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7
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1
348
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listlengths
1
8
score
int64
1
2.35k
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int64
-14,827
666,262,453B
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1999-12-11 03:00:00
2025-07-19 00:40:46
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32
32
A355601
a(1) = 47. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).
[ "47", "53", "521", "6037", "3347", "4931", "105667", "1131259", "4739509", "175166071", "3834885547" ]
[ "nonn", "hard", "more" ]
8
1
1
[ "A249162", "A355597", "A355598", "A355599", "A355600", "A355601", "A355602" ]
null
Felix Fröhlich, Jul 09 2022
2023-01-31T12:58:07
oeisdata/seq/A355/A355601.seq
f05bd3274ae650421e61dcdbcc45d4a8
A355602
a(1) = 61. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).
[ "61", "601", "2269", "13499", "58313", "1950827", "57480139", "713589493", "4722480517" ]
[ "nonn", "hard", "more" ]
4
1
1
[ "A249162", "A355597", "A355598", "A355599", "A355600", "A355601", "A355602" ]
null
Felix Fröhlich, Jul 09 2022
2022-07-16T01:32:28
oeisdata/seq/A355/A355602.seq
642ea847be1f2c88ced55b0127023c1d
A355603
Expansion of e.g.f. (1 + x)^(x^4/24).
[ "1", "0", "0", "0", "0", "5", "-15", "70", "-420", "3024", "-22050", "202950", "-2113650", "24324300", "-305645340", "4174483950", "-61253992800", "961049212200", "-16054949350440", "284505099278400", "-5329752594075000", "105239780964864000", "-2184466455408699000", "47550052231211237400" ]
[ "sign" ]
12
0
6
[ "A007113", "A355603", "A355605" ]
null
Seiichi Manyama, Jul 09 2022
2022-07-10T06:32:15
oeisdata/seq/A355/A355603.seq
fdbe8f1b7a0eb0cce8687ce1e21e7e53
A355604
Table T(n, k), n >= 0, k = 0..n, read by rows; row n is obtained by replacing in row n of Pascal's triangle (A007318) runs of k consecutive even numbers by the terms of row k+1 of the present triangle.
[ "1", "1", "1", "1", "1", "1", "1", "3", "3", "1", "1", "1", "1", "1", "1", "1", "5", "1", "1", "5", "1", "1", "1", "15", "1", "15", "1", "1", "1", "7", "21", "35", "35", "21", "7", "1", "1", "1", "1", "15", "1", "15", "1", "1", "1", "1", "9", "1", "5", "1", "1", "5", "1", "9", "1", "1", "1", "45", "1", "1", "1", "1", "1", "45", "1", "1", "1", "11", "55", "165", "1", "3", "3", "1", "165", "55", "11", "1", "1", "1", "1", "1", "495", "1", "1", "1", "495", "1", "1", "1", "1" ]
[ "nonn", "look", "tabl" ]
12
0
8
[ "A007318", "A014421", "A065040", "A143333", "A348648", "A355604" ]
null
Rémy Sigrist, Jul 09 2022
2022-07-11T20:48:41
oeisdata/seq/A355/A355604.seq
14086fc7d82ffa9102e1f93ed76b8222
A355605
Expansion of e.g.f. (1 + x)^(x^2/2).
[ "1", "0", "0", "3", "-6", "20", "0", "-126", "1260", "-4320", "5040", "180180", "-2601720", "31309200", "-372756384", "4877195400", "-70178799600", "1099333347840", "-18429818232960", "327676010785200", "-6146676161388000", "121301442091851840", "-2512746856371628800", "54527094987619716000" ]
[ "sign" ]
8
0
4
[ "A007121", "A355603", "A355605" ]
null
Seiichi Manyama, Jul 09 2022
2022-07-09T11:05:49
oeisdata/seq/A355/A355605.seq
e86f5dae985d9125e22a2c46a23bf80d
A355606
The indices where A354606(n) = 1.
[ "1", "2", "4", "9", "14", "25", "37", "57", "99", "133", "182", "191", "404", "469", "595", "640", "780", "1195", "1884", "2407", "2808", "3010", "3217", "3444", "4245", "4383", "5773", "8703", "10069", "10731", "12640", "14470", "17998", "18535", "22648", "23341", "24286", "27431", "33702", "37019", "45593", "53759", "56598", "57578", "76640", "96729", "99557", "106881", "125900", "144162" ]
[ "nonn" ]
12
1
2
[ "A000005", "A354606", "A355606" ]
null
Scott R. Shannon, Jul 09 2022
2024-12-12T11:02:06
oeisdata/seq/A355/A355606.seq
ad05134511f090087795a49441ac31bf
A355607
Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. (1 + x)^(x^k).
[ "1", "1", "1", "1", "0", "0", "1", "0", "2", "0", "1", "0", "0", "-3", "0", "1", "0", "0", "6", "20", "0", "1", "0", "0", "0", "-12", "-90", "0", "1", "0", "0", "0", "24", "40", "594", "0", "1", "0", "0", "0", "0", "-60", "180", "-4200", "0", "1", "0", "0", "0", "0", "120", "240", "-1512", "34544", "0", "1", "0", "0", "0", "0", "0", "-360", "-1260", "11760", "-316008", "0", "1", "0", "0", "0", "0", "0", "720", "1680", "28224", "-38880", "3207240", "0" ]
[ "sign", "tabl", "look" ]
21
0
9
[ "A007113", "A007121", "A292892", "A353229", "A354625", "A355607", "A355609", "A355619" ]
null
Seiichi Manyama, Jul 09 2022
2022-07-11T03:36:13
oeisdata/seq/A355/A355607.seq
2b0aa4adef04a7e7352c01aab7990cc3
A355608
Zeroless numbers k such that x^2 - s*x + p has only integer roots, where s and p denote the sum and product of the digits of k respectively.
[ "4", "11", "12", "13", "14", "15", "16", "17", "18", "19", "21", "22", "23", "24", "25", "26", "27", "28", "29", "31", "32", "33", "34", "35", "36", "37", "38", "39", "41", "42", "43", "44", "45", "46", "47", "48", "49", "51", "52", "53", "54", "55", "56", "57", "58", "59", "61", "62", "63", "64", "65", "66", "67", "68", "69", "71", "72", "73", "74", "75", "76", "77", "78", "79", "81", "82", "83", "84", "85", "86", "87", "88", "89", "91", "92", "93", "94", "95", "96", "97", "98", "99", "122", "134", "143", "146" ]
[ "base", "nonn" ]
46
1
1
[ "A007953", "A007954", "A052382", "A355497", "A355547", "A355608" ]
null
Jean-Marc Rebert, Jul 09 2022
2023-01-24T10:30:26
oeisdata/seq/A355/A355608.seq
8e91f9cd5cb8f1ca3671793a0e0891a0
A355609
Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. (1 - x)^(-x^k).
[ "1", "1", "1", "1", "0", "2", "1", "0", "2", "6", "1", "0", "0", "3", "24", "1", "0", "0", "6", "20", "120", "1", "0", "0", "0", "12", "90", "720", "1", "0", "0", "0", "24", "40", "594", "5040", "1", "0", "0", "0", "0", "60", "540", "4200", "40320", "1", "0", "0", "0", "0", "120", "240", "3528", "34544", "362880", "1", "0", "0", "0", "0", "0", "360", "1260", "25200", "316008", "3628800", "1", "0", "0", "0", "0", "0", "720", "1680", "28224", "263520", "3207240", "39916800" ]
[ "nonn", "tabl" ]
18
0
6
[ "A000142", "A066166", "A353228", "A353229", "A354624", "A355607", "A355609", "A355610" ]
null
Seiichi Manyama, Jul 09 2022
2022-07-11T03:36:16
oeisdata/seq/A355/A355609.seq
bc3d0823a8f5e03c14c0a2ae3834dd0f
A355610
Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. (1 - x)^(-x^k/k!).
[ "1", "1", "1", "1", "0", "2", "1", "0", "2", "6", "1", "0", "0", "3", "24", "1", "0", "0", "3", "20", "120", "1", "0", "0", "0", "6", "90", "720", "1", "0", "0", "0", "4", "20", "594", "5040", "1", "0", "0", "0", "0", "10", "180", "4200", "40320", "1", "0", "0", "0", "0", "5", "40", "1134", "34544", "362880", "1", "0", "0", "0", "0", "0", "15", "210", "7980", "316008", "3628800", "1", "0", "0", "0", "0", "0", "6", "70", "1904", "71280", "3207240", "39916800" ]
[ "nonn", "tabl" ]
18
0
6
[ "A000142", "A066166", "A351492", "A351493", "A355507", "A355609", "A355610", "A355619" ]
null
Seiichi Manyama, Jul 09 2022
2022-07-11T03:36:20
oeisdata/seq/A355/A355610.seq
43d9b09f0d9fb4d57d98e9f0e85a502f
A355611
a(0) = 0; for n > 0, a(n) is the smallest positive number not occurring earlier such that the binary string of |a(n) - a(n-1)| does not appear in the binary string concatenation of a(0)..a(n-1).
[ "0", "1", "3", "5", "9", "17", "7", "23", "2", "12", "22", "6", "16", "37", "58", "10", "38", "4", "32", "60", "14", "48", "82", "8", "42", "85", "15", "61", "107", "11", "67", "131", "18", "86", "13", "77", "141", "21", "89", "25", "93", "20", "84", "148", "19", "83", "147", "27", "91", "155", "26", "90", "154", "24", "88", "152", "28", "92", "156", "36", "100", "164", "30", "94", "158", "29", "142", "78", "191", "31", "95", "159" ]
[ "nonn", "base", "look" ]
46
0
3
[ "A007088", "A030302", "A118248", "A341766", "A355611", "A357082", "A357377" ]
null
Scott R. Shannon, Sep 12 2022
2023-01-16T09:10:46
oeisdata/seq/A355/A355611.seq
b266b8f339f992b68fb6ddcf2ef1547e
A355612
Number of labeled digraphs on [n] such that for any pair C_1,C_2 of distinct strongly connected components, if x in C_1 is directed to y in C_2 then every vertex in C_1 is directed to every vertex in C_2.
[ "1", "1", "4", "52", "2524", "629296", "750098464", "3540134362192", "63605185617860464", "4402130837352016607296", "1190565802204629673473661504", "1270503156085666608161173288964992", "5381113705726490960372769906727545572224", "90765998703828737395601069325546106634460887296", "6109068274998388232409260496587163340177606642565219584" ]
[ "nonn" ]
6
0
3
[ "A003024", "A003030", "A355612" ]
null
Geoffrey Critzer, Jul 09 2022
2022-07-10T08:28:07
oeisdata/seq/A355/A355612.seq
02cd19aa7b8b081428b2a3a3a0bc5db4
A355613
Number of n-tuples (p_1, p_2, ..., p_n) of positive integers such that p_{i-1} <= p_i <= i^n.
[ "1", "1", "4", "188", "249776", "16633660072", "83928799192724928", "45137673586198237802064960", "3471414431114929157135319840692727552", "49384542120790045258798151330072200190915129956928", "163311862970149172566335309591606099705654956202533457675827916800" ]
[ "nonn" ]
10
0
3
[ "A355613", "A355614" ]
null
Alois P. Heinz, Jul 09 2022
2022-07-10T08:34:36
oeisdata/seq/A355/A355613.seq
a730ab4e323d186db1a6068431389065
A355614
Number A(n,k) of n-tuples (p_1, p_2, ..., p_n) of positive integers such that p_{i-1} <= p_i <= i^k; square array A(n,k), n>=0, k>=0, read by antidiagonals.
