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oeis

Dataset card Data Studio Files
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1999-12-11 03:00:00
2025-04-28 00:58:08
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A358101
Positions of records in A358099, i.e., integers whose number of divisors whose decimal digits are in strictly decreasing order sets a new record.
[ "1", "2", "4", "6", "12", "20", "30", "40", "60", "120", "240", "360", "420", "840", "1260", "2520", "5040", "8640", "10080", "15120", "20160", "30240", "60480", "120960", "181440", "362880", "544320", "786240", "1572480", "1874880", "3749760", "5624640", "7862400", "14938560", "23587200", "24373440", "31872960", "63745920", "95618880" ]
[ "nonn", "base", "fini" ]
18
1
2
[ "A009995", "A093036", "A190219", "A340548", "A357173", "A358099", "A358100", "A358101" ]
null
Bernard Schott, Nov 03 2022
2022-11-05T05:47:22
oeisdata/seq/A358/A358101.seq
3f8f47496b5e87b0d965673d0486ad7b
A358102
Numbers of the form prime(w)*prime(x)*prime(y) with w >= x >= y such that 2w = 3x + 4y.
[ "66", "153", "266", "609", "806", "1295", "1599", "1634", "2107", "3021", "3055", "3422", "5254", "5369", "5795", "5829", "7138", "8769", "9443", "9581", "10585", "10706", "12337", "12513", "13298", "16465", "16511", "16849", "17013", "18602", "21983", "22145", "23241", "23542", "26159", "29014", "29607", "29945", "30943", "32623", "32809" ]
[ "nonn" ]
8
1
1
[ "A000009", "A000040", "A000041", "A000720", "A001221", "A001222", "A003963", "A008676", "A056239", "A215366", "A296150", "A318283", "A357489", "A357849", "A358102" ]
null
Gus Wiseman, Nov 02 2022
2022-11-02T11:54:09
oeisdata/seq/A358/A358102.seq
206cfc12fc6f3db941a2d355502b1b42
A358103
Quotient of the n-th divisible pair, where pairs are ordered by Heinz number. Quotient of prime indices of A318990(n).
[ "1", "2", "1", "3", "4", "2", "5", "1", "6", "7", "8", "3", "9", "1", "4", "10", "11", "2", "12", "13", "14", "5", "15", "16", "6", "3", "17", "1", "18", "7", "2", "19", "20", "21", "22", "8", "23", "1", "24", "9", "4", "25", "26", "27", "10", "28", "29", "30", "5", "11", "31", "3", "32", "12", "33", "34", "1", "35", "36", "13", "6", "37", "2", "14", "38", "39", "15", "40", "41", "1", "42", "7", "4", "43" ]
[ "nonn" ]
16
1
2
[ "A000040", "A000720", "A001221", "A001222", "A001358", "A003963", "A006881", "A027751", "A032741", "A056239", "A215366", "A289508", "A289509", "A296150", "A300912", "A318990", "A318991", "A318992", "A339005", "A358103", "A358104", "A358105", "A358106", "A358192", "A358193" ]
null
Gus Wiseman, Nov 02 2022
2023-07-15T10:36:18
oeisdata/seq/A358/A358103.seq
c9f354fde50447a3cd029188ea3d61f5
A358104
Unreduced numerator of the n-th divisible pair, where pairs are ordered by Heinz number. Greater prime index of A318990(n).
[ "1", "2", "2", "3", "4", "4", "5", "3", "6", "7", "8", "6", "9", "4", "8", "10", "11", "6", "12", "13", "14", "10", "15", "16", "12", "9", "17", "5", "18", "14", "8", "19", "20", "21", "22", "16", "23", "6", "24", "18", "12", "25", "26", "27", "20", "28", "29", "30", "15", "22", "31", "12", "32", "24", "33", "34", "7", "35", "36", "26", "18", "37", "10", "28", "38", "39", "30", "40", "41", "8", "42" ]
[ "nonn" ]
9
1
2
[ "A000040", "A000720", "A001221", "A001222", "A001358", "A003963", "A006881", "A032741", "A056239", "A128301", "A215366", "A289508", "A289509", "A296150", "A300912", "A318990", "A318991", "A318992", "A338913", "A339005", "A358103", "A358104", "A358105", "A358106", "A358192", "A358193" ]
null
Gus Wiseman, Nov 02 2022
2023-01-27T21:07:38
oeisdata/seq/A358/A358104.seq
f4393191bea8e584b66d0483dc4f2964
A358105
Unreduced denominator of the n-th divisible pair, where pairs are ordered by Heinz number. Lesser prime index of A318990(n).
