222197", "A270273", "A321172", "A359855" ]
null
Andrew Howroyd, Feb 18 2025
2025-02-18T15:34:02
oeisdata/seq/A359/A359855.seq
a3b2e8df00d3eb684cd33cc3af52051b
A359856
Number of permutations of [1..n] which are indecomposable by direct and skew sums.
[ "1", "1", "0", "0", "2", "22", "202", "1854", "17866", "183806", "2029850", "24081006", "306486314", "4175102110", "60708557626", "939518187726", "15430666746826", "268214861561726", "4921023843969242", "95066628485598126", "1929291834938927210", "41042364285004263262", "913409469123533445754", "21227246586149632119438" ]
[ "nonn" ]
14
0
5
[ "A003319", "A111111", "A359856" ]
null
Ludovic Schwob, Jan 16 2023
2023-02-10T22:15:27
oeisdata/seq/A359/A359856.seq
4d773b1ea3ed00ce9723f056e0250d45
A359857
a(1) = 1, a(2) = 2, and let i,j represent a(n-2), a(n-1) respectively. For n > 2: If only one of i,j is prime, a(n) = least novel multiple of i+j. If i,j are both prime, a(n) = least novel multiple of i*j. If both i,j are nonprime, a(n) is least novel k prime to both i and j.
[ "1", "2", "3", "6", "9", "5", "14", "19", "33", "52", "7", "59", "413", "472", "11", "483", "494", "17", "511", "528", "13", "541", "7033", "7574", "15", "23", "38", "61", "99", "160", "29", "189", "218", "25", "21", "4", "31", "35", "66", "37", "103", "3811", "3914", "27", "41", "68", "109", "177", "286", "43", "329", "372", "53", "425", "478", "39", "47", "86", "133", "45", "8" ]
[ "nonn" ]
14
0
5
[ "A359256", "A359557", "A359857" ]
null
David James Sycamore, Jan 16 2023
2023-01-16T11:10:28
oeisdata/seq/A359/A359857.seq
8c27231234ce48f03c19d1ec2ebab1f7
A359858
a(0) = 0; for n > 0, a(n) is the smallest positive number not occurring earlier such that the ones' complement of the binary string of a(n-1) + a(n) does not appear in the binary string concatenation of a(0)..a(n-1).
[ "0", "2", "6", "5", "3", "8", "14", "18", "20", "12", "24", "23", "9", "27", "37", "10", "22", "25", "7", "40", "39", "52", "42", "49", "15", "32", "59", "35", "56", "38", "53", "41", "50", "44", "47", "81", "13", "78", "16", "75", "57", "34", "94", "61", "30", "98", "60", "31", "97", "58", "33", "122", "63", "28", "127", "55", "36", "126", "65", "118", "67", "95", "88", "74", "109", "76", "86", "99", "84", "101", "82", "80", "103", "187" ]
[ "nonn", "base", "look" ]
10
0
5
[ "A007088", "A035327", "A355611", "A357082", "A359858" ]
null
Scott R. Shannon, Jan 16 2023
2023-01-16T09:07:41
oeisdata/seq/A359/A359858.seq
1e44e451181eed9ed849bb87fb799ec9
A359859
Number of vertices among all distinct circles that can be constructed from a 2 x n square grid of points using only a compass.
[ "2", "40", "190", "740", "1824", "3956", "7314", "12956", "20684", "32276", "47348", "68516", "94550", "128780", "170106", "222252", "283418", "358756", "445534", "550868", "670358", "811556", "970740", "1157168", "1363700", "1601384", "1864524", "2164668", "2493136", "2865176", "3269606", "3724112", "4215536", "4762284", "5353050" ]
[ "nonn" ]
20
0
5
[ "A001859", "A359252", "A359859", "A359860", "A359861", "A359862" ]
null
Scott R. Shannon, Jan 16 2023
2024-10-11T09:15:35
oeisdata/seq/A359/A359859.seq
bbcc4f2f61f77871c2f32e118d77a4cd
A359860
Number of regions among all distinct circles that can be constructed from a 2 X n square grid of points using only a compass.
[ "3", "45", "231", "865", "2081", "4489", "8211", "14401", "22857", "35445", "51741", "74397", "102271", "138801", "182739", "238181", "303175", "383097", "474995", "586021", "712003", "860829", "1028225", "1223773", "1440593", "1689993", "1965525", "2279509", "2622993", "3011405", "3433615", "3907241", "4419261", "4988781", "5603271" ]
[ "nonn" ]
15
0
5
[ "A001859", "A359253", "A359859", "A359860", "A359861", "A359862" ]
null
Scott R. Shannon, Jan 16 2023
2024-10-11T13:57:35
oeisdata/seq/A359/A359860.seq
72be8596cc2a0ef21870e9e99e7e46a1
A359861
Number of edges among all distinct circles that can be constructed from a 2 X n square grid of points using only a compass.