[ "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "4", "5", "1", "1", "1", "8", "30", "14", "1", "1", "1", "16", "188", "340", "42", "1", "1", "1", "32", "1176", "9280", "5235", "132", "1", "1", "1", "64", "7280", "249776", "804322", "102756", "429", "1", "1", "1", "128", "44640", "6518784", "119088660", "109506040", "2464898", "1430", "1" ]
[ "nonn", "tabl" ]
12
0
9
[ "A000012", "A000079", "A000108", "A209440", "A355613", "A355614" ]
null
Alois P. Heinz, Jul 09 2022
2022-07-10T08:35:49
oeisdata/seq/A355/A355614.seq
4964aeab9b1d41faff3da77d0a7bb8a5
A355615
Define a rational sequence {b(n)} as b(1) = 1, b(n) = b(n-1) + 1/(n + 1 - b(n-1)) for n > 1; a(n) is the numerator of b(n).
[ "1", "3", "19", "689", "902919", "1610893922869", "5422187846648306990942459", "65408471597507349805723190837012905483968615226329" ]
[ "nonn", "frac" ]
17
1
2
[ "A079278", "A355615" ]
null
Leonid Broukhis, Jul 09 2022
2022-07-11T02:15:36
oeisdata/seq/A355/A355615.seq
ef1968aecd949035fe6522ada04e4340
A355616
a(n) is the number of distinct lengths between consecutive points of the Farey sequence of order n.
[ "1", "1", "2", "3", "5", "6", "9", "11", "14", "15", "21", "23", "29", "31", "34", "38", "48", "49", "59", "63", "67", "71", "83", "86", "97", "100", "110", "115", "132", "133", "150", "158", "165", "169", "182", "187", "208", "213", "222", "228", "252", "254", "280", "287", "297", "304", "331", "337", "362", "367", "379", "387", "418", "423", "437", "450", "464", "472", "509", "513", "548", "556", "573", "589", "608", "611", "652", "665", "681", "685" ]
[ "nonn" ]
31
1
3
[ "A005728", "A006842", "A006843", "A355616" ]
null
Travis Hoppe, Jul 09 2022
2022-07-16T12:04:18
oeisdata/seq/A355/A355616.seq
3e72b188dcbad2a49bbfd320f0dee36c
A355617
a(1) = 1; a(2) = 2; for n > 2, a(n) = R(a(n-1)) if a(n-1) != R(a(n-2)) and R(a(n-1)) has not yet been used, where R is the digit reversal function A004086, otherwise a(n) is the smallest positive integer > a(n-1) that has not yet been used.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "21", "22", "23", "32", "33", "34", "43", "44", "45", "54", "55", "56", "65", "66", "67", "76", "77", "78", "87", "88", "89", "98", "99", "100", "101", "102", "201", "202", "203", "302", "303", "304", "403", "404", "405", "504", "505", "506", "605", "606", "607", "706", "707", "708", "807", "808", "809", "908", "909" ]
[ "base", "easy", "look", "nonn" ]
37
1
2
[ "A004086", "A355617" ]
null
Sylvia Zevi Abrams, Jul 09 2022
2023-10-18T10:06:16
oeisdata/seq/A355/A355617.seq
7a451ad4cb734691915b9266d95beb2b
A355618
a(n) is the least prime that is the sum of a list of numbers > 1 whose product is n, or -1 if there is no such prime.
[ "2", "3", "-1", "5", "5", "7", "-1", "-1", "7", "11", "7", "13", "-1", "-1", "-1", "17", "11", "19", "-1", "-1", "13", "23", "11", "-1", "-1", "-1", "11", "29", "11", "31", "-1", "-1", "19", "-1", "11", "37", "-1", "-1", "11", "41", "13", "43", "-1", "11", "-1", "47", "11", "-1", "-1", "-1", "17", "53", "11", "-1", "13", "-1", "31", "59", "13", "61", "-1", "13", "-1", "-1", "17", "67", "-1", "-1", "17", "71", "13", "73", "-1", "13", "23", "-1" ]
[ "sign", "look" ]
17
2
1
[ "A046315", "A355618" ]
null
J. M. Bergot and Robert Israel, Jul 10 2022
2022-07-13T15:54:09
oeisdata/seq/A355/A355618.seq
310cecc3ab933eb2315c7b18f75cda41
A355619
Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. (1 + x)^(x^k/k!).
[ "1", "1", "1", "1", "0", "0", "1", "0", "2", "0", "1", "0", "0", "-3", "0", "1", "0", "0", "3", "20", "0", "1", "0", "0", "0", "-6", "-90", "0", "1", "0", "0", "0", "4", "20", "594", "0", "1", "0", "0", "0", "0", "-10", "0", "-4200", "0", "1", "0", "0", "0", "0", "5", "40", "-126", "34544", "0", "1", "0", "0", "0", "0", "0", "-15", "-210", "1260", "-316008", "0", "1", "0", "0", "0", "0", "0", "6", "70", "1904", "-4320", "3207240", "0" ]
[ "sign", "tabl" ]
17
0
9
[ "A007113", "A351493", "A355603", "A355605", "A355607", "A355610", "A355619" ]
null
Seiichi Manyama, Jul 10 2022
2022-07-11T03:36:09
oeisdata/seq/A355/A355619.seq
fdbc6f0e308040a9d35c90983da201f2
A355620
a(n) is the sum of the divisors of n whose decimal expansions appear as substrings in the decimal expansion of n.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "11", "12", "15", "14", "15", "21", "17", "18", "19", "20", "22", "22", "24", "23", "30", "30", "28", "27", "30", "29", "33", "32", "34", "36", "34", "40", "45", "37", "38", "42", "44", "42", "44", "43", "48", "50", "46", "47", "60", "49", "55", "52", "54", "53", "54", "60", "56", "57", "58", "59", "66", "62", "64", "66", "68", "70", "72", "67" ]
[ "nonn", "base" ]
20
1
2
[ "A000203", "A002275", "A121041", "A121042", "A239058", "A355620", "A355633" ]
null
Rémy Sigrist, Jul 10 2022
2024-07-23T14:58:03
oeisdata/seq/A355/A355620.seq
8f219c0e2aaa067576ed2350af85736a
A355621
a(1) = 1; for n > 1, a(n) is the number of terms in the first n-1 terms of the sequence that share a 1-bit with a(n-1) in their binary expansions.
[ "1", "1", "2", "1", "3", "5", "5", "6", "5", "8", "1", "8", "2", "4", "5", "11", "15", "17", "12", "11", "19", "17", "15", "23", "22", "19", "22", "21", "24", "16", "10", "18", "20", "21", "29", "33", "22", "30", "33", "23", "38", "31", "42", "28", "35", "37", "38", "37", "40", "22", "41", "40", "24", "33", "35", "46", "49", "49", "50", "47", "59", "60", "55", "61", "62", "61", "64", "1", "39", "63", "69", "58", "60", "64", "3", "60", "65", "46", "67" ]
[ "nonn", "base" ]
16
1
3
[ "A030190", "A129760", "A352763", "A353989", "A354606", "A355621", "A355625" ]
null
Scott R. Shannon, Jul 10 2022
2022-07-11T08:35:10
oeisdata/seq/A355/A355621.seq
f0b5f525cb6460e570ef3a3b7a26cc3f
A355622
a(n) is the n-digit positive number with no trailing zeros and coprime to its digital reversal R(a(n)) at which abs(a(n)/R(a(n))-Pi) is minimized.
[ "1", "92", "581", "5471", "52861", "998713", "7774742", "93630892", "422334431", "9190135292", "45425395441", "472539314051", "5784475521481", "49371008251751", "939253175379892", "9265811239939492", "52949745472445861", "952186420153090303", "9836241210282790313", "36386277546811128511", "442327789252803797041" ]
[ "nonn", "base", "frac" ]
54
1
2
[ "A000796", "A002485", "A004086", "A067251", "A355622", "A355623" ]
null
Stefano Spezia, Jul 10 2022
2022-09-06T10:29:04
oeisdata/seq/A355/A355622.seq
63d490bbbc803d1a81d91765701b5d11
A355623
a(n) is the n-digit positive number with no trailing zeros and coprime to its digital reversal R(a(n)) at which abs(R(a(n))/a(n)-Pi) is minimized.
[ "1", "29", "185", "1745", "16825", "317899", "2474777", "29803639", "134433224", "2925310919", "14459352454", "150413935274", "1841255744875", "15715280017394", "298973571352939", "2949399321185629", "16854427454794925", "303090351024681259", "3130972820121426389", "11582111864577268363", "140797308252987723244" ]
[ "nonn", "base", "frac" ]
46
1
2
[ "A000796", "A002485", "A004086", "A067251", "A355622", "A355623" ]
null
Stefano Spezia, Jul 10 2022
2022-09-06T10:28:59
oeisdata/seq/A355/A355623.seq
d092c245b0f8d67d6a4ca2f3393b7ac6
A355624
a(0) = 0, and for any n > 0, a(3*n) = 3*a(n), a(3*n+1) = 1-3*a(n), a(3*n+2) = 2-3*a(n).
[ "0", "1", "2", "3", "-2", "-1", "6", "-5", "-4", "9", "-8", "-7", "-6", "7", "8", "-3", "4", "5", "18", "-17", "-16", "-15", "16", "17", "-12", "13", "14", "27", "-26", "-25", "-24", "25", "26", "-21", "22", "23", "-18", "19", "20", "21", "-20", "-19", "24", "-23", "-22", "-9", "10", "11", "12", "-11", "-10", "15", "-14", "-13", "54", "-53", "-52", "-51", "52", "53", "-48", "49" ]
[ "sign", "base", "easy" ]
12
0
3
[ "A038754", "A065620", "A355624", "A355675" ]
null
Rémy Sigrist, Jul 14 2022
2022-07-18T14:16:41
oeisdata/seq/A355/A355624.seq
00576335e33d317e22aea250aae63b71
A355625
a(1) = 1; for n > 1, a(n) is the number of terms in the first n-1 terms of the sequence that share a 1-bit with n in their binary expansions.
[ "1", "0", "1", "0", "2", "1", "4", "0", "3", "2", "6", "2", "6", "7", "11", "0", "6", "9", "13", "6", "13", "13", "18", "6", "11", "17", "21", "16", "21", "22", "26", "0", "14", "16", "26", "14", "23", "25", "31", "12", "22", "27", "34", "27", "33", "34", "39", "19", "31", "35", "43", "36", "44", "44", "49", "36", "42", "48", "52", "47", "52", "53", "57", "0", "29", "32", "48", "30", "48", "48", "57", "25", "41", "46", "56", "47", "57", "58", "65", "34" ]
[ "nonn", "base" ]
15
1
5
[ "A030190", "A129760", "A352763", "A353989", "A354606", "A355621", "A355625" ]
null
Scott R. Shannon, Jul 10 2022
2022-07-11T08:35:06
oeisdata/seq/A355/A355625.seq
8b0115d8922689f5b6da042515f94322
A355626
a(n) is the number of tuples (t_1, ..., t_n) with integers 2 <= t_1 <= ... <= t_n such that Product_{i = 1..n} (3 + 1/t_i) is an integer.