[ "1", "1", "2", "1", "1", "2", "1", "3", "1", "1", "1", "2", "1", "4", "2", "1", "1", "3", "1", "1", "1", "2", "1", "1", "2", "3", "1", "5", "1", "2", "4", "1", "1", "1", "1", "2", "1", "6", "1", "2", "3", "1", "1", "1", "2", "1", "1", "1", "3", "2", "1", "4", "1", "2", "1", "1", "7", "1", "1", "2", "3", "1", "5", "2", "1", "1", "2", "1", "1", "8", "1", "3", "4", "1", "1", "2", "1", "1", "2", "1", "3", "1", "2", "1", "1", "1", "1" ]
[ "nonn" ]
7
1
3
[ "A000040", "A000720", "A001221", "A001222", "A001358", "A003963", "A006881", "A027751", "A056239", "A128301", "A215366", "A289508", "A289509", "A296150", "A300912", "A318990", "A318991", "A318992", "A338912", "A338913", "A339005", "A358103", "A358105", "A358106", "A358192", "A358193" ]
null
Gus Wiseman, Nov 02 2022
2023-11-04T13:16:27
oeisdata/seq/A358/A358105.seq
52084500988a3630fcf3fa042d12d80b
A358106
Quotient of the n-th divisible pair, where pairs are ordered first by sum and then by denominator.
[ "1", "2", "3", "1", "4", "5", "2", "1", "6", "7", "3", "1", "8", "2", "9", "4", "1", "10", "11", "5", "3", "2", "1", "12", "13", "6", "1", "14", "4", "2", "15", "7", "3", "1", "16", "17", "8", "5", "2", "1", "18", "19", "9", "4", "3", "1", "20", "6", "2", "21", "10", "1", "22", "23", "11", "7", "5", "3", "2", "1", "24", "4", "25", "12", "1", "26", "8", "2", "27", "13", "6", "3", "1", "28", "29", "14", "9", "5", "4", "2", "1" ]
[ "nonn", "tabf" ]
7
2
2
[ "A000009", "A000041", "A000837", "A001358", "A003238", "A006881", "A027751", "A032741", "A122934", "A208460", "A318990", "A318991", "A339005", "A358103", "A358104", "A358105", "A358106", "A358192", "A358193" ]
null
Gus Wiseman, Nov 03 2022
2022-11-04T14:44:25
oeisdata/seq/A358/A358106.seq
548ef459f39c498d6e9e8f22f57878a0
A358107
Number of unlabeled trees covering 2n nodes, n+1 of which are leaves.
[ "1", "1", "2", "6", "26", "119", "626", "3495", "20688", "127339", "810418", "5293790", "35351571", "240478715", "1662071181", "11646620758", "82601643511", "592110678762", "4284830131865", "31271691087861", "229980550743717", "1703097703162249", "12691879796699486", "95129358337729084", "716801612475691847" ]
[ "nonn" ]
17
1
3
[ "A000055", "A000088", "A000272", "A001187", "A001349", "A001433", "A002494", "A006125", "A006129", "A014068", "A055290", "A055314", "A163395", "A185650", "A358107", "A358732", "A359398" ]
null
Gus Wiseman, Dec 02 2022
2023-01-02T15:25:24
oeisdata/seq/A358/A358107.seq
05f369eabdb3b952dabbdca8e53a3dc2
A358108
a(n) = 16^n * Sum_{k=0..n} binomial(-1/2, k)^2 * binomial(n, k).
[ "1", "20", "420", "9296", "216868", "5313360", "135866640", "3599688000", "98122746660", "2735243498960", "77595234251920", "2231860533960000", "64904359322352400", "1904342118510144320", "56285527873777258560", "1673824975976543421696", "50036226313229526706980", "1502471400349641645458640" ]
[ "nonn" ]
12
0
2
[ "A143583", "A358108" ]
null
Peter Luschny, Nov 12 2022
2022-11-13T16:24:19
oeisdata/seq/A358/A358108.seq
aab911de7ab52f5c46d321834c57e2a2
A358109
a(n) = 16^n * Sum_{k=0..n} binomial(1/2, k)^2 * binomial(n, k).