[ "4", "84", "420", "1604", "3904", "8444", "15524", "27356", "43540", "67720", "99088", "142912", "196820", "267580", "352844", "460432", "586592", "741852", "920528", "1136888", "1382360", "1672384", "1998964", "2380940", "2804292", "3291376", "3830048", "4444176", "5116128", "5876580", "6703220", "7631352", "8634796", "9751064", "10956320" ]
[ "nonn" ]
13
0
5
[ "A001859", "A359254", "A359859", "A359860", "A359861", "A359862" ]
null
Scott R. Shannon, Jan 16 2023
2024-10-11T07:56:17
oeisdata/seq/A359/A359861.seq
6e3afb33b8b2966bcf2d9d98a9d196f2
A359862
Irregular table read by rows: T(n,k) is the number of k-gons, k>=2, among all distinct circles that can be constructed from a 2 x n square grid of points using only a compass.
[ "3", "0", "16", "29", "0", "102", "117", "10", "2", "4", "368", "402", "64", "26", "1", "12", "860", "903", "252", "52", "0", "2", "12", "1812", "2028", "520", "110", "4", "3", "24", "3168", "3841", "960", "204", "8", "6", "32", "5420", "6804", "1748", "362", "24", "11", "44", "8388", "10987", "2826", "552", "46", "14", "56", "12808", "17122", "4448", "922", "72", "17", "64", "18348", "25257", "6594", "1370", "82", "26" ]
[ "nonn", "tabf" ]
12
0
5
[ "A001859", "A359258", "A359859", "A359860", "A359861", "A359862" ]
null
Scott R. Shannon, Jan 16 2023
2023-01-17T09:56:59
oeisdata/seq/A359/A359862.seq
61c1c17933248e5a2d2a71ca986b7885
A359863
a(n) = Sum_{d|n} d^(n/d) * (n/d)^d.
[ "1", "4", "6", "24", "10", "156", "14", "528", "747", "1620", "22", "15000", "26", "12572", "60780", "98336", "34", "397908", "38", "1484840", "1500324", "495660", "46", "18514992", "9765675", "2768948", "28697868", "85098552", "58", "375843660", "62", "570425408", "471565380", "75759684", "2626093820", "7623165384", "74", "378536012" ]
[ "nonn" ]
22
0
5
[ "A359004", "A359863" ]
null
Seiichi Manyama, Jan 16 2023
2023-08-09T02:03:54
oeisdata/seq/A359/A359863.seq
88a14ec6f420e62ac7d021792cf8995f
A359864
a(n) is the number of solutions to the congruence x^y == y^x (mod n) where 0 <= x,y <= n.
[ "4", "3", "4", "7", "8", "9", "18", "19", "18", "17", "22", "27", "30", "31", "28", "67", "40", "37", "60", "55", "52", "57", "80", "87", "64", "73", "108", "85", "78", "75", "102", "239", "74", "97", "74", "115", "102", "125", "110", "191", "108", "123", "118", "151", "140", "149", "162", "331", "134", "133", "128", "201", "184", "217", "178", "299", "202", "163", "178", "251" ]
[ "nonn" ]
25
0
5
[ "A355069", "A359864" ]
null
Darío Clavijo, Jan 16 2023
2023-07-12T11:20:00
oeisdata/seq/A359/A359864.seq
269c5f37ebf0a98ade5ffbe6f318b0be
A359865
a(n) is the number of k > 0 such that n-1-2*k >= 0 and a(n-1-2*k) * a(n-1) = a(n-1-k)^2.
[ "0", "0", "0", "1", "1", "1", "1", "1", "2", "0", "0", "1", "2", "0", "2", "0", "3", "2", "3", "2", "1", "2", "2", "1", "0", "2", "3", "1", "0", "2", "2", "4", "4", "2", "3", "1", "4", "1", "1", "1", "4", "3", "1", "1", "5", "0", "2", "4", "4", "2", "1", "3", "0", "2", "0", "3", "1", "4", "2", "1", "5", "0", "3", "1", "5", "0", "4", "3", "0", "5", "1", "6", "1", "2", "3", "0", "6", "2", "4", "4", "2", "4", "3", "2", "2", "5", "2" ]
[ "nonn" ]
13
0
5
[ "A308638", "A359865" ]
null
Rémy Sigrist, Jan 16 2023
2023-12-22T10:36:13
oeisdata/seq/A359/A359865.seq
ed38bc6b44feefa0a179561c91bf0e37
A359866
a(n) is the number of k > 0 such that n-1-2*k >= 0 and a(n-1-2*k) >= a(n-1-k) >= a(n-1).
[ "0", "0", "0", "1", "0", "1", "0", "1", "1", "0", "3", "0", "4", "0", "3", "0", "3", "1", "0", "7", "0", "6", "0", "7", "0", "6", "0", "7", "1", "0", "9", "0", "10", "0", "8", "0", "10", "0", "9", "0", "10", "1", "0", "11", "0", "14", "0", "13", "0", "14", "0", "12", "0", "13", "1", "1", "3", "0", "17", "0", "17", "0", "18", "0", "17", "0", "18", "0", "17", "1", "2", "3", "0", "21", "0", "23", "0", "22", "0", "23", "0" ]
[ "nonn", "look" ]
11
0
5
[ "A359866", "A359867" ]
null
Rémy Sigrist, Jan 16 2023
2023-01-22T03:01:36
oeisdata/seq/A359/A359866.seq
966b1004c2d686691bcf6adb42eaa0d5
A359867
a(n) is the number of k > 0 such that n-1-2*k >= 0 and a(n-1-2*k) >= a(n-1-k) + a(n-1).