[ "0", "3", "80", "15222" ]
[ "bref", "hard", "more", "nonn" ]
28
1
2
[ "A355626", "A355627", "A355628", "A355629", "A355630", "A355631" ]
null
Markus Sigg, Jul 15 2022
2025-01-09T02:55:05
oeisdata/seq/A355/A355626.seq
32a920bb956a6bfd801a6bdd530d640b
A355627
a(n) is the number of tuples (t_1, ..., t_k) with a positive integer k and integers 2 <= t_1 <= ... <= t_k such that n = Product_{i = 1..k} (3 + 1/t_i).
[ "2", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "50", "14", "0", "2", "9", "0", "2", "2", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "9291", "1668", "0", "2170", "226", "0", "1052", "59", "0" ]
[ "nonn" ]
19
10
1
[ "A355626", "A355627", "A355628", "A355629", "A355630", "A355631" ]
null
Markus Sigg, Jul 15 2022
2025-03-22T23:34:31
oeisdata/seq/A355/A355627.seq
f95bfca41b0046408283934aa2ef0f1d
A355628
a(n) is the number of positive integers p that can be written as p = Product_{i = 1..n} (3 + 1/t_i) with integers t_i >= 2.
[ "0", "2", "7", "25", "96", "364", "1344", "4921" ]
[ "hard", "more", "nonn" ]
14
1
2
[ "A355626", "A355627", "A355628", "A355629", "A355630", "A355631" ]
null
Markus Sigg, Jul 15 2022
2023-12-10T09:28:04
oeisdata/seq/A355/A355628.seq
c89ad2e7982fc2bcb0431268a5697bf1
A355629
a(n) is the number of tuples (t_1, ..., t_n) with integers 2 <= t_1 <= ... <= t_n such that 3^n + 1 = Product_{i = 1..n} (3 + 1/t_i).
[ "0", "2", "50", "9291" ]
[ "bref", "hard", "more", "nonn" ]
17
1
2
[ "A034472", "A355626", "A355627", "A355628", "A355629", "A355630", "A355631", "A356210" ]
null
Markus Sigg, Jul 15 2022
2022-09-18T17:05:36
oeisdata/seq/A355/A355629.seq
bc22637aee6d761dee62b8ea7187beaa
A355630
a(n) is the largest integer that can be written as Product_{i = 1..n} (3 + 1/t_i) with integers t_i >= 2.
[ "11", "37", "121", "413", "1442", "5047", "16807", "58457", "204085", "709667", "2483663", "8068753", "30415033" ]
[ "more", "nonn" ]
12
2
1
[ "A355626", "A355627", "A355628", "A355629", "A355630", "A355631" ]
null
Markus Sigg, Jul 15 2022
2022-08-02T09:19:12
oeisdata/seq/A355/A355630.seq
e8cc3b151951113d2c0f13e71c283c79
A355631
List of numbers k such that A355627(k) > 0.
[ "10", "11", "28", "29", "31", "32", "34", "35", "37", "82", "83", "85", "86", "88", "89", "91", "92", "94", "95", "97", "98", "100", "101", "103", "104", "106", "110", "112", "113", "115", "116", "118", "119", "121", "244", "245", "247", "248", "250", "251", "253", "254", "256", "257", "259", "260", "262", "263", "265", "266", "268", "269", "271", "272", "274", "275", "277", "278", "280" ]
[ "nonn" ]
17
1
1
[ "A001651", "A355626", "A355627", "A355628", "A355629", "A355630", "A355631" ]
null
Markus Sigg, Jul 15 2022
2022-08-02T10:52:59
oeisdata/seq/A355/A355631.seq
fb2f06beef235e591ff213f3b9f0601a
A355632
Irregular triangle T(n, k), n > 0, k = 1..A121041(n), read by rows; the n-th row contains in ascending order the divisors of n whose decimal expansions appear as substrings in the decimal expansion of n.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "1", "10", "1", "11", "1", "2", "12", "1", "13", "1", "14", "1", "5", "15", "1", "16", "1", "17", "1", "18", "1", "19", "2", "20", "1", "21", "2", "22", "23", "2", "4", "24", "5", "25", "2", "26", "27", "2", "28", "29", "3", "30", "1", "31", "2", "32", "3", "33", "34", "5", "35", "3", "6", "36", "37", "38", "3", "39", "4", "40", "1", "41", "2", "42", "43", "4", "44" ]
[ "nonn", "base", "tabf" ]
15
1
2
[ "A027750", "A121041", "A121042", "A355620", "A355632", "A355634" ]
null
Rémy Sigrist, Jul 11 2022
2024-07-23T13:35:35
oeisdata/seq/A355/A355632.seq
c6728dbee134415e42341a2f768e58e7
A355633
a(n) is the sum of the divisors of n whose binary expansions appear as substrings in the binary expansion of n.
[ "1", "3", "4", "7", "6", "12", "8", "15", "10", "18", "12", "28", "14", "24", "19", "31", "18", "30", "20", "42", "22", "36", "24", "60", "26", "42", "31", "56", "30", "57", "32", "63", "34", "54", "36", "70", "38", "60", "43", "90", "42", "66", "44", "84", "54", "72", "48", "124", "50", "78", "55", "98", "54", "93", "72", "120", "61", "90", "60", "133", "62", "96", "74", "127", "66" ]
[ "nonn", "base" ]
17
1
2
[ "A000203", "A027750", "A093640", "A355620", "A355633", "A355634" ]
null
Rémy Sigrist, Jul 11 2022
2022-07-16T07:18:04
oeisdata/seq/A355/A355633.seq
4113eeb2b64758293df9de665f2390a7
A355634
Irregular triangle T(n, k), n > 0, k = 1..A093640(n), read by rows; the n-th row contains in ascending order the divisors of n whose binary expansions appear as substrings in the binary expansion of n.
[ "1", "1", "2", "1", "3", "1", "2", "4", "1", "5", "1", "2", "3", "6", "1", "7", "1", "2", "4", "8", "1", "9", "1", "2", "5", "10", "1", "11", "1", "2", "3", "4", "6", "12", "1", "13", "1", "2", "7", "14", "1", "3", "15", "1", "2", "4", "8", "16", "1", "17", "1", "2", "9", "18", "1", "19", "1", "2", "4", "5", "10", "20", "1", "21", "1", "2", "11", "22", "1", "23", "1", "2", "3", "4", "6", "8", "12", "24", "1", "25" ]
[ "nonn", "base", "tabf" ]
9
1
3
[ "A027750", "A093640", "A355632", "A355633", "A355634" ]
null
Rémy Sigrist, Jul 11 2022
2024-07-23T08:17:14
oeisdata/seq/A355/A355634.seq
b57b8e042c28c5168c5ba3295b5e0668
A355635
Triangle read by rows. Row n gives the coefficients of Product_{k=0..n-1} (x - binomial(n-1,k)) expanded in decreasing powers of x, with row 0 = {1}.
[ "1", "1", "-1", "1", "-2", "1", "1", "-4", "5", "-2", "1", "-8", "22", "-24", "9", "1", "-16", "93", "-238", "256", "-96", "1", "-32", "386", "-2180", "5825", "-6500", "2500", "1", "-64", "1586", "-19184", "117561", "-345600", "407700", "-162000", "1", "-128", "6476", "-164864", "2229206", "-15585920", "51583084", "-64538880", "26471025" ]
[ "sign", "tabl" ]
14
0
5
[ "A000079", "A000346", "A001142", "A025131", "A025133", "A025134", "A025135", "A355635" ]
null
Thomas Scheuerle, Jul 11 2022
2022-07-26T13:42:14
oeisdata/seq/A355/A355635.seq
1ca0556f91acc52419eb6671065f0840
A355636
a(1) = a(2) = 1; for n > 2, a(n) is the smallest positive number that has not yet appeared that has the same number of divisors as the sum a(n-2) + a(n-1) but does not equal the sum.
[ "1", "1", "3", "9", "18", "6", "30", "100", "24", "12", "196", "48", "20", "28", "80", "60", "72", "84", "90", "40", "42", "8", "32", "54", "10", "729", "2", "14", "81", "15", "108", "21", "22", "5", "26", "7", "27", "33", "96", "34", "56", "126", "66", "320", "35", "38", "11", "4", "39", "13", "44", "46", "132", "51", "55", "57", "162", "58", "140", "150", "70", "156", "62", "65", "17", "69", "74", "77", "19", "160", "23", "82", "78" ]
[ "nonn" ]
17
1
3
[ "A000005", "A351001", "A352768", "A352774", "A352867", "A355636", "A355637" ]
null
Scott R. Shannon, Jul 11 2022
2022-07-26T13:38:21
oeisdata/seq/A355/A355636.seq
d8a8f9f425846638fc49e8b8e169b25e
A355637
The fixed points of A355636.
[ "1", "3", "6", "55", "58", "189", "372", "1133", "1135", "1374", "1874", "3958", "3959", "3963", "8724", "26492", "29115", "29152", "37628", "39028", "40340", "42183", "42676", "42678", "43731", "44925" ]
[ "nonn", "more" ]
5
1
2
[ "A355636", "A355637" ]
null
Scott R. Shannon, Jul 11 2022
2022-07-11T16:11:26
oeisdata/seq/A355/A355637.seq
39ebf206aabadc22ef34d529f3377130
A355638
Number of polyhedra (3-polytopes) of graph radius 1 on n edges.
[ "1", "0", "1", "1", "1", "1", "2", "2", "4", "5", "7", "10", "16", "27", "42", "67", "116", "187", "329", "570", "970", "1723", "3021", "5338", "9563", "16981", "30517", "54913", "98847", "179119", "324333", "589059", "1072997", "1955207", "3573129", "6538088" ]
[ "nonn", "more" ]
8
6
7
[ "A002840", "A355638" ]
null
Riccardo Maffucci, Jul 11 2022
2022-07-11T16:04:32
oeisdata/seq/A355/A355638.seq
00b00926fc9fe34461b0bad0b38a0a21
A355639
a(n) is the least k > 0 such that the balanced ternary expansion of k*n contains as many negative trits as positive trits.
[ "1", "2", "1", "2", "2", "4", "1", "8", "1", "2", "2", "14", "2", "2", "4", "4", "1", "8", "1", "14", "1", "8", "7", "2", "1", "16", "1", "2", "2", "8", "2", "2", "1", "14", "4", "2", "2", "2", "7", "2", "2", "4", "4", "2", "10", "4", "1", "4", "1", "2", "8", "8", "1", "8", "1", "8", "1", "14", "4", "4", "1", "8", "1", "8", "5", "2", "7", "14", "2", "2", "1", "2", "1", "2", "1", "16", "7", "2", "1", "8", "1", "2", "2", "8" ]
[ "nonn", "base" ]
7
0
2
[ "A065363", "A174658", "A351599", "A355639", "A355640" ]
null
Rémy Sigrist, Jul 11 2022
2022-07-13T14:43:22
oeisdata/seq/A355/A355639.seq
e9cd3ee29cbc0f25b7365933e77bf085
A355640
a(0) = 0, and for any n > 0, a(n) is the least positive multiple of n whose balanced ternary expansion contains as many negative trits as positive trits.