[ "1", "20", "388", "7376", "138340", "2572880", "47652240", "882388800", "16402291620", "307411770320", "5837516987920", "112918906836800", "2237687548230160", "45677390764531520", "964818477552462400", "21148251536958233856", "481370160754727691300", "11360399185583414128848", "277079154699775861823376" ]
[ "nonn" ]
11
0
2
[ "A143583", "A358108", "A358109" ]
null
Peter Luschny, Nov 12 2022
2022-11-13T16:24:27
oeisdata/seq/A358/A358109.seq
5716e66b8af3d0d7ba2531b2cb6d8303
A358110
Indices of the harmonic numbers in the Stern-Brocot sequence (A002487).
[ "0", "1", "5", "125", "8195", "32675", "755", "34763", "520283", "37773179", "21743337467", "4647489635464983347207", "1236947931143", "272658152711", "604398345569737906323527", "9595849053479089263878087", "3693713292455", "288389531265129191", "11150032316898390632304469945009811031588839" ]
[ "nonn" ]
23
0
3
[ "A001008", "A002487", "A002805", "A355090", "A358110" ]
null
Peter Luschny, Nov 08 2022
2022-11-08T18:02:28
oeisdata/seq/A358/A358110.seq
d13392e2b267a311fa3c4be6c640b458
A358111
The multiplicative inverse of the coefficients of the factorially normalized Bernoulli polynomials (provided they do not vanish, otherwise by convention 0).
[ "1", "-2", "1", "12", "-2", "2", "0", "12", "-4", "6", "-720", "0", "24", "-12", "24", "0", "-720", "0", "72", "-48", "120", "30240", "0", "-1440", "0", "288", "-240", "720", "0", "30240", "0", "-4320", "0", "1440", "-1440", "5040", "-1209600", "0", "60480", "0", "-17280", "0", "8640", "-10080", "40320", "0", "-1209600", "0", "181440", "0", "-86400", "0", "60480", "-80640", "362880" ]
[ "sign", "tabl" ]
13
0
2
[ "A000142", "A196838", "A196839", "A227830", "A358111" ]
null
Peter Luschny, Oct 30 2022
2024-03-07T08:31:58
oeisdata/seq/A358/A358111.seq
141917267ecfd17ecd417fa5091865d1
A358112
Table read by rows. A statistic of permutations of the multiset {1,1,2,2,...,n,n}.
[ "1", "5", "1", "47", "42", "1", "641", "1659", "219", "1", "11389", "72572", "28470", "968", "1", "248749", "3610485", "3263402", "357746", "4017", "1", "6439075", "204023334", "371188155", "95559940", "3853617", "16278", "1", "192621953", "12989570167", "43844432805", "22448025251", "2216662051", "38270373", "65399", "1" ]
[ "nonn", "tabl" ]
15
1
2
[ "A000680", "A006902", "A358112" ]
null
Peter Luschny, Oct 30 2022
2022-11-13T14:32:57
oeisdata/seq/A358/A358112.seq
24d7b77a9a04af208a06107a629fd22a
A358113
a(n) = 16^n * Sum_{k=0..n} (-1)^k * binomial(1/2, k)^2 * binomial(n, k).
[ "1", "12", "132", "1200", "5220", "-132048", "-5451376", "-139104576", "-3034129500", "-61171843920", "-1176294856176", "-21916435874112", "-399241706218992", "-7151078337480000", "-126420386691188160", "-2211675290036790528", "-38363623542890191836", "-660751288131343246416", "-11312478475520480652400" ]
[ "sign" ]
13
0
2
[ "A143583", "A358108", "A358109", "A358113" ]
null
Peter Luschny, Nov 12 2022
2024-03-18T06:06:30
oeisdata/seq/A358/A358113.seq
81f3fac0b12c41b6a56eac5a329b77b0
A358114
a(n) = [x^n] (16*x*(32*x - 3) + 1)^(-1/2).