[ "0", "0", "0", "1", "0", "1", "1", "0", "3", "0", "2", "1", "1", "3", "0", "4", "0", "4", "1", "1", "2", "1", "3", "0", "6", "0", "7", "0", "8", "0", "6", "2", "1", "7", "0", "8", "0", "10", "0", "9", "1", "7", "2", "4", "4", "2", "7", "1", "11", "0", "15", "0", "13", "1", "9", "2", "7", "3", "4", "7", "2", "12", "0", "18", "0", "18", "1", "11", "2", "9", "3", "7", "5", "5", "6", "4", "7", "3", "10", "1", "15", "0", "19" ]
[ "nonn" ]
9
0
5
[ "A359866", "A359867" ]
null
Rémy Sigrist, Jan 16 2023
2023-01-22T03:01:33
oeisdata/seq/A359/A359867.seq
6b175c5193a75692a11bdb91051fccd8
A359868
a(n) is the smallest prime q such that A305411(n) + q is a square.
[ "13", "11", "19", "107", "101", "257", "467", "173", "167", "1601", "719", "701", "347", "569", "929", "1931", "479", "467", "719", "1163", "683", "1613", "2843", "941", "1997", "1307", "1907", "2549", "1823", "6869", "2957", "1487", "2141", "2777", "1931", "1823", "1811", "4253", "2273", "4877", "5711", "2663", "7673", "5081", "4871", "4799", "4643" ]
[ "nonn" ]
19
0
5
[ "A000040", "A000290", "A305411", "A359868" ]
null
Can Güllü, Jan 16 2023
2023-02-03T12:21:44
oeisdata/seq/A359/A359868.seq
360c7b2552078aeb4257c4170f971a4a
A359869
Numbers whose product of distinct prime factors is less than the sum of its prime factors (with repetition).
[ "4", "8", "9", "12", "16", "18", "24", "25", "27", "32", "36", "40", "48", "49", "50", "54", "64", "72", "80", "81", "96", "98", "100", "108", "112", "121", "125", "128", "144", "160", "162", "169", "192", "196", "200", "216", "224", "225", "242", "243", "250", "256", "288", "289", "320", "324", "338", "343", "361", "375", "384", "392", "400", "405", "432", "448", "484", "486", "500" ]
[ "nonn" ]
19
0
5
[ "A001414", "A007947", "A359869" ]
null
Johan Lindgren, Jan 16 2023
2023-01-20T09:03:24
oeisdata/seq/A359/A359869.seq
12af9d6ad2134addcfe40fdc4d182bc2
A359870
Numbers whose product of distinct prime factors is greater than the sum of its prime factors (with repetition).
[ "1", "6", "10", "14", "15", "20", "21", "22", "26", "28", "30", "33", "34", "35", "38", "39", "42", "44", "45", "46", "51", "52", "55", "56", "57", "58", "60", "62", "63", "65", "66", "68", "69", "70", "74", "75", "76", "77", "78", "82", "84", "85", "86", "87", "88", "90", "91", "92", "93", "94", "95", "99", "102", "104", "105", "106", "110", "111", "114", "115", "116", "117" ]
[ "nonn" ]
45
0
5
[ "A001414", "A006881", "A007947", "A120944", "A359869", "A359870" ]
null
Johan Lindgren, Jan 16 2023
2023-02-24T04:54:22
oeisdata/seq/A359/A359870.seq
43a96e78cb2e93e579dc4c03c5ccff61
A359871
Absolute discriminants of imaginary quadratic number fields with elementary bicyclic 5-class group (5,5)
[ "11199", "12451", "17944", "30263", "33531", "37363", "38047", "39947", "42871", "53079", "54211", "58424", "61556", "62632", "63411", "64103", "65784", "66328", "67031", "67063", "67128", "69811", "72084", "74051", "75688", "83767", "84271", "85099", "85279", "87971", "89751", "90795", "90868", "92263", "98591", "99031", "99743" ]
[ "easy", "nonn" ]
13
0
5
[ "A242863", "A359291", "A359871", "A359872" ]
null
Daniel Constantin Mayer, Jan 16 2023
2023-02-10T21:13:21
oeisdata/seq/A359/A359871.seq
c45d43ef1f5239399a860e789aadd260
A359872
Absolute discriminants of imaginary quadratic number fields with elementary bicyclic 7-class group (7,7).
[ "63499", "118843", "124043", "149519", "159592", "170679", "183619", "185723", "220503", "226691", "227387", "227860", "236931", "240347", "240655", "247252", "260111", "268739", "272179", "275636", "294935", "299627", "301211", "308531", "318547", "346883", "361595", "366295", "373655", "465719", "489576", "491767", "501576", "506551", "511988", "518879", "528243", "546792", "553791" ]
[ "easy", "nonn" ]
26
0
5
[ "A242863", "A359296", "A359871", "A359872" ]
null
Daniel Constantin Mayer, Jan 16 2023
2023-02-25T18:07:38
oeisdata/seq/A359/A359872.seq
8a6e235bb557a774b5c7dba90bfd9658
A359873
Minimum number of consecutive positive integers to guarantee n abundant or perfect numbers.