[ "0", "2", "2", "6", "8", "20", "6", "56", "8", "18", "20", "154", "24", "26", "56", "60", "16", "136", "18", "266", "20", "168", "154", "46", "24", "400", "26", "54", "56", "232", "60", "62", "32", "462", "136", "70", "72", "74", "266", "78", "80", "164", "168", "86", "440", "180", "46", "188", "48", "98", "400", "408", "52", "424", "54", "440", "56", "798", "232", "236", "60" ]
[ "nonn", "base" ]
6
0
2
[ "A065363", "A143146", "A174658", "A355639", "A355640" ]
null
Rémy Sigrist, Jul 11 2022
2022-07-13T14:43:36
oeisdata/seq/A355/A355640.seq
5eb0a8b8366378e0dc93e3c670af7f03
A355641
Numbers k that can be written as the sum of 5 divisors of k (not necessarily distinct).
[ "5", "6", "8", "9", "10", "12", "14", "15", "16", "18", "20", "21", "24", "25", "27", "28", "30", "32", "35", "36", "40", "42", "45", "48", "50", "54", "55", "56", "60", "63", "64", "65", "66", "70", "72", "75", "78", "80", "81", "84", "85", "88", "90", "95", "96", "98", "99", "100", "102", "104", "105", "108", "110", "112", "114", "115", "117", "120", "125", "126", "128", "130", "132", "135", "136", "138" ]
[ "nonn" ]
32
1
1
[ "A000027", "A299174", "A354591", "A355200", "A355641", "A356609", "A356635", "A356657", "A356659", "A356660" ]
null
Wesley Ivan Hurt, Aug 18 2022
2023-08-08T03:22:14
oeisdata/seq/A355/A355641.seq
6cd046d0908e072699cdaebf1b76ecc0
A355642
Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the balanced ternary expansion of n * a(n) contains as many negative trits as positive trits.
[ "0", "2", "1", "6", "4", "12", "3", "8", "7", "16", "13", "14", "5", "10", "11", "26", "9", "24", "23", "28", "20", "22", "21", "18", "17", "32", "15", "46", "19", "30", "29", "40", "25", "42", "34", "48", "36", "38", "37", "44", "31", "52", "33", "54", "39", "58", "27", "74", "35", "56", "55", "68", "41", "70", "43", "50", "49", "64", "45", "66", "60", "72", "63", "62", "57", "76", "59", "80" ]
[ "nonn", "base" ]
9
0
2
[ "A065363", "A174658", "A306993", "A355639", "A355642" ]
null
Rémy Sigrist, Jul 11 2022
2022-07-14T09:34:28
oeisdata/seq/A355/A355642.seq
a456f7c9b552053f31296f7658c9a4a9
A355643
Numbers k having a divisor d such that d+k/d is prime.
[ "1", "2", "4", "6", "10", "12", "16", "18", "22", "24", "28", "30", "34", "36", "40", "42", "46", "48", "52", "54", "58", "60", "66", "70", "72", "76", "78", "82", "84", "88", "90", "96", "100", "102", "106", "108", "112", "114", "118", "120", "126", "130", "132", "136", "138", "142", "148", "150", "154", "156", "160", "162", "166", "168", "172", "174", "178", "180", "184", "186", "190", "192", "196", "198", "202", "204", "208" ]
[ "nonn" ]
16
1
2
[ "A006093", "A355643", "A355644" ]
null
J. M. Bergot and Robert Israel, Jul 11 2022
2022-07-13T13:07:54
oeisdata/seq/A355/A355643.seq
6a4ef46129aed0f6a61ea951d0802632
A355644
Primes p such that p^2-1 does not have a divisor d with d + (p^2-1)/d prime.
[ "2", "3", "467", "487", "787", "887", "1279", "2063", "2557", "2657", "2903", "3323", "3413", "3547", "3583", "4273", "4373", "4517", "4567", "4801", "5233", "5393", "5443", "6047", "6823", "6911", "7507", "9133", "9137", "9721", "9973", "10103", "10313", "10937", "12227", "12763", "13183", "13627", "14407", "15073", "15083", "15187", "15359", "15787", "16903", "17047", "17911", "18013", "18587" ]
[ "nonn" ]
12
1
1
[ "A355643", "A355644" ]
null
J. M. Bergot and Robert Israel, Jul 11 2022
2022-07-13T17:41:50
oeisdata/seq/A355/A355644.seq
1f86cdde36eb8f81c4283b0f9b8b154a
A355645
The number of regions in the G-Shi arrangement when G is the cycle graph C_n.
[ "1", "3", "16", "61", "206", "659", "2052", "6297", "19162", "58015", "175088", "527333", "1586118", "4766571", "14316124", "42981169", "129009074", "387158327", "1161737160", "3485735805", "10458256030", "31376865283", "94134790196", "282412759241", "847255054986", "2541798719439", "7625463267232" ]
[ "nonn", "easy" ]
30
1
2
[ "A000244", "A001906", "A004146", "A355645" ]
null
Robin Truax, Jul 11 2022
2024-05-24T16:26:11
oeisdata/seq/A355/A355645.seq
7dad87ba2155a0f73003cfe565b8cfdc
A355646
Term in Recamán's sequence A005132 where n appears for the last time, or -1 if n never appears.
[ "0", "1", "4", "2", "131", "129", "3", "5", "16", "14", "12", "10", "8", "6", "31", "29", "27", "25", "23", "99734", "7", "9", "11", "13", "15", "17", "64", "62", "60", "58", "56", "54", "52", "50", "48", "46", "44", "42", "40", "38", "111", "22", "24", "26", "28", "30", "32", "222", "220", "218", "216", "214", "212", "210", "208", "206", "204", "202", "200", "198", "196", "181653" ]
[ "nonn" ]
9
0
3
[ "A005132", "A057167", "A355646" ]
null
Iain Fox, Jul 11 2022
2022-09-06T15:31:20
oeisdata/seq/A355/A355646.seq
3367b25b6a257bfc93fc4b4678c86a20
A355647
a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that has the same number of divisors as the sum a(n-2) + a(n-1).
[ "1", "2", "3", "5", "6", "7", "11", "12", "13", "4", "17", "8", "9", "19", "18", "23", "29", "20", "25", "28", "31", "37", "32", "10", "24", "14", "15", "41", "30", "43", "47", "60", "53", "59", "48", "61", "67", "40", "71", "21", "44", "22", "42", "64", "26", "72", "45", "50", "27", "33", "84", "52", "54", "34", "56", "90", "35", "38", "73", "39", "80", "46", "96", "51", "63", "66", "55", "49", "70", "57", "79", "78", "83", "58", "62", "120" ]
[ "nonn" ]
17
1
2
[ "A000005", "A351001", "A352768", "A352774", "A352867", "A355636", "A355647", "A355648" ]
null
Scott R. Shannon, Jul 12 2022
2022-07-26T13:38:29
oeisdata/seq/A355/A355647.seq
0f55a071eb13e965584b7fe528cfa742
A355648
The fixed points of A355647.
[ "1", "2", "3", "52", "66", "322", "1034", "1065", "1431", "3266", "4790", "4887", "33604", "54784", "125888" ]
[ "nonn", "more" ]
4
1
2
[ "A355647", "A355648" ]
null
Scott R. Shannon, Jul 12 2022
2022-07-12T08:39:04
oeisdata/seq/A355/A355648.seq
73d7869ef0258f42e17112aee6369c21
A355649
a(1) = a(2) = 1; for n > 2, a(n) is the smallest positive number that has the same number of divisors as the sum a(n-2) + a(n-1).
[ "1", "1", "2", "2", "4", "6", "6", "12", "12", "24", "36", "60", "60", "120", "180", "180", "360", "360", "720", "840", "840", "1680", "2520", "2520", "5040", "7560", "10080", "10080", "20160", "27720", "27720", "55440", "83160", "110880", "110880", "221760", "332640", "554400", "554400", "1108800", "1441440", "1441440", "2882880", "4324320", "7207200", "7207200", "14414400", "21621600" ]
[ "nonn" ]
9
1
3
[ "A000005", "A351001", "A352768", "A352774", "A352867", "A355636", "A355649" ]
null
Scott R. Shannon, Jul 12 2022
2022-07-14T09:53:31
oeisdata/seq/A355/A355649.seq
517e6075be36ffd39aa179a0a4d4b05c
A355650
Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. exp(x^k/k! * (exp(x) - 1)).
[ "1", "1", "1", "1", "0", "2", "1", "0", "2", "5", "1", "0", "0", "3", "15", "1", "0", "0", "3", "16", "52", "1", "0", "0", "0", "6", "65", "203", "1", "0", "0", "0", "4", "10", "336", "877", "1", "0", "0", "0", "0", "10", "105", "1897", "4140", "1", "0", "0", "0", "0", "5", "20", "651", "11824", "21147", "1", "0", "0", "0", "0", "0", "15", "35", "2968", "80145", "115975", "1", "0", "0", "0", "0", "0", "6", "35", "616", "18936", "586000", "678570" ]
[ "nonn", "tabl" ]
18
0
6
[ "A000110", "A052506", "A145460", "A292892", "A354000", "A354001", "A355610", "A355650" ]
null
Seiichi Manyama, Jul 12 2022
2022-07-12T14:36:19
oeisdata/seq/A355/A355650.seq
6dba14a09a02a03f964a6d5f8bf49697
A355651
Emirps p such that (p*q) mod (p+q) is also an emirp, where q is the digit reversal of p.
[ "389", "709", "907", "983", "1669", "3163", "3613", "7349", "9349", "9437", "9439", "9661", "11071", "11959", "12841", "13513", "13751", "13757", "13873", "14549", "14593", "14713", "14821", "14923", "15013", "15731", "15919", "16573", "16937", "17011", "17681", "18133", "18671", "30197", "31051", "31531", "31741", "32579", "32783", "32941", "33181", "33287", "35129", "36217", "37561" ]
[ "nonn", "base", "less" ]
36
1
1
[ "A004086", "A006567", "A355651", "A356740" ]
null
J. M. Bergot and Robert Israel, Sep 04 2022
2022-09-18T11:06:05
oeisdata/seq/A355/A355651.seq
8a140ea89682fd0c9cdf209d2f6ce542
A355652
Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. 1/(1 + x^k/k! * log(1 - x)).
[ "1", "1", "1", "1", "0", "3", "1", "0", "2", "14", "1", "0", "0", "3", "88", "1", "0", "0", "3", "32", "694", "1", "0", "0", "0", "6", "150", "6578", "1", "0", "0", "0", "4", "20", "1524", "72792", "1", "0", "0", "0", "0", "10", "270", "12600", "920904", "1", "0", "0", "0", "0", "5", "40", "1764", "147328", "13109088", "1", "0", "0", "0", "0", "0", "15", "210", "12600", "1705536", "207360912", "1", "0", "0", "0", "0", "0", "6", "70", "2464", "146880", "23681520", "3608233056" ]
[ "nonn", "tabl" ]
41
0
6
[ "A007840", "A052830", "A351505", "A351506", "A355610", "A355652", "A355665" ]
null
Seiichi Manyama, Jul 13 2022
2022-07-13T12:07:25
oeisdata/seq/A355/A355652.seq
3475544ed29d4fc1fe5a531a2e32a98b
A355653
For any number n with runs in binary expansion (r_w, ..., r_0), let p(n) be the polynomial of a single indeterminate x where the coefficient of x^e is r_e for e = 0..w and otherwise 0, and let q be the inverse of p; a(n) = q(p(n)').