[ "1", "24", "608", "16128", "443904", "12570624", "363708416", "10694295552", "318301929472", "9562594738176", "289380790960128", "8807948507676672", "269349580129173504", "8268747111256817664", "254668380196759928832", "7865254221563736096768", "243493498808268962660352", "7553805204299934842486784" ]
[ "nonn" ]
13
0
2
[ "A098430", "A358114" ]
null
Peter Luschny, Nov 12 2022
2023-01-25T09:26:10
oeisdata/seq/A358/A358114.seq
9eec3e78bc2c28598f885361c5dbeccb
A358115
a(n) = 64^n * hypergeometric([1/2, 1/2, 1/2, -n], [1, 1, 1], 1).
[ "1", "56", "3288", "197312", "11992024", "734961216", "45312662976", "2806150276608", "174385474327512", "10867238335817024", "678767129043750208", "42476876703235742208", "2662498434919062169024", "167121637293079702800896", "10502764033533202152955392", "660751064709823030602903552" ]
[ "nonn" ]
10
0
2
[ "A358115", "A358116", "A358117" ]
null
Peter Luschny, Nov 12 2022
2024-02-17T14:55:16
oeisdata/seq/A358/A358115.seq
89d7ea26a128c8a24cf855c387ab850f
A358116
a(n) = 64^n * hypergeometric([1/2, 1/2, 1/2, -n], [1, 1, 1], -1).
[ "1", "72", "5336", "409920", "32865240", "2764504512", "244568268224", "22731850578432", "2210652884587480", "223568522839008960", "23355989488375500096", "2504727132759950771712", "274275125399986388723136", "30537418979006689934661120", "3445701451953128810934443520", "393048128243054017436740669440" ]
[ "nonn" ]
9
0
2
[ "A358115", "A358116", "A358117" ]
null
Peter Luschny, Nov 12 2022
2024-02-17T15:04:49
oeisdata/seq/A358/A358116.seq
18649dfcf72499241fed236ad8dfa3f3
A358117
a(n) = 64^n * hypergeom([-1/2, -1/2, -1/2, -n], [1, 1, 1], 1).
[ "1", "72", "5112", "358976", "24984600", "1726182336", "118527759552", "8095995597312", "550493745978456", "37283830177899200", "2516416350265032768", "169320882931135520256", "11361845611339758248896", "760535818250019673548288", "50795721177620909117683200", "3385797370455910806595080192" ]
[ "nonn" ]
12
0
2
[ "A358115", "A358116", "A358117" ]
null
Peter Luschny, Nov 12 2022
2024-02-17T14:30:50
oeisdata/seq/A358/A358117.seq
3658735901d743aa00ddcd9eedaa3af7
A358118
a(n) = Sum_{j=0..n} (-1)^j*binomial(2*n - j, j)*c(n - j + 1)^2, where c(n) is the n-th Catalan number.
[ "1", "3", "14", "94", "728", "6220", "56960", "549412", "5517746", "57235402", "609632284", "6638455152", "73653980850", "830429715762", "9494320306104", "109882451968812", "1285515149382226", "15184272319785322", "180901975355930990", "2171974459996885630", "26260944994924397048", "319547523490735463404" ]
[ "nonn" ]
15
0
2
[ "A000108", "A358118", "A358119" ]
null
Peter Luschny, Nov 11 2022
2022-11-12T02:10:25
oeisdata/seq/A358/A358118.seq
b258a7d4dadbb5f140a492dcd5b81f03
A358119
a(n) = Sum_{j=0..n} (-1)^j*binomial(2*n - j, j)*c(n - j)*c(n - j + 2), where c(n) is the n-th Catalan number.
[ "2", "3", "15", "98", "750", "6359", "57939", "556896", "5578764", "57759397", "614328561", "6682078770", "74071710414", "834535805445", "9535609593441", "110306008352832", "1289937458160684", "15231176767392691", "181406519662622559", "2177471166182909994", "26321521760571055830", "320222147815305416123" ]
[ "nonn" ]
14
0
1
[ "A000108", "A358118", "A358119" ]
null
Peter Luschny, Nov 11 2022
2022-11-12T03:02:13
oeisdata/seq/A358/A358119.seq
361762e22fc15bdc5a67e2b0e0eadb59
A358120
Partial inventory of positions as an irregular table; rows 1 and 2 contain 1, for n > 2, row n contains the 1-based positions of 1's, followed by the positions of 2's, 3's, etc. in rows n-1 and n-2 flattened.