[ "6", "12", "18", "24", "30", "36", "38", "42", "48", "52", "56", "60", "66", "72", "78" ]
[ "nonn", "more" ]
51
0
5
[ "A023196", "A359873" ]
null
Lincoln Liu, May 20 2023
2023-07-27T08:29:17
oeisdata/seq/A359/A359873.seq
3beea2151c316758cdec256113d53a51
A359874
a(1) = 1, a(2) = 2. For n > 2, a(n) is the least novel power of the greatest prime divisor of a(n-2) + a(n-1).
[ "1", "2", "3", "5", "4", "9", "13", "11", "27", "19", "23", "7", "25", "8", "121", "43", "41", "49", "125", "29", "1331", "17", "337", "59", "14641", "343", "1873", "277", "1849", "1063", "169", "161051", "2687", "81869", "21139", "37", "2647", "61", "677", "1681", "131", "151", "47", "1771561", "761", "295387", "1369", "74189", "257", "37223", "937", "53", "19487171" ]
[ "nonn" ]
17
0
5
[ "A000961", "A359874" ]
null
David James Sycamore, Jan 16 2023
2023-01-29T10:55:34
oeisdata/seq/A359/A359874.seq
0813115255c03fdbfec208f8279fe014
A359875
Numbers k such that A002322(k) = A023900(k).
[ "1", "6", "10", "12", "14", "20", "22", "24", "26", "28", "34", "38", "40", "44", "46", "52", "56", "58", "62", "68", "74", "76", "80", "82", "86", "88", "92", "94", "104", "106", "116", "118", "122", "124", "134", "136", "142", "146", "148", "152", "158", "164", "166", "172", "178", "184", "188", "194", "202", "206", "208", "212", "214", "218", "226", "232", "236", "244", "248" ]
[ "nonn" ]
21
0
5
[ "A002322", "A023900", "A359875" ]
null
Torlach Rush, Jan 16 2023
2023-02-17T22:34:25
oeisdata/seq/A359/A359875.seq
9cee11534de510e5c22da3bfec74b6ec
A359876
a(n) is the smallest tribonacci number (A000073) with exactly n prime factors (counted with multiplicity).
[ "1", "2", "4", "44", "24", "5768", "504", "10562230626642", "3136", "7046319384", "615693474", "53798080", "4680045560037375", "35574238430251050319992", "4659412488735286161146176", "23523635785731871586396890786299881280", "79932289960699059086717998848" ]
[ "nonn" ]
7
0
5
[ "A000073", "A001222", "A072397", "A359848", "A359876", "A359877", "A359878" ]
null
Ilya Gutkovskiy, Jan 16 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359876.seq
d4eb35a1cf936b7fa677d4585fc06e63
A359877
a(n) is the smallest tetranacci number (A000078) with exactly n prime factors (counted with multiplicity).
[ "1", "2", "4", "8", "56", "108", "5536", "28074040", "39648", "147312", "18566888967365603514688", "9966792788887776", "2775641472", "2505471397838180985096739296", "1445523368993397560000765219760086502994234237205516083525719052320", "44092571484448511101335177770183225655413760" ]
[ "nonn" ]
7
0
5
[ "A000078", "A001222", "A072397", "A359849", "A359876", "A359877", "A359879" ]
null
Ilya Gutkovskiy, Jan 16 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359877.seq
30ce508100523848abfe98057c104c9d
A359878
a(n) is the index of the smallest tribonacci number (A000073) with exactly n prime factors (counted with multiplicity).
[ "2", "4", "5", "9", "8", "17", "13", "52", "16", "40", "36", "32", "62", "88", "96", "144", "112", "221", "256", "208", "400", "192" ]
[ "nonn", "more" ]
9
0
5
[ "A000073", "A001222", "A072396", "A359850", "A359876", "A359878", "A359879" ]
null
Ilya Gutkovskiy, Jan 16 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359878.seq
2c6589ef5d8ce55af02bc8f6166b07b3
A359879
a(n) is the index of the smallest tetranacci number (A000078) with exactly n prime factors (counted with multiplicity).
[ "3", "5", "6", "7", "10", "11", "17", "30", "20", "22", "82", "60", "37", "100", "236", "157", "156", "242", "240" ]
[ "nonn", "more" ]
9
0
5
[ "A000078", "A001222", "A072396", "A359851", "A359877", "A359878", "A359879" ]
null
Ilya Gutkovskiy, Jan 16 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359879.seq
b1f33208c5dcc21f44c7b4aeb3f31d55
A359880
a(n) is the smallest Fibonacci n-step number with exactly n prime factors (counted with multiplicity).
[ "21", "44", "56", "120", "1936", "2000", "2035872", "32512", "265816832", "523008", "8565824256", "67047424", "134156288", "1073463296", "35176050802688", "8589344768", "562914520154112", "18013762856812544", "144112508021833728", "2305819919496904704", "1099509006336", "137438822400" ]
[ "nonn" ]
7
0
5
[ "A001222", "A072397", "A359852", "A359876", "A359877", "A359880", "A359881" ]
null
Ilya Gutkovskiy, Jan 16 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359880.seq
00529a5f036a03ea698b679fa10e64f6
A359881
a(n) is the index of the smallest Fibonacci n-step number with exactly n prime factors (counted with multiplicity).