[ "0", "0", "1", "0", "1", "6", "3", "0", "1", "12", "57", "6", "3", "30", "7", "0", "1", "24", "225", "12", "57", "966", "115", "6", "3", "60", "505", "30", "7", "126", "15", "0", "1", "48", "897", "24", "225", "7686", "451", "12", "57", "1932", "31801", "966", "115", "3870", "231", "6", "3", "120", "2017", "60", "505", "16326", "1011", "30", "7", "252", "4089", "126", "15", "510" ]
[ "nonn", "base" ]
12
0
6
[ "A000225", "A005811", "A101211", "A355653", "A355654" ]
null
Rémy Sigrist, Jul 12 2022
2022-07-14T15:02:01
oeisdata/seq/A355/A355653.seq
1efb4318b66747d767ce37ad76c02a62
A355654
For any number n with runs in binary expansion (r_w, ..., r_0), let p(n) be the polynomial of a single indeterminate x where the coefficient of x^e is r_e for e = 0..w and otherwise 0, and let q be the inverse of p; a(n) = q(p(n)^2).
[ "0", "1", "9", "15", "271", "313", "481", "511", "33279", "34785", "39993", "40719", "61455", "61689", "65409", "65535", "16842751", "17039233", "17809657", "17821711", "20455183", "20479033", "20842465", "20939263", "31457791", "31465441", "31584313", "31588111", "33488911", "33489913", "33553921", "33554431", "34393292799" ]
[ "nonn", "base" ]
6
0
3
[ "A005811", "A101211", "A212739", "A355653", "A355654" ]
null
Rémy Sigrist, Jul 12 2022
2022-07-14T09:35:11
oeisdata/seq/A355/A355654.seq
96206741e9bd804145712fddeb5a7416
A355655
a(n) = 1 if the smallest b > 1 such that b^(p-1) == 1 (mod p^2) is prime, 0 otherwise, with p = prime(n).
[ "1", "0", "1", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "1", "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", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0" ]
[ "nonn" ]
7
1
null
[ "A010051", "A039678", "A355655", "A355656", "A355657" ]
null
Felix Fröhlich, Jul 12 2022
2022-07-16T01:32:19
oeisdata/seq/A355/A355655.seq
c0d89968faef2e98c3a413093c30afcb
A355656
Primes p such that A355655(i) = 0, where i is the index of p in A000040.
[ "3", "7", "17", "19", "23", "29", "31", "37", "41", "53", "61", "67", "73", "83", "89", "107", "109", "113", "127", "131", "139", "151", "157", "163", "167", "173", "179", "181", "191", "193", "197", "199", "211", "223", "227", "229", "233", "239", "241", "257", "269", "271", "277", "281", "283", "293", "307", "311", "313", "317", "331", "337", "347", "353", "367", "373" ]
[ "nonn" ]
5
1
1
[ "A000040", "A355655", "A355656", "A355657" ]
null
Felix Fröhlich, Jul 12 2022
2022-07-16T01:32:37
oeisdata/seq/A355/A355656.seq
45a0121936d8aada3f20d3c717c7c7ae
A355657
Primes p such that A355655(i) = 1, where i is the index of p in A000040.
[ "2", "5", "11", "13", "43", "47", "59", "71", "79", "97", "101", "103", "137", "149", "251", "263", "349", "359", "383", "409", "421", "433", "467", "523", "569", "659", "743", "853", "859", "863", "907", "919", "937", "983", "1069", "1087", "1091", "1093", "1223", "1229", "1259", "1279", "1483", "1499", "1583", "1637", "1663", "1667", "1697", "1709", "1777" ]
[ "nonn" ]
5
1
1
[ "A000040", "A355655", "A355656", "A355657" ]
null
Felix Fröhlich, Jul 12 2022
2022-07-16T01:32:48
oeisdata/seq/A355/A355657.seq
687d85edde23dc9924c6a5d07de20e47
A355658
Smallest prime base q such that q^(p-1) == 1 (mod p^2), where p = prime(n).
[ "5", "17", "7", "19", "3", "19", "131", "127", "263", "41", "229", "691", "313", "19", "53", "521", "53", "601", "1301", "11", "619", "31", "269", "3187", "53", "181", "43", "317", "499", "373", "911", "659", "19", "3659", "313", "751", "233", "4373", "3307", "419", "2591", "313", "1249", "2897", "349", "709", "331", "1973", "1933", "503", "821", "977", "2371", "263" ]
[ "nonn" ]
8
1
1
[ "A001220", "A039678", "A125636", "A355658" ]
null
Felix Fröhlich, Jul 12 2022
2022-07-17T10:51:36
oeisdata/seq/A355/A355658.seq
fb54c913e7f6d1d5a4e36c9918994107
A355659
Martingale win/loss triangle, read by rows: T(n,k) = total number of dollars won (or lost) using the martingale method on all possible n trials that have exactly k losses and n-k wins, for 0 <= k <= n.
[ "0", "1", "-1", "2", "1", "-3", "3", "5", "-1", "-7", "4", "11", "7", "-7", "-15", "5", "19", "24", "4", "-21", "-31", "6", "29", "53", "38", "-12", "-51", "-63", "7", "41", "97", "111", "41", "-57", "-113", "-127", "8", "55", "159", "243", "187", "5", "-163", "-239", "-255", "9", "71", "242", "458", "500", "248", "-130", "-394", "-493", "-511", "10", "89", "349", "784", "1084", "874", "202", "-488", "-878", "-1003", "-1023" ]
[ "sign", "tabl" ]
56
0
4
[ "A000225", "A070313", "A165900", "A355659" ]
null
Greg Dresden and Max Winnick, Jul 12 2022
2024-03-31T15:35:53
oeisdata/seq/A355/A355659.seq
0951f21d59f2b12afd78063d1342c36d
A355660
Numbers m such that the smallest number of pentagonal numbers (A000326) which sum to m is exactly 4.
[ "4", "8", "16", "19", "20", "26", "30", "33", "38", "42", "50", "54", "60", "65", "67", "77", "81", "84", "88", "90", "96", "99", "100", "101", "111", "112", "113", "120", "125", "131", "135", "138", "142", "154", "159", "160", "166", "170", "171", "183", "195", "204", "205", "207", "217", "224", "225", "226", "229", "230", "236", "240", "241", "243", "255", "265", "275", "277", "286", "306", "308", "345" ]
[ "nonn" ]
30
1
1
[ "A000326", "A003679", "A100878", "A133929", "A355660" ]
null
Bernard Schott, Jul 12 2022
2022-07-14T11:21:12
oeisdata/seq/A355/A355660.seq
0179162baf3a63e9291c973b2003028b
A355661
Largest number of children of any vertex in the rooted tree with Matula-Goebel number n.
[ "0", "1", "1", "2", "1", "2", "2", "3", "2", "2", "1", "3", "2", "2", "2", "4", "2", "3", "3", "3", "2", "2", "2", "4", "2", "2", "3", "3", "2", "3", "1", "5", "2", "2", "2", "4", "3", "3", "2", "4", "2", "3", "2", "3", "3", "2", "2", "5", "2", "3", "2", "3", "4", "4", "2", "4", "3", "2", "2", "4", "3", "2", "3", "6", "2", "3", "3", "3", "2", "3", "3", "5", "2", "3", "3", "3", "2", "3", "2", "5", "4", "2", "2", "4", "2", "2", "2" ]
[ "nonn" ]
14
1
4
[ "A001222", "A007097", "A354322", "A355661", "A355662" ]
null
Kevin Ryde, Jul 14 2022
2022-07-15T02:37:50
oeisdata/seq/A355/A355661.seq
eac7a0c4ee1b88fcecd2d8d6baaaf2bf
A355662
Smallest number of children of any vertex which has children, in the rooted tree with Matula-Goebel number n.
[ "0", "1", "1", "2", "1", "1", "1", "3", "1", "1", "1", "1", "1", "2", "1", "4", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "5", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "6", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1" ]
[ "nonn" ]
12
1
4
[ "A000720", "A001222", "A291636", "A354322", "A355661", "A355662" ]
null
Kevin Ryde, Jul 15 2022
2022-09-08T08:14:21
oeisdata/seq/A355/A355662.seq
3837f96ecdc4c20f19f4fb491d9fc431
A355663
Square array A(n, k), n, k >= 0, read by antidiagonals; for any number n with runs in binary expansion (r_w, ..., r_0), let p(n) be the polynomial of a single indeterminate x where the coefficient of x^e is r_e for e = 0..w and otherwise 0, and let q be the inverse of p; A(n, k) = q(p(n) + p(k)).
[ "0", "1", "1", "2", "3", "2", "3", "4", "4", "3", "4", "7", "12", "7", "4", "5", "8", "8", "8", "8", "5", "6", "11", "24", "15", "24", "11", "6", "7", "12", "19", "16", "16", "19", "12", "7", "8", "15", "28", "23", "48", "23", "28", "15", "8", "9", "16", "16", "24", "39", "39", "24", "16", "16", "9", "10", "19", "48", "31", "56", "51", "56", "31", "48", "19", "10", "11", "20", "35", "32", "32", "35", "35", "32", "32", "35", "20", "11" ]
[ "nonn", "base", "tabl" ]
5
0
4
[ "A001196", "A014601", "A101211", "A355663", "A355664" ]
null
Rémy Sigrist, Jul 13 2022
2022-07-14T09:35:21
oeisdata/seq/A355/A355663.seq
983c8203eaafa9fb1080261acfa0d797
A355664
Square array A(n, k), n, k >= 0, read by antidiagonals; for any number n with runs in binary expansion (r_w, ..., r_0), let p(n) be the polynomial of a single indeterminate x where the coefficient of x^e is r_e for e = 0..w and otherwise 0, and let q be the inverse of p; A(n, k) = q(p(n) * p(k)).
[ "0", "0", "0", "0", "1", "0", "0", "2", "2", "0", "0", "3", "9", "3", "0", "0", "4", "12", "12", "4", "0", "0", "5", "35", "15", "35", "5", "0", "0", "6", "38", "48", "48", "38", "6", "0", "0", "7", "49", "51", "271", "51", "49", "7", "0", "0", "8", "56", "60", "284", "284", "60", "56", "8", "0", "0", "9", "135", "63", "387", "313", "387", "63", "135", "9", "0", "0", "10", "142", "192", "448", "398", "398", "448", "192", "142", "10", "0" ]
[ "nonn", "base", "tabl" ]
4
0
8
[ "A001196", "A097254", "A101211", "A355663", "A355664" ]
null
Rémy Sigrist, Jul 13 2022
2022-07-14T09:35:26
oeisdata/seq/A355/A355664.seq
e9705e581ec8bb73a2a005322b0d879f
A355665
Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. 1/(1 + x^k * log(1 - x)).