[ "1", "1", "1", "2", "1", "3", "2", "1", "4", "3", "5", "2", "1", "6", "5", "8", "3", "7", "2", "4", "1", "9", "7", "13", "5", "11", "8", "10", "3", "12", "2", "6", "4", "1", "14", "11", "20", "9", "18", "13", "21", "5", "16", "12", "15", "3", "19", "7", "17", "2", "8", "6", "10", "4", "1", "22", "17", "32", "13", "30", "21", "34", "9", "26", "19", "33", "15", "24", "18", "28", "5", "23", "20", "29", "3", "27", "11", "31", "7", "25", "2", "12", "10", "16", "6", "14", "4", "8" ]
[ "nonn", "tabf" ]
15
1
4
[ "A000045", "A001611", "A342585", "A356784", "A358090", "A358120", "A358124" ]
null
Rémy Sigrist, Oct 30 2022
2022-11-03T10:06:52
oeisdata/seq/A358/A358120.seq
68bd4dfa617995537bfe1f4b4210ab46
A358121
Distinct values of A358085, in order of appearance.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "22", "23", "24", "21", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "39", "40", "41", "37", "42", "43", "46", "47", "48", "49", "50", "38", "44", "45", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67" ]
[ "nonn", "base" ]
14
1
2
[ "A358085", "A358121", "A358140" ]
null
Rémy Sigrist, Oct 30 2022
2022-11-03T10:06:56
oeisdata/seq/A358/A358121.seq
f384169962ee84de44fe7900bb556d05
A358122
Distinct values of A358086, in order of appearance.
[ "1", "2", "3", "4", "5", "6", "8", "7", "9", "10", "12", "15", "11", "14", "13", "16", "17", "18", "20", "23", "32", "19", "22", "26", "21", "25", "28", "30", "24", "29", "31", "27", "33", "34", "36", "39", "48", "58", "35", "38", "42", "61", "37", "41", "46", "49", "51", "59", "40", "45", "50", "53", "54", "55", "43", "60", "44", "52", "56", "47", "57", "64", "62", "63", "65", "66", "68" ]
[ "nonn" ]
12
1
2
[ "A358086", "A358122", "A358141" ]
null
Rémy Sigrist, Oct 30 2022
2022-11-03T10:07:00
oeisdata/seq/A358/A358122.seq
1a48f31fcc7a0e7a20e352f91c0cf288
A358123
Distinct values of A358090, in order of appearance.
[ "1", "2", "3", "4", "5", "6", "7", "8", "10", "11", "9", "12", "13", "15", "17", "16", "19", "14", "18", "20", "21", "24", "22", "26", "28", "25", "29", "31", "27", "23", "32", "30", "33", "34", "36", "40", "42", "38", "44", "46", "39", "47", "43", "49", "51", "41", "35", "50", "37", "45", "53", "48", "52", "54", "55", "59", "63", "67", "65", "57", "71", "61", "69", "73", "75", "62", "74" ]
[ "nonn" ]
12
1
2
[ "A358090", "A358123", "A358142" ]
null
Rémy Sigrist, Oct 30 2022
2022-11-03T10:07:09
oeisdata/seq/A358/A358123.seq
4c7ef9cb95bc3bfaeaea8777fde6d407
A358124
Distinct values of A358120, in order of appearance.
[ "1", "2", "3", "4", "5", "6", "8", "7", "9", "13", "11", "10", "12", "14", "20", "18", "21", "16", "15", "19", "17", "22", "32", "30", "34", "26", "33", "24", "28", "23", "29", "27", "31", "25", "35", "51", "47", "55", "43", "53", "49", "52", "39", "54", "37", "45", "41", "36", "46", "44", "50", "40", "48", "38", "42", "56", "82", "76", "88", "72", "86", "80", "89", "64", "84", "78", "83" ]
[ "nonn" ]
11
1
2
[ "A358120", "A358124", "A358143" ]
null
Rémy Sigrist, Oct 30 2022
2022-11-03T10:07:04
oeisdata/seq/A358/A358124.seq
f0bc9a80076e7dc488cdc8ab2d7805d7
A358125
Triangle read by rows: T(n, k) = 2^n - 2^(n-k-1) - 2^k, 0 <= k <= n-1.