[ "8", "9", "10", "12", "17", "18", "29", "24", "38", "30", "45", "39", "41", "45", "61", "50", "67", "73", "77", "82", "62", "60", "71", "70", "127", "161", "112", "111", "86", "154", "91", "127", "99", "100", "141", "109", "109", "115", "159", "122", "122", "125", "131", "133", "134", "329", "138", "147", "196", "407", "150", "256", "320", "165", "163", "223", "170", "173" ]
[ "nonn" ]
9
0
5
[ "A001222", "A072396", "A359853", "A359878", "A359879", "A359880", "A359881" ]
null
Ilya Gutkovskiy, Jan 16 2023
2025-02-16T08:34:04
oeisdata/seq/A359/A359881.seq
5c82d1361eae25d7850dfd28d50972e6
A359882
a(n) = Sum_{d|n} d^n * (n/d)^d.
[ "1", "6", "30", "324", "3130", "53070", "823550", "17829896", "387951939", "10312525610", "285311670622", "9056807631948", "302875106592266", "11198819379685518", "437901307945957140", "18518802767263301648", "827240261886336764194", "39423330565860716459946" ]
[ "nonn" ]
13
0
5
[ "A066108", "A308594", "A359103", "A359882" ]
null
Seiichi Manyama, Jan 16 2023
2023-08-09T02:03:50
oeisdata/seq/A359/A359882.seq
d7b3b8831f62e206dfdbc22722929356
A359883
a(n) = Sum_{d|n} d^(n-d) * (n/d)^d.
[ "1", "3", "4", "21", "6", "367", "8", "5129", "19693", "106411", "12", "9590989", "14", "105614223", "2439477016", "8590983185", "18", "1788338285659", "20", "44174380774421", "1483406745548512", "584318428289047", "24", "2300697575522919961", "298023223876953151", "2481152876039086107" ]
[ "nonn" ]
14
0
5
[ "A359882", "A359883" ]
null
Seiichi Manyama, Jan 16 2023
2023-08-09T02:03:46
oeisdata/seq/A359/A359883.seq
cd54cd9a916f7c0ff810854eaa8626ab
A359884
Number of 3-dimensional tilings of a 2 X 2 X n box using 2 X 2 X 1 plates and 1 X 2 X 1 dominos.
[ "1", "3", "24", "133", "839", "5056", "30969", "188603", "1150952", "7018621", "42811231", "261110416", "1592592465", "9713598835", "59245780536", "361354997685", "2203996629559", "13442737199456", "81990685695721", "500082110459883", "3050128402768520", "18603511408241453", "113467563119685583" ]
[ "nonn", "easy" ]
31
0
5
[ "A001045", "A006253", "A335559", "A359884", "A359885", "A359886" ]
null
Gerhard Kirchner, Jan 20 2023
2024-06-24T15:53:35
oeisdata/seq/A359/A359884.seq
cb29e5793134a9fd50b1afbe3ccdbc65
A359885
Number of 3-dimensional tilings of a 2 X 2 X 3n box using trominos (three 1 X 1 X 1 cubes).
[ "1", "44", "2512", "145088", "8383744", "484453376", "27994083328", "1617634967552", "93474855387136", "5401434047381504", "312121261353336832", "18035892123135377408", "1042202005934895529984", "60223526164332403490816", "3480009713100277581611008", "201091971436982107249836032" ]
[ "nonn", "easy" ]
19
0
5
[ "A001045", "A006253", "A335559", "A359884", "A359885", "A359886" ]
null
Gerhard Kirchner, Jan 20 2023
2024-06-25T02:07:10
oeisdata/seq/A359/A359885.seq
4cdd99e5758879a6f5e9747c1f99897a
A359886
Number of 3-dimensional tilings of a 2 X 2 X n box using 2 X 2 X 1 plates and trominos (three 1 X 1 X 1 cubes).
[ "1", "1", "3", "49", "231", "789", "4771", "27225", "122799", "607469", "3255979", "16253649", "80098519", "409480005", "2079921395", "10411734921", "52523676351", "266059774429", "1341128940795", "6758479842689", "34138205819239", "172324729379509", "869131661400259", "4386075013348025", "22138673661637327" ]
[ "nonn", "easy" ]
21
0
5
[ "A001045", "A006253", "A335559", "A359884", "A359885", "A359886" ]
null
Gerhard Kirchner, Jan 20 2023
2024-06-24T18:05:39
oeisdata/seq/A359/A359886.seq
ec6d0bbba90106c649c42e5f4011076c
A359887
Square array A(n, k), n, k > 0, read by antidiagonals; A(n, k) is the numerator of the unique rational q such that for any m, floor(2^m/n) AND floor(2^m/k) = floor(q*2^m) (where AND denotes the bitwise AND operator); see A359888 for the denominators.
[ "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "1", "1", "0", "0", "0", "0", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "2", "2", "0", "0", "0", "0", "0", "0", "5", "0", "57", "1", "57", "0", "5", "0", "0", "0", "0", "1", "0", "1", "8", "8", "1", "0", "1", "0", "0", "0", "0", "85", "0", "37", "1", "1", "1", "37", "0", "85", "0", "0" ]
[ "nonn", "base", "frac", "tabf" ]
8
0
5
[ "A300630", "A306231", "A359806", "A359887", "A359888" ]
null
Rémy Sigrist, Jan 17 2023
2023-01-19T11:10:12
oeisdata/seq/A359/A359887.seq
80a09ab3e04b7f60d27780d921d830a0
A359888
Square array A(n, k), n, k > 0, read by antidiagonals; A(n, k) is the denominator of the unique rational q such that for any m, floor(2^m/n) AND floor(2^m/k) = floor(q*2^m) (where AND denotes the bitwise AND operator); see A359887 for the numerators.