[ "1", "1", "1", "1", "0", "3", "1", "0", "2", "14", "1", "0", "0", "3", "88", "1", "0", "0", "6", "32", "694", "1", "0", "0", "0", "12", "150", "6578", "1", "0", "0", "0", "24", "40", "1524", "72792", "1", "0", "0", "0", "0", "60", "900", "12600", "920904", "1", "0", "0", "0", "0", "120", "240", "6048", "147328", "13109088", "1", "0", "0", "0", "0", "0", "360", "1260", "43680", "1705536", "207360912" ]
[ "nonn", "tabl" ]
15
0
6
[ "A007840", "A052830", "A351503", "A351504", "A355609", "A355652", "A355665" ]
null
Seiichi Manyama, Jul 13 2022
2022-07-13T06:35:26
oeisdata/seq/A355/A355665.seq
46dc501e61f3891f617b35fd34e32b23
A355666
Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. 1/(1 - x^k/k! * (exp(x) - 1)).
[ "1", "1", "1", "1", "0", "3", "1", "0", "2", "13", "1", "0", "0", "3", "75", "1", "0", "0", "3", "28", "541", "1", "0", "0", "0", "6", "125", "4683", "1", "0", "0", "0", "4", "10", "1146", "47293", "1", "0", "0", "0", "0", "10", "195", "8827", "545835", "1", "0", "0", "0", "0", "5", "20", "1281", "94200", "7087261", "1", "0", "0", "0", "0", "0", "15", "35", "5908", "1007001", "102247563", "1", "0", "0", "0", "0", "0", "6", "35", "1176", "68076", "12814390", "1622632573" ]
[ "nonn", "tabl" ]
18
0
6
[ "A000670", "A052848", "A351703", "A353998", "A353999", "A355652", "A355666" ]
null
Seiichi Manyama, Jul 13 2022
2022-09-02T12:07:37
oeisdata/seq/A355/A355666.seq
32fe00cc377497036aa459828f0696e5
A355667
Least number phi(k) such that n * phi(k) < k, where phi is Euler's totient function.
[ "1", "2", "8", "48", "5760", "36495360", "1854081073152000", "400440702414394285778534400000", "165062110921422523175104166476600499887194872217600000000" ]
[ "nonn" ]
49
1
2
[ "A091439", "A091456", "A355667" ]
null
Nico Mexis, Jul 13 2022
2025-03-22T23:34:07
oeisdata/seq/A355/A355667.seq
0dade1410fd6c4295e60766f33567d4a
A355668
Array read by upwards antidiagonals T(n,k) = J(k) + n*J(k+1) where J(n) = A001045(n) is the Jacobsthal numbers.
[ "0", "1", "1", "2", "2", "1", "3", "3", "4", "3", "4", "4", "7", "8", "5", "5", "5", "10", "13", "16", "11", "6", "6", "13", "18", "27", "32", "21", "7", "7", "16", "23", "38", "53", "64", "43", "8", "8", "19", "28", "49", "74", "107", "128", "85", "9", "9", "22", "33", "60", "95", "150", "213", "256", "171", "10", "10", "25", "38", "71", "116", "193", "298", "427", "512", "341" ]
[ "nonn", "tabl", "easy" ]
28
0
4
[ "A000027", "A001477", "A016777", "A016885", "A017449", "A320933", "A321373", "A355668" ]
null
Paul Curtz, Jul 13 2022
2022-07-14T22:55:20
oeisdata/seq/A355/A355668.seq
df359f98f3d19539a6ff11e3f4564462
A355669
a(n) = n! * Sum_{d|n} (d!)^(d - n/d).
[ "1", "6", "222", "331824", "24883200120", "139314069504005400", "82606411253903523840005040", "6984964247141514123629140377623274720", "109110688415571316480344899355894085582848000725760", "395940866122425193243875570782668457763038822400000006270570482400" ]
[ "nonn" ]
28
1
2
[ "A061095", "A345465", "A351165", "A355669", "A356662" ]
null
Seiichi Manyama, Aug 21 2022
2022-08-21T14:10:20
oeisdata/seq/A355/A355669.seq
ded5c8c4915038930286b28cef92bd85
A355670
Numbers k such that A246600(k) < A000005(k).
[ "2", "4", "6", "8", "9", "10", "12", "14", "16", "18", "20", "21", "22", "24", "25", "26", "28", "30", "32", "33", "34", "35", "36", "38", "39", "40", "42", "44", "45", "46", "48", "49", "50", "52", "54", "55", "56", "57", "58", "60", "62", "64", "65", "66", "68", "69", "70", "72", "74", "75", "76", "77", "78", "80", "81", "82", "84", "86", "87", "88", "90", "91", "92", "93", "94", "96" ]
[ "nonn", "base" ]
13
1
1
[ "A000005", "A102553", "A102554", "A246600", "A336375", "A355670", "A359080" ]
null
Chai Wah Wu, Dec 19 2022
2023-01-20T08:33:58
oeisdata/seq/A355/A355670.seq
7223361dcab91f4e8ab660a4e7148b34
A355671
Number of labeled trees on [n] that are bicentered.
[ "0", "0", "1", "0", "12", "60", "570", "8190", "134456", "2408616", "49307670", "1159112130", "30619757652", "891045909468", "28244653953698", "969331283419590", "35858099428919280", "1423688804991442896", "60402176709135347502", "2726896792761748601226", "130498364319404393167820" ]
[ "nonn" ]
21
0
5
[ "A000272", "A000677", "A034854", "A355671", "A356292" ]
null
Geoffrey Critzer, Aug 02 2022
2022-08-02T23:51:25
oeisdata/seq/A355/A355671.seq
f44d886de44f1a90d977de6a80fb01b6
A355672
Expansion of e.g.f. exp(1/(1-x) - exp(x)).
[ "1", "0", "1", "5", "26", "169", "1329", "12088", "124221", "1422307", "17947550", "247318851", "3693469273", "59396067080", "1022975862713", "18781241965081", "366070181352802", "7547972562003093", "164113696105503057", "3752143293971556144", "89976991297720804061", "2257905394760969948079" ]
[ "nonn" ]
19
0
4
[ "A000262", "A000587", "A033312", "A186755", "A352294", "A355672" ]
null
Seiichi Manyama, Jul 14 2022
2022-07-21T06:45:06
oeisdata/seq/A355/A355672.seq
16a18fefbe61f0a8b70973f3a26695a8
A355673
Decimal expansion of 265/153.
[ "1", "7", "3", "2", "0", "2", "6", "1", "4", "3", "7", "9", "0", "8", "4", "9", "6", "7", "3", "2", "0", "2", "6", "1", "4", "3", "7", "9", "0", "8", "4", "9", "6", "7", "3", "2", "0", "2", "6", "1", "4", "3", "7", "9", "0", "8", "4", "9", "6", "7", "3", "2", "0", "2", "6", "1", "4", "3", "7", "9", "0", "8", "4", "9", "6", "7", "3", "2", "0", "2", "6", "1", "4", "3", "7", "9", "0", "8", "4", "9", "6", "7", "3", "2", "0", "2", "6", "1" ]
[ "nonn", "cons", "easy" ]
8
1
2
[ "A002194", "A355673", "A355674" ]
null
Stefano Spezia, Jul 14 2022
2022-07-14T22:55:34
oeisdata/seq/A355/A355673.seq
0e73db551d906dbefce98e484e9fd0da
A355674
Decimal expansion of 1351/780.
[ "1", "7", "3", "2", "0", "5", "1", "2", "8", "2", "0", "5", "1", "2", "8", "2", "0", "5", "1", "2", "8", "2", "0", "5", "1", "2", "8", "2", "0", "5", "1", "2", "8", "2", "0", "5", "1", "2", "8", "2", "0", "5", "1", "2", "8", "2", "0", "5", "1", "2", "8", "2", "0", "5", "1", "2", "8", "2", "0", "5", "1", "2", "8", "2", "0", "5", "1", "2", "8", "2", "0", "5", "1", "2", "8", "2", "0", "5", "1", "2", "8", "2", "0", "5", "1", "2", "8", "2" ]
[ "nonn", "cons", "easy" ]
18
1
2
[ "A002194", "A021316", "A355673", "A355674" ]
null
Stefano Spezia, Jul 14 2022
2024-04-19T02:00:32
oeisdata/seq/A355/A355674.seq
215771055e404088ed8089a3aa3044b8
A355675
a(0) = 0, and for any n > 0 and d = 1..9, a(10*n) = 10*a(n), a(10*n + d) = d - 10*a(n).
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "-9", "-8", "-7", "-6", "-5", "-4", "-3", "-2", "-1", "20", "-19", "-18", "-17", "-16", "-15", "-14", "-13", "-12", "-11", "30", "-29", "-28", "-27", "-26", "-25", "-24", "-23", "-22", "-21", "40", "-39", "-38", "-37", "-36", "-35", "-34", "-33", "-32", "-31", "50", "-49", "-48", "-47", "-46", "-45", "-44", "-43", "-42" ]
[ "sign", "base", "easy" ]
10
0
3
[ "A037124", "A065620", "A073835", "A334387", "A355624", "A355675" ]
null
Rémy Sigrist, Jul 14 2022
2022-07-18T14:16:45
oeisdata/seq/A355/A355675.seq
736c06245c8701983d3f8557dae7b6bb
A355676
a(n) is the least k such that p(16*k+n) is odd where p is the number of partitions A000041.
[ "0", "0", "1", "0", "0", "0", "0", "0", "1", "2", "5", "2", "0", "0", "0", "3", "0", "0", "0", "1", "0", "1", "1", "0", "0", "1", "4", "1", "1", "0", "10", "2", "0", "0", "3", "0", "0", "0", "0", "0", "1", "0", "3", "0", "0", "1", "9", "1", "0", "0", "2", "0", "0", "0", "0", "1", "0", "1", "2", "2", "0", "0", "8", "0", "5", "1", "1", "0", "0", "0", "2", "0", "0", "0", "1", "1", "0", "0", "7", "1", "4", "0", "0", "0", "3", "0", "1", "0", "0", "0" ]
[ "nonn" ]
16
0
10
[ "A000041", "A040051", "A355676", "A355677" ]
null
Michel Marcus, Jul 14 2022
2022-07-15T02:30:26
oeisdata/seq/A355/A355676.seq
439496b0ba164cbe6c1d351fd499ed66
A355677
Companion sequence to A355676.
[ "4", "5", "4", "7", "8", "3", "1", "2", "1", "3", "4", "2", "7", "8", "3", "4", "2", "6", "4", "6", "0", "5", "0", "3", "1", "3", "4", "2", "6", "0", "5", "4", "3", "1", "5", "6", "4", "5", "0", "7", "0", "3", "4", "2", "6", "2", "5", "4", "7", "8", "5", "1", "2", "6", "4", "6", "0", "5", "4", "5", "1", "2", "5", "4", "4", "4", "5", "8", "3", "1", "7", "6", "4", "5", "4", "5", "8", "3", "5", "3", "4", "4", "5", "0", "1", "8", "7" ]
[ "nonn" ]
7
0
1
[ "A010878", "A355676", "A355677" ]
null
Michel Marcus, Jul 14 2022
2022-07-16T01:25:16
oeisdata/seq/A355/A355677.seq
9f2c478de08e95b4c0ef42f06abeb0a9
A355678
For any nonnegative number n with factorial base expansion Sum_{k > 0} d_k * k!, a(n) = Sum_{k > 0} d_k * k! * (-1)^(Sum_{i < k} sign(d_i)).