[ "0", "1", "1", "3", "4", "3", "7", "10", "10", "7", "15", "22", "24", "22", "15", "31", "46", "52", "52", "46", "31", "63", "94", "108", "112", "108", "94", "63", "127", "190", "220", "232", "232", "220", "190", "127", "255", "382", "444", "472", "480", "472", "444", "382", "255", "511", "766", "892", "952", "976", "976", "952", "892", "766", "511", "1023", "1534", "1788", "1912", "1968", "1984", "1968", "1912", "1788", "1534", "1023" ]
[ "nonn", "easy", "tabl" ]
36
1
4
[ "A000225", "A005061", "A033484", "A053208", "A358125", "A359200" ]
null
Ambrosio Valencia-Romero, Dec 20 2022
2022-12-20T11:29:32
oeisdata/seq/A358/A358125.seq
b2de8346bd069f9a191c0a8d61d187b0
A358126
Replace 2^k in binary expansion of n with 2^(2^k).
[ "0", "2", "4", "6", "16", "18", "20", "22", "256", "258", "260", "262", "272", "274", "276", "278", "65536", "65538", "65540", "65542", "65552", "65554", "65556", "65558", "65792", "65794", "65796", "65798", "65808", "65810", "65812", "65814", "4294967296", "4294967298", "4294967300" ]
[ "nonn", "base" ]
70
0
2
[ "A001146", "A060803", "A133457", "A197819", "A228539", "A253315", "A253317", "A358126" ]
null
Tilman Piesk, Oct 30 2022
2023-12-31T00:26:24
oeisdata/seq/A358/A358126.seq
8d66311c06a90d3ad953069fff5c1080
A358127
a(n) is the cardinality of the set of pairwise gcd's of {prime(1)+1, ..., prime(n)+1}.
[ "1", "3", "4", "5", "5", "5", "5", "7", "8", "8", "8", "9", "9", "11", "12", "14", "14", "14", "14", "14", "14", "15", "15", "15", "16", "16", "18", "19", "20", "21", "22", "22", "23", "23", "23", "23", "23", "24", "24", "26", "27", "29", "29", "30", "32", "32", "33", "35", "36", "36", "37", "37", "37", "37", "38", "38", "39", "39", "39", "39", "40", "40", "42", "42", "43", "43", "43", "44", "45", "45", "48", "48", "48", "48", "50", "50", "50", "50" ]
[ "nonn" ]
14
2
2
[ "A008864", "A214799", "A356371", "A358127" ]
null
Gleb Ivanov, Oct 30 2022
2022-11-02T11:53:24
oeisdata/seq/A358/A358127.seq
287992a031d5f456678c57be722a15f3
A358128
a(n) is the least semiprime x such that x-2*n and x+2*n are prime.
[ "9", "9", "25", "15", "21", "25", "33", "21", "25", "33", "25", "35", "33", "33", "49", "35", "39", "65", "51", "57", "55", "57", "51", "55", "57", "55", "77", "93", "69", "77", "65", "87", "85", "111", "87", "77", "77", "87", "85", "87", "85", "95", "93", "91", "121", "159", "177", "115", "129", "111", "121", "123", "123", "115", "123", "115", "119", "123", "121", "143", "129", "183", "143", "141", "133", "145", "177", "141", "143" ]
[ "nonn" ]
11
1
1
[ "A001358", "A358128" ]
null
J. M. Bergot and Robert Israel, Oct 30 2022
2022-11-10T07:43:29
oeisdata/seq/A358/A358128.seq
4a14ca7795183cbd69b6d9c4d3db6520
A358129
Lexicographically earliest sequence of distinct nonnegative integers on a square spiral such that no number shares a digit with any of its four orthogonally adjacent neighbors.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "20", "11", "22", "10", "24", "13", "25", "16", "23", "14", "26", "15", "28", "17", "30", "12", "33", "18", "27", "19", "32", "40", "29", "31", "42", "36", "21", "34", "50", "41", "35", "44", "37", "45", "38", "46", "39", "47", "53", "48", "55", "49", "52", "43", "56", "70", "51", "60", "57", "61", "54", "63", "58", "64", "59", "66", "71", "62", "73", "68", "72", "65", "74", "69", "77", "90", "75" ]
[ "nonn", "base" ]
11
0
3
[ "A343530", "A344325", "A344367", "A354111", "A358021", "A358048", "A358129" ]
null
Scott R. Shannon and Eric Angelini, Oct 30 2022
2022-11-04T07:32:46
oeisdata/seq/A358/A358129.seq
4d0b3dc0be7da7632b514f8e369109fe
A358130
Indices k such that A358128(k) is a square.