[ "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "4", "4", "1", "1", "1", "1", "15", "4", "15", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "63", "1", "5", "1", "63", "1", "1", "1", "1", "1", "1", "15", "15", "1", "1", "1", "1", "1", "1", "63", "1", "455", "6", "455", "1", "63", "1", "1", "1", "1", "15", "1", "8", "63", "63", "8", "1", "15", "1", "1", "1", "1", "1023", "1", "585", "8", "7", "8", "585", "1", "1023", "1", "1" ]
[ "nonn", "base", "frac", "tabf" ]
6
0
5
[ "A300630", "A306231", "A359806", "A359887", "A359888" ]
null
Rémy Sigrist, Jan 17 2023
2023-01-19T11:10:17
oeisdata/seq/A359/A359888.seq
6cf1fee37eb1cfa5cf2cb2cf569e70d5
A359889
Numbers that are 1 or whose prime indices have the same mean as median.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "13", "14", "15", "16", "17", "19", "21", "22", "23", "25", "26", "27", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "41", "43", "46", "47", "49", "51", "53", "55", "57", "58", "59", "61", "62", "64", "65", "67", "69", "71", "73", "74", "77", "79", "81", "82", "83", "85", "86", "87", "89", "90", "91", "93", "94" ]
[ "nonn" ]
7
0
5
[ "A001222", "A008284", "A026424", "A056239", "A058398", "A088529", "A088530", "A112798", "A124010", "A240219", "A316413", "A326567", "A326568", "A327473", "A327482", "A359889", "A359890", "A359891", "A359892", "A359893", "A359894", "A359895", "A359897", "A359899", "A359901", "A359902", "A359903", "A359905", "A359908", "A359909", "A360005", "A360006", "A360007", "A360008", "A360009" ]
null
Gus Wiseman, Jan 22 2023
2023-01-23T09:10:47
oeisdata/seq/A359/A359889.seq
114676178e43a2855b26cceeb343ea23
A359890
Numbers whose prime indices do not have the same mean as median.
[ "12", "18", "20", "24", "28", "40", "42", "44", "45", "48", "50", "52", "54", "56", "60", "63", "66", "68", "70", "72", "75", "76", "78", "80", "84", "88", "92", "96", "98", "99", "102", "104", "108", "112", "114", "116", "117", "120", "124", "126", "130", "132", "135", "136", "138", "140", "144", "147", "148", "150", "152", "153", "154", "156", "160", "162", "164", "165" ]
[ "nonn" ]
6
0
5
[ "A001222", "A008284", "A056239", "A058398", "A088529", "A088530", "A112798", "A124010", "A240219", "A316413", "A326567", "A326568", "A327473", "A327476", "A327482", "A348551", "A359889", "A359890", "A359891", "A359892", "A359894", "A359898", "A359900", "A359903", "A359908", "A359911", "A359912", "A360005", "A360006", "A360009" ]
null
Gus Wiseman, Jan 22 2023
2023-01-23T09:10:52
oeisdata/seq/A359/A359890.seq
ee7627ff5c3017d3eafcacc50033b68a
A359891
Members of A026424 (numbers with an odd number of prime factors) whose prime indices have the same mean as median.
[ "2", "3", "5", "7", "8", "11", "13", "17", "19", "23", "27", "29", "30", "31", "32", "37", "41", "43", "47", "53", "59", "61", "67", "71", "73", "79", "83", "89", "97", "101", "103", "105", "107", "109", "110", "113", "125", "127", "128", "131", "137", "139", "149", "151", "157", "163", "167", "173", "179", "181", "191", "193", "197", "199", "211", "223", "227", "229", "233" ]
[ "nonn" ]
6
0
5
[ "A001222", "A008284", "A026424", "A056239", "A058398", "A112798", "A240219", "A316413", "A326567", "A326568", "A327473", "A327482", "A359889", "A359890", "A359891", "A359892", "A359893", "A359894", "A359895", "A359899", "A359901", "A359902", "A359908", "A359910", "A360005", "A360007", "A360009" ]
null
Gus Wiseman, Jan 22 2023
2023-01-23T09:10:56
oeisdata/seq/A359/A359891.seq
425cc709b6e6c831e6e4aa8823eba7da
A359892
Members of A026424 (numbers with an odd number of prime factors) whose prime indices do not have the same mean as median.
[ "12", "18", "20", "28", "42", "44", "45", "48", "50", "52", "63", "66", "68", "70", "72", "75", "76", "78", "80", "92", "98", "99", "102", "108", "112", "114", "116", "117", "120", "124", "130", "138", "147", "148", "153", "154", "162", "164", "165", "168", "170", "171", "172", "174", "175", "176", "180", "182", "186", "188", "190", "192", "195", "200", "207", "208" ]
[ "nonn" ]
6
0
5
[ "A001222", "A008284", "A026424", "A056239", "A058398", "A112798", "A240219", "A316413", "A326567", "A326568", "A327473", "A327476", "A327482", "A348551", "A359889", "A359890", "A359891", "A359892", "A359894", "A359895", "A359896", "A359898", "A359899", "A359900", "A359902", "A359911", "A359912", "A360005", "A360006", "A360009" ]
null
Gus Wiseman, Jan 22 2023
2023-01-23T09:11:00
oeisdata/seq/A359/A359892.seq
6cccc22b52838985483c9c28de2471ef
A359893
Triangle read by rows where T(n,k) is the number of integer partitions of n with median k, where k ranges from 1 to n in steps of 1/2.