[ "0", "1", "2", "-1", "4", "-3", "6", "-5", "-4", "5", "-2", "3", "12", "-11", "-10", "11", "-8", "9", "18", "-17", "-16", "17", "-14", "15", "24", "-23", "-22", "23", "-20", "21", "-18", "19", "20", "-19", "22", "-21", "-12", "13", "14", "-13", "16", "-15", "-6", "7", "8", "-7", "10", "-9", "48", "-47", "-46", "47", "-44", "45", "-42", "43", "44", "-43", "46", "-45", "-36", "37" ]
[ "sign", "base" ]
10
0
3
[ "A051683", "A065620", "A355678", "A355679" ]
null
Rémy Sigrist, Jul 14 2022
2022-07-18T14:16:49
oeisdata/seq/A355/A355678.seq
e184fe5d7079617ce3af0fd5d20e18f3
A355679
For any nonnegative number n with primorial base expansion Sum_{k >= 0} d_k * A002110(k), a(n) = Sum_{k >= 0} d_k * A002110(k) * (-1)^(Sum_{i < k} sign(d_i)).
[ "0", "1", "2", "-1", "4", "-3", "6", "-5", "-4", "5", "-2", "3", "12", "-11", "-10", "11", "-8", "9", "18", "-17", "-16", "17", "-14", "15", "24", "-23", "-22", "23", "-20", "21", "30", "-29", "-28", "29", "-26", "27", "-24", "25", "26", "-25", "28", "-27", "-18", "19", "20", "-19", "22", "-21", "-12", "13", "14", "-13", "16", "-15", "-6", "7", "8", "-7", "10", "-9", "60", "-59" ]
[ "sign", "base" ]
10
0
3
[ "A002110", "A060735", "A065620", "A355678", "A355679" ]
null
Rémy Sigrist, Jul 14 2022
2022-07-18T14:16:54
oeisdata/seq/A355/A355679.seq
197511fda72941cce7cc2ab1c0541c3e
A355680
Numerator generator for offsets from the quarter points of the Cantor ternary set to the center points of deleted middle thirds: 1 is in the list and if m is in the list -3m-4 and -3m+4 are in the list, which is ordered by absolute value.
[ "1", "-7", "17", "25", "-47", "-55", "-71", "-79", "137", "145", "161", "169", "209", "217", "233", "241", "-407", "-415", "-431", "-439", "-479", "-487", "-503", "-511", "-623", "-631", "-647", "-655", "-695", "-703", "-719", "-727", "1217", "1225", "1241", "1249", "1289", "1297", "1313", "1321", "1433", "1441", "1457", "1465", "1505", "1513", "1529", "1537", "1865" ]
[ "sign", "easy" ]
10
1
2
[ "A191108", "A355680", "A355682" ]
null
Peter Munn, Jul 14 2022
2025-02-16T08:34:03
oeisdata/seq/A355/A355680.seq
08a1214d78a70e1e6416fbf173908911
A355681
The "coarser" of 2 representations of the Cantor middle thirds set viewed from a quarter point that lies at a(0) (the third 1 in the data).
[ "-1", "1", "0", "0", "-1", "1", "0", "0", "0", "0", "0", "0", "-1", "1", "0", "0", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "1", "0", "0", "-1", "1", "0", "0", "0", "0", "0", "0", "-1", "1", "0", "0", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign", "easy" ]
12
-13
null
[ "A088917", "A355681", "A355682" ]
null
Peter Munn, Jul 14 2022
2025-02-16T08:34:03
oeisdata/seq/A355/A355681.seq
7ea9494edfddfc8cf1f941531b9494f2
A355682
The "finer" of 2 representations of the Cantor middle thirds set viewed from a quarter point that lies at a(0) (the second 1 in the data).
[ "2", "1", "0", "-1", "-2", "0", "0", "0", "2", "1", "0", "-1", "-2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "1", "0", "-1", "-2", "0", "0", "0", "2", "1", "0", "-1", "-2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign", "easy" ]
11
-9
1
[ "A088917", "A355680", "A355681", "A355682" ]
null
Peter Munn, Jul 14 2022
2025-02-16T08:34:03
oeisdata/seq/A355/A355682.seq
c0aad6c5a33cbb426cfe1a049673eacb
A355683
Multiplicative with a(p^e) = 0 if e=1 and a(p^e)= -1 if e>1.
[ "1", "0", "0", "-1", "0", "0", "0", "-1", "-1", "0", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "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", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1" ]
[ "sign", "mult", "changed" ]
13
1
null
[ "A076479", "A112526", "A355683" ]
null
Antti Karttunen, Jul 14 2022, after R. J. Mathar's Apr 04 2011 comment in A112526
2025-07-09T04:59:23
oeisdata/seq/A355/A355683.seq
43c7c3709d547951be3d21d34dd7347c
A355684
Dirichlet inverse of A355448.
[ "1", "0", "0", "-1", "0", "0", "0", "-1", "-1", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "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", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1" ]
[ "sign", "mult" ]
14
1
null
[ "A112526", "A355448", "A355684" ]
null
Antti Karttunen, Jul 14 2022
2023-02-09T01:55:22
oeisdata/seq/A355/A355684.seq
683a6b371972b0944a207b69004b34e3
A355685
Dirichlet inverse of A353380.
[ "1", "0", "0", "-1", "0", "-1", "0", "-1", "-1", "0", "0", "-1", "0", "-1", "-1", "1", "0", "-1", "0", "-1", "0", "0", "0", "2", "-1", "-1", "-1", "-1", "0", "0", "0", "1", "-1", "0", "-1", "2", "0", "-1", "0", "0", "0", "0", "0", "-1", "-1", "0", "0", "3", "-1", "-1", "-1", "-1", "0", "2", "0", "2", "0", "-1", "0", "1", "0", "0", "-1", "-1", "-1", "0", "0", "-1", "-1", "0", "0", "5", "0", "-1", "-1", "-1", "-1", "0", "0", "2", "1", "0", "0", "1", "0", "-1", "0", "0", "0", "1", "0", "-1", "-1", "0", "-1", "-2", "0", "-1", "-1", "1", "0", "0", "0", "2", "0" ]
[ "sign" ]
8
1
24
[ "A003961", "A048675", "A332823", "A348717", "A353348", "A353354", "A353355", "A353380", "A353418", "A355685" ]
null
Antti Karttunen, Jul 14 2022
2022-07-15T09:54:40
oeisdata/seq/A355/A355685.seq
451721bda2d7a9011c3b7f2cb8d5699b
A355686
Dirichlet inverse of A276150, where A276150(n) is the sum of digits when n is written in primorial base.
[ "1", "-1", "-2", "-1", "-3", "3", "-2", "1", "1", "3", "-4", "2", "-3", "1", "8", "-1", "-5", "-5", "-4", "5", "3", "3", "-6", "-7", "4", "1", "-2", "2", "-7", "-11", "-2", "3", "13", "7", "8", "4", "-3", "5", "8", "-5", "-5", "-1", "-4", "10", "-7", "7", "-6", "8", "-1", "-4", "14", "7", "-7", "9", "18", "1", "9", "7", "-8", "-16", "-3", "1", "4", "-1", "13", "-17", "-4", "7", "19", "-3", "-6", "16", "-5", "1", "-16", "4", "9", "-7", "-6", "3", "6", "3", "-8", "-5", "23", "1", "20" ]
[ "sign", "base" ]
8
1
3
[ "A276150", "A319715", "A355686", "A355687" ]
null
Antti Karttunen, Jul 14 2022
2022-07-15T09:54:48
oeisdata/seq/A355/A355686.seq
daae369516af6f70bfbabb5657386418
A355687
Sum of A276150 and its Dirichlet inverse.
[ "2", "0", "0", "1", "0", "4", "0", "3", "4", "6", "0", "4", "0", "4", "12", "3", "0", "-2", "0", "9", "8", "8", "0", "-3", "9", "6", "4", "8", "0", "-10", "0", "5", "16", "10", "12", "6", "0", "8", "12", "-1", "0", "2", "0", "14", "-2", "12", "0", "12", "4", "1", "20", "13", "0", "14", "24", "7", "16", "14", "0", "-14", "0", "4", "8", "3", "18", "-14", "0", "11", "24", "2", "0", "20", "0", "6", "-10", "10", "16", "-2", "0", "9", "13", "10", "0", "1", "30", "8", "28", "-3", "0", "28", "12", "16" ]
[ "sign", "base" ]
9
1
1
[ "A276150", "A355686", "A355687" ]
null
Antti Karttunen, Jul 14 2022
2022-07-15T08:10:57
oeisdata/seq/A355/A355687.seq
d28f877f0bc89a714d3d1c943ca1e200
A355688
Dirichlet inverse of A354354, characteristic function of numbers that are neither multiples of 2 nor 3.
[ "1", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "1", "0", "-1", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "-1", "0", "0", "0", "0", "0", "-1", "0", "1", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "1", "0", "-1", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "1", "0", "-1", "0", "0", "0", "-1", "0", "1", "0", "0", "0", "-1", "0", "1", "0", "0", "0", "1", "0", "-1", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "-1", "0" ]
[ "sign", "mult" ]
19
1
null
[ "A007310", "A008683", "A354354", "A355688", "A355689", "A355690" ]
null
Antti Karttunen, Jul 15 2022
2022-12-27T02:30:08
oeisdata/seq/A355/A355688.seq
2def2342f2a8f2419d33192341cfa268
A355689
Dirichlet inverse of A166486, characteristic function of numbers that are not multiples of 4.
[ "1", "-1", "-1", "1", "-1", "1", "-1", "-1", "0", "1", "-1", "-1", "-1", "1", "1", "1", "-1", "0", "-1", "-1", "1", "1", "-1", "1", "0", "1", "0", "-1", "-1", "-1", "-1", "-1", "1", "1", "1", "0", "-1", "1", "1", "1", "-1", "-1", "-1", "-1", "0", "1", "-1", "-1", "0", "0", "1", "-1", "-1", "0", "1", "1", "1", "1", "-1", "1", "-1", "1", "0", "1", "1", "-1", "-1", "-1", "1", "-1", "-1", "0", "-1", "1", "0", "-1", "1", "-1", "-1", "-1", "0", "1", "-1", "1", "1", "1", "1", "1", "-1", "0", "1", "-1", "1", "1", "1", "1", "-1", "0", "0", "0", "-1", "-1", "-1", "1", "-1", "1", "-1", "0" ]
[ "sign", "mult" ]
29
1
null
[ "A008683", "A008836", "A087003", "A166486", "A353627", "A355688", "A355689", "A355690", "A358839", "A359156", "A359157", "A359158", "A359159" ]
null
Antti Karttunen, Jul 15 2022
2022-12-31T11:19:22
oeisdata/seq/A355/A355689.seq
53d08855bd81927c9c4d146dabf6af30
A355690
Dirichlet inverse of A152822, where A152822 is the characteristic function of numbers not congruent to 2 mod 4.