[ "1", "2", "3", "6", "9", "11", "15", "45", "51", "59", "81", "126", "165", "174", "179", "255", "681", "831", "839", "921", "1734", "1739", "1845", "2499", "2519", "2661", "3119", "5061", "5094", "5099", "5289", "5301", "8061", "8571", "8579", "9654", "9659", "11094", "11399", "12315", "13254", "16011", "16379", "18225", "18234", "18239", "19401", "19689", "26214", "26219", "27141", "28554", "29039" ]
[ "nonn" ]
12
1
2
[ "A358128", "A358130" ]
null
J. M. Bergot and Robert Israel, Oct 30 2022
2022-11-10T07:43:25
oeisdata/seq/A358/A358130.seq
51ea33df2d77dd1e0cc8f3f2e9190c44
A358131
Triangle T(n,k) read by rows, where each row lists the value of n coins, in cents, using k dimes (10 cents) and n-k quarters (25 cents).
[ "0", "25", "10", "50", "35", "20", "75", "60", "45", "30", "100", "85", "70", "55", "40", "125", "110", "95", "80", "65", "50", "150", "135", "120", "105", "90", "75", "60", "175", "160", "145", "130", "115", "100", "85", "70", "200", "185", "170", "155", "140", "125", "110", "95", "80", "225", "210", "195", "180", "165", "150", "135", "120", "105", "90", "250", "235", "220", "205", "190" ]
[ "nonn", "easy", "tabl" ]
12
0
2
[ "A008592", "A008607", "A351726", "A358131" ]
null
Wesley Ivan Hurt, Oct 30 2022
2022-11-10T16:12:27
oeisdata/seq/A358/A358131.seq
16d5ad438658558c4abb9ed3e87acf90
A358132
Numbers k such that there exists a pair of primes (p,q) with p+q = k such that p*q + k, p*q - k, p*q + A001414(k) and p*q - A001414(k) are all prime.
[ "7", "60", "72", "114", "186", "378", "474", "480", "762", "884", "1266", "1338", "1374", "2004", "2742", "3012", "3234", "3246", "3276", "3282", "3618", "3936", "4230", "4620", "5154", "5514", "5544", "5724", "5886", "6006", "6054", "6084", "6234", "6306", "6414", "6510", "6522", "6762", "6774", "6858", "7410", "7422", "7764", "8286", "8394", "8538", "8688", "8826", "8892", "8916", "9186", "9264" ]
[ "nonn" ]
15
1
1
[ "A001414", "A358132" ]
null
J. M. Bergot and Robert Israel, Oct 31 2022
2022-11-10T07:43:21
oeisdata/seq/A358/A358132.seq
4dc7c6d547fff932838038888b6fc178
A358133
Triangle read by rows whose n-th row lists the first differences of the n-th composition in standard order (row n of A066099).
[ "0", "-1", "1", "0", "0", "-2", "0", "-1", "0", "2", "1", "-1", "0", "1", "0", "0", "0", "-3", "-1", "-2", "0", "1", "0", "-1", "-1", "1", "-1", "0", "0", "3", "2", "-2", "1", "0", "1", "-1", "0", "0", "2", "0", "1", "-1", "0", "0", "1", "0", "0", "0", "0", "-4", "-2", "-3", "0", "0", "-1", "-1", "-2", "1", "-2", "0", "0", "2", "1", "-2", "0", "0", "0", "-1", "0", "-1", "2", "-1", "1", "-1", "-1", "0", "1", "-1" ]
[ "sign", "tabf" ]
9
3
6
[ "A000120", "A001511", "A011782", "A029837", "A029931", "A048896", "A066099", "A070939", "A133494", "A242628", "A253566", "A351014", "A355536", "A357135", "A357187", "A358133", "A358134", "A358135" ]
null
Gus Wiseman, Oct 31 2022
2022-10-31T15:23:45
oeisdata/seq/A358/A358133.seq
f9a20bd7e7422f6c5387cd60c702c439
A358134
Triangle read by rows whose n-th row lists the partial sums of the n-th composition in standard order (row n of A066099).
[ "1", "2", "1", "2", "3", "2", "3", "1", "3", "1