[ "1", "1", "0", "1", "1", "1", "0", "0", "1", "2", "0", "2", "0", "0", "0", "1", "3", "0", "1", "2", "0", "0", "0", "0", "1", "4", "1", "2", "0", "3", "0", "0", "0", "0", "0", "1", "6", "1", "3", "0", "1", "3", "0", "0", "0", "0", "0", "0", "1", "8", "1", "6", "0", "2", "0", "4", "0", "0", "0", "0", "0", "0", "0", "1", "11", "2", "7", "1", "3", "0", "1", "4", "0", "0", "0", "0", "0", "0", "0", "0", "1" ]
[ "nonn", "tabf" ]
7
0
5
[ "A000041", "A005408", "A008284", "A026424", "A027193", "A027336", "A058398", "A067538", "A067659", "A102627", "A240219", "A316413", "A325347", "A326567", "A326568", "A327482", "A349156", "A359889", "A359893", "A359894", "A359895", "A359901", "A359902", "A359906", "A359907", "A360005", "A360006", "A360007", "A360008" ]
null
Gus Wiseman, Jan 21 2023
2023-01-22T09:16:56
oeisdata/seq/A359/A359893.seq
9a999a35fff5ae45acca5347e8d7559f
A359894
Number of integer partitions of n whose parts do not have the same mean as median.
[ "0", "0", "0", "0", "1", "3", "3", "10", "13", "20", "28", "49", "53", "93", "113", "145", "203", "287", "329", "479", "556", "724", "955", "1242", "1432", "1889", "2370", "2863", "3502", "4549", "5237", "6825", "8108", "9839", "12188", "14374", "16958", "21617", "25852", "30582", "36100", "44561", "51462", "63238", "73386", "85990", "105272", "124729" ]
[ "nonn" ]
6
0
5
[ "A000009", "A000041", "A008284", "A008289", "A026424", "A027193", "A058398", "A066571", "A067538", "A067659", "A102627", "A237984", "A240219", "A240850", "A316313", "A316413", "A325347", "A326567", "A326568", "A326622", "A327472", "A327473", "A327482", "A328966", "A349156", "A359889", "A359890", "A359891", "A359892", "A359893", "A359894", "A359895", "A359896", "A359897", "A359898", "A359899", "A359900", "A359901", "A359902", "A359906", "A359907", "A359908", "A359909", "A359910" ]
null
Gus Wiseman, Jan 20 2023
2023-01-20T18:08:05
oeisdata/seq/A359/A359894.seq
ad50d8e208927d254ecc614bbaf1fa29
A359895
Number of odd-length integer partitions of n whose parts have the same mean as median.
[ "0", "1", "1", "2", "1", "2", "3", "2", "1", "5", "5", "2", "5", "2", "8", "18", "1", "2", "19", "2", "24", "41", "20", "2", "9", "44", "31", "94", "102", "2", "125", "2", "1", "206", "68", "365", "382", "2", "98", "433", "155", "2", "716", "2", "1162", "2332", "196", "2", "17", "1108", "563", "1665", "3287", "2", "3906", "5474", "2005", "3083", "509", "2", "9029" ]
[ "nonn" ]
11
0
5
[ "A000009", "A000041", "A008284", "A008289", "A026424", "A027193", "A058398", "A067538", "A067659", "A102627", "A237984", "A240219", "A240850", "A316313", "A316413", "A325347", "A326567", "A326568", "A327472", "A327473", "A327475", "A327482", "A359889", "A359891", "A359892", "A359893", "A359894", "A359895", "A359896", "A359897", "A359899", "A359900", "A359901", "A359902", "A359906", "A359907", "A359908", "A359910" ]
null
Gus Wiseman, Jan 20 2023
2023-01-21T19:44:52
oeisdata/seq/A359/A359895.seq
796e9b249346069fcf6330e1e6b12d7d
A359896
Number of odd-length integer partitions of n whose parts do not have the same mean as median.
[ "0", "0", "0", "0", "1", "2", "2", "6", "9", "11", "15", "27", "32", "50", "58", "72", "112", "149", "171", "246", "286", "359", "477", "630", "773", "941", "1181", "1418", "1749", "2289", "2668", "3429", "4162", "4878", "6074", "7091", "8590", "10834", "12891", "15180", "18491", "22314", "25845", "31657", "36394", "42269", "52547", "62414", "73576", "85701" ]
[ "nonn" ]
7
0
5
[ "A000009", "A000041", "A008284", "A008289", "A026424", "A027193", "A058398", "A066571", "A067538", "A067659", "A102627", "A237984", "A240219", "A240850", "A316313", "A316413", "A325347", "A326567", "A326568", "A327472", "A327473", "A327482", "A359890", "A359891", "A359892", "A359893", "A359894", "A359895", "A359896", "A359898", "A359899", "A359900", "A359901", "A359902", "A359906", "A359907", "A359908", "A359910" ]
null
Gus Wiseman, Jan 20 2023
2023-01-21T16:28:35
oeisdata/seq/A359/A359896.seq
f3c3817a4646b986ca3c095062b0a347
A359897
Number of strict integer partitions of n whose parts have the same mean as median.