[ "1", "0", "-1", "-1", "-1", "0", "-1", "-1", "0", "0", "-1", "1", "-1", "0", "1", "0", "-1", "0", "-1", "1", "1", "0", "-1", "1", "0", "0", "0", "1", "-1", "0", "-1", "1", "1", "0", "1", "0", "-1", "0", "1", "1", "-1", "0", "-1", "1", "0", "0", "-1", "0", "0", "0", "1", "1", "-1", "0", "1", "1", "1", "0", "-1", "-1", "-1", "0", "0", "1", "1", "0", "-1", "1", "1", "0", "-1", "0", "-1", "0", "0", "1", "1", "0", "-1", "0", "0", "0", "-1", "-1", "1", "0", "1", "1", "-1", "0", "1", "1", "1", "0", "1", "-1", "-1", "0", "0", "0", "-1", "0", "-1", "1", "-1", "0", "-1", "0" ]
[ "sign", "mult", "easy" ]
20
1
null
[ "A010892", "A042965", "A152822", "A355688", "A355689", "A355690", "A355691", "A359590", "A359605", "A359606" ]
null
Antti Karttunen, Jul 15 2022
2023-01-12T18:43:19
oeisdata/seq/A355/A355690.seq
f7e1ece10398d393a9790315691eb381
A355691
Dirichlet inverse of A320111, number of divisors of n that are not of the form 4k+2.
[ "1", "-1", "-2", "-1", "-2", "2", "-2", "0", "1", "2", "-2", "2", "-2", "2", "4", "1", "-2", "-1", "-2", "2", "4", "2", "-2", "0", "1", "2", "0", "2", "-2", "-4", "-2", "1", "4", "2", "4", "-1", "-2", "2", "4", "0", "-2", "-4", "-2", "2", "-2", "2", "-2", "-2", "1", "-1", "4", "2", "-2", "0", "4", "0", "4", "2", "-2", "-4", "-2", "2", "-2", "0", "4", "-4", "-2", "2", "4", "-4", "-2", "0", "-2", "2", "-2", "2", "4", "-4", "-2", "-2", "0", "2", "-2", "-4", "4", "2", "4", "0", "-2", "2", "4", "2", "4", "2", "4", "-2", "-2", "-1", "-2", "-1", "-2", "-4", "-2", "0", "-8" ]
[ "sign", "mult" ]
15
1
3
[ "A010892", "A320111", "A355690", "A355691" ]
null
Antti Karttunen, Jul 15 2022
2022-12-30T06:30:49
oeisdata/seq/A355/A355691.seq
5daeefd3aba8aae5e61df909b1bb8cc6
A355692
Dirichlet inverse of A355442, gcd(A003961(n), A276086(n)), where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.
[ "1", "-3", "-1", "0", "-1", "1", "-1", "24", "-4", "3", "-1", "16", "-1", "3", "-3", "-72", "-1", "6", "-1", "6", "-3", "3", "-1", "-68", "0", "3", "-116", "0", "-1", "21", "-1", "24", "1", "3", "-5", "72", "-1", "3", "-3", "-120", "-1", "23", "-1", "6", "-158", "3", "-1", "28", "0", "-18", "-3", "0", "-1", "632", "-5", "-24", "-3", "3", "-1", "-54", "-1", "3", "16", "504", "-5", "-1", "-1", "6", "-3", "15", "-1", "-400", "-1", "3", "-236", "0", "1", "23", "-1", "474", "136" ]
[ "sign" ]
8
1
2
[ "A003961", "A276086", "A346242", "A354347", "A354348", "A354823", "A354824", "A355692" ]
null
Antti Karttunen, Jul 18 2022
2022-07-18T16:39:17
oeisdata/seq/A355/A355692.seq
a647fa243f1f0633f8a8d4967a26c808
A355693
Dirichlet inverse of A330749, gcd(n, A064989(n)), where A064989 shifts the prime factorization one step towards lower primes.
[ "1", "-1", "-1", "0", "-1", "0", "-1", "0", "0", "1", "-1", "1", "-1", "1", "-1", "0", "-1", "1", "-1", "0", "1", "1", "-1", "0", "0", "1", "0", "0", "-1", "0", "-1", "0", "1", "1", "-3", "-2", "-1", "1", "1", "0", "-1", "0", "-1", "0", "2", "1", "-1", "0", "0", "0", "1", "0", "-1", "0", "1", "0", "1", "1", "-1", "1", "-1", "1", "0", "0", "1", "0", "-1", "0", "1", "3", "-1", "1", "-1", "1", "2", "0", "-5", "0", "-1", "0", "0", "1", "-1", "-1", "1", "1", "1", "0", "-1", "3", "1", "0", "1", "1", "1", "0" ]
[ "sign" ]
8
1
35
[ "A064989", "A330749", "A354365", "A354366", "A355693" ]
null
Antti Karttunen, Jul 18 2022
2022-07-18T16:39:20
oeisdata/seq/A355/A355693.seq
91728685f01cf25a008381bf4ce7ca65
A355694
Dirichlet inverse of A277791, denominator of sum of reciprocals of proper divisors of n.
[ "1", "-1", "-1", "-1", "-1", "-4", "-1", "-1", "-2", "-8", "-1", "9", "-1", "-12", "-13", "-1", "-1", "6", "-1", "1", "-19", "-20", "-1", "-10", "-4", "-24", "-4", "1", "-1", "26", "-1", "-1", "-31", "-32", "-33", "27", "-1", "-36", "-37", "10", "-1", "34", "-1", "1", "-12", "-44", "-1", "35", "-6", "2", "-49", "1", "-1", "-14", "-53", "62", "-55", "-56", "-1", "87", "-1", "-60", "-18", "-1", "-63", "110", "-1", "1", "-67", "42", "-1", "-57", "-1", "-72", "12" ]
[ "sign" ]
9
1
6
[ "A277791", "A355694" ]
null
Antti Karttunen, Jul 18 2022
2022-07-18T16:39:24
oeisdata/seq/A355/A355694.seq
997e8c11e5f86feda310eeb99c2b7f36
A355695
a(n) is the smallest number that has exactly n nonpalindromic divisors (A029742).
[ "1", "10", "20", "30", "48", "72", "60", "140", "144", "120", "210", "180", "300", "240", "560", "504", "360", "420", "780", "1764", "900", "960", "720", "1200", "840", "1560", "2640", "1260", "1440", "2400", "3900", "3024", "1680", "3120", "2880", "4800", "7056", "3600", "2520", "3780", "3360", "5460", "6480", "16848", "6300", "8820", "7200", "9240", "6720", "12480", "5040" ]
[ "nonn", "base" ]
16
0
2
[ "A029742", "A087991", "A087997", "A093037", "A333456", "A334391", "A355303", "A355594", "A355695" ]
null
Bernard Schott, Jul 14 2022
2022-07-27T13:33:00
oeisdata/seq/A355/A355695.seq
249a9a8572d29db9d907bc85cad128ce
A355696
First of four consecutive primes p,q,r,s such that the sum of numerator and denominator of p/q + q/r, p/q + r/s, and q/r + r/s, are all prime.
[ "11", "29", "1811", "2531", "3373", "4153", "5927", "7121", "7127", "8419", "11743", "14347", "14419", "17659", "26357", "26729", "33529", "43051", "57809", "61223", "81689", "87991", "99527", "99529", "113123", "125107", "141959", "146359", "152993", "154849", "162629", "165709", "168323", "197927", "198437", "205483", "207679", "207821", "216851", "216991", "221729", "228457" ]
[ "nonn" ]
24
1
1
null
null
J. M. Bergot and Robert Israel, Jul 19 2022
2022-08-03T23:22:50
oeisdata/seq/A355/A355696.seq
6f721b002739bab4398d87edc40fa0f2
A355697
a(0) = 0, a(1) = 1; for n > 1, a(n) = a(n-1) + g - 1 if a(n-1) is prime, otherwise a(n) = a(n-1) + g + 1, where g = a(n-1) - a(n-2).
[ "0", "1", "3", "4", "6", "9", "13", "16", "20", "25", "31", "36", "42", "49", "57", "66", "76", "87", "99", "112", "126", "141", "157", "172", "188", "205", "223", "240", "258", "277", "295", "314", "334", "355", "377", "400", "424", "449", "473", "498", "524", "551", "579", "608", "638", "669", "701", "732", "764", "797", "829", "860", "892", "925", "959", "994", "1030", "1067", "1105", "1144", "1184" ]
[ "nonn", "easy" ]
80
0
3
[ "A000217", "A104589", "A116533", "A332410", "A355697", "A356445" ]
null
John Tyler Rascoe, Jul 19 2022
2022-09-21T12:00:17
oeisdata/seq/A355/A355697.seq
6b562f1f0b639ba2d6e4b7e2b48b7e98
A355698
a(n) is the number of repdigits divisors of n (A010785).
[ "1", "2", "2", "3", "2", "4", "2", "4", "3", "3", "2", "5", "1", "3", "3", "4", "1", "5", "1", "4", "3", "4", "1", "6", "2", "2", "3", "4", "1", "5", "1", "4", "4", "2", "3", "6", "1", "2", "2", "5", "1", "5", "1", "6", "4", "2", "1", "6", "2", "3", "2", "3", "1", "5", "4", "5", "2", "2", "1", "6", "1", "2", "4", "4", "2", "8", "1", "3", "2", "4", "1", "7", "1", "2", "3", "3", "4", "4", "1", "5", "3", "2", "1", "6", "2", "2", "2", "8", "1", "6", "2", "3", "2", "2", "2", "6", "1", "3", "6", "4", "1", "4", "1", "4", "4" ]
[ "nonn", "base" ]
27
1
2
[ "A010785", "A065444", "A083230", "A087990", "A087991", "A190217", "A332268", "A340548", "A355302", "A355698", "A355699" ]
null
Bernard Schott, Jul 14 2022
2025-04-17T08:08:11
oeisdata/seq/A355/A355698.seq
333b873909c8eaab0c120a87923c8659
A355699
a(n) is the smallest number that has exactly n repdigit divisors.
[ "1", "2", "4", "6", "12", "24", "72", "66", "666", "132", "1332", "264", "2664", "792", "13320", "3960", "14652", "26664", "48840", "29304", "79992", "341880", "146520", "399960", "1333332", "1025640", "2799720", "8879112", "2666664", "18666648", "7999992", "44395560", "13333320", "93333240", "39999960", "279999720", "269333064" ]
[ "nonn", "base", "look" ]
44
1
2
[ "A010785", "A087990", "A087997", "A190217", "A333456", "A340548", "A355303", "A355695", "A355698", "A355699" ]
null
Bernard Schott, Jul 14 2022
2024-08-02T12:04:09
oeisdata/seq/A355/A355699.seq
73cfb5794baeee31c00b25dd1c4a3601
A355700
Triangle T(n,k), n > 2, 1 < k < n, read by rows, where T(n,k) is in base n, the smallest prime consisting of digits d from a set of k nonzero consecutive digits, d times each, or -1 if no such number exists.
[ "17", "41", "1787", "37", "1011749", "-1", "8070191", "18919", "31783046759", "-1", "107", "13588859", "-1", "906611171779", "106661882252960131", "9883", "40487203", "173127971", "5664484284773", "696222287901816728317439", "-1", "101", "97453813", "-1", "28631342754671", "15215869393552811003", "629657070248572792452284791790843", "-1", "32233", "123323", "334444555566656663", "122334444555553", "122334444555566566663", "1223334444555556666677767777", "22333444455555666666777777788888898999999989", "-1" ]
[ "sign", "base", "tabl" ]
100
3
1
null
null
Jean-Marc Rebert, Jul 14 2022
2022-08-15T08:34:11
oeisdata/seq/A355/A355700.seq
21b77f4aee052b28337945ba23a7a068