[ "0", "1", "1", "2", "2", "3", "4", "4", "4", "7", "6", "6", "10", "7", "10", "13", "11", "9", "20", "10", "20", "18", "21", "12", "30", "24", "28", "27", "30", "15", "73", "16", "37", "43", "45", "67", "74", "19", "55", "71", "126", "21", "150", "22", "75", "225", "78", "24", "183", "126", "245", "192", "132", "27", "284", "244", "403", "303", "120", "30", "828" ]
[ "nonn" ]
6
0
5
[ "A000009", "A000041", "A008284", "A008289", "A058398", "A065795", "A066571", "A067659", "A082550", "A102627", "A135342", "A237984", "A240219", "A240850", "A240851", "A316313", "A325347", "A326567", "A326568", "A327472", "A327473", "A327475", "A327482", "A328966", "A359889", "A359894", "A359897", "A359898", "A359899", "A359900", "A359907", "A359908", "A359909" ]
null
Gus Wiseman, Jan 20 2023
2023-01-21T16:28:31
oeisdata/seq/A359/A359897.seq
6d80d5964fc911b82b17e7ba20677d81
A359898
Number of strict integer partitions of n whose parts do not have the same mean as median.
[ "0", "0", "0", "0", "0", "0", "0", "1", "2", "1", "4", "6", "5", "11", "12", "14", "21", "29", "26", "44", "44", "58", "68", "92", "92", "118", "137", "165", "192", "241", "223", "324", "353", "405", "467", "518", "594", "741", "809", "911", "987", "1239", "1276", "1588", "1741", "1823", "2226", "2566", "2727", "3138", "3413", "3905", "4450", "5093", "5434", "6134" ]
[ "nonn" ]
7
0
5
[ "A000009", "A000016", "A000041", "A008284", "A008289", "A058398", "A065795", "A066571", "A067538", "A082550", "A102627", "A135342", "A237984", "A240219", "A240850", "A240851", "A316413", "A325347", "A326567", "A326568", "A327473", "A327475", "A327482", "A328966", "A359889", "A359890", "A359893", "A359894", "A359897", "A359898", "A359899", "A359900", "A359901", "A359902", "A359906", "A359907", "A359908" ]
null
Gus Wiseman, Jan 20 2023
2023-01-21T16:28:27
oeisdata/seq/A359/A359898.seq
c25d39cf1f33ffa3e6951d823b7e13e2
A359899
Number of strict odd-length integer partitions of n whose parts have the same mean as median.
[ "0", "1", "1", "1", "1", "1", "2", "1", "1", "3", "1", "1", "4", "1", "1", "6", "1", "1", "6", "1", "5", "7", "1", "1", "8", "12", "1", "9", "2", "1", "33", "1", "1", "11", "1", "50", "12", "1", "1", "13", "70", "1", "46", "1", "1", "122", "1", "1", "16", "102", "155", "17", "1", "1", "30", "216", "258", "19", "1", "1", "310", "1", "1", "666", "1", "382", "23", "1", "1", "23", "1596", "1", "393", "1", "1" ]
[ "nonn" ]
12
0
5
[ "A000009", "A000016", "A000041", "A008284", "A008289", "A026424", "A027193", "A058398", "A065795", "A066571", "A067538", "A067659", "A102627", "A237984", "A240219", "A240850", "A240851", "A316413", "A325347", "A326567", "A326568", "A327473", "A327482", "A359889", "A359891", "A359893", "A359894", "A359895", "A359896", "A359897", "A359898", "A359899", "A359900", "A359901", "A359902", "A359903", "A359906", "A359907", "A359908", "A359910" ]
null
Gus Wiseman, Jan 20 2023
2023-01-21T14:28:21
oeisdata/seq/A359/A359899.seq
b6c6a659ad8c079ab0d45c34465881ec
A359900
Number of strict odd-length integer partitions of n whose parts do not have the same mean as median.
[ "0", "0", "0", "0", "0", "0", "0", "1", "2", "1", "4", "5", "4", "8", "10", "8", "15", "18", "17", "26", "27", "31", "43", "51", "53", "59", "81", "87", "109", "127", "115", "169", "194", "213", "255", "243", "322", "379", "431", "478", "487", "629", "667", "804", "907", "902", "1151", "1294", "1439", "1530", "1674", "2031", "2290", "2559", "2829", "2973", "3296", "3939" ]
[ "nonn" ]
7
0
5
[ "A000009", "A000016", "A000041", "A008284", "A008289", "A026424", "A027193", "A058398", "A065795", "A066571", "A067659", "A102627", "A240850", "A240851", "A326567", "A326568", "A327475", "A327482", "A359892", "A359893", "A359894", "A359895", "A359896", "A359897", "A359898", "A359899", "A359900", "A359901", "A359902", "A359906", "A359907", "A359910", "A360005" ]
null
Gus Wiseman, Jan 21 2023
2023-01-21T09:33:25
oeisdata/seq/A359/A359900.seq
47d3ededfdb62f182ae0ea2c80fb3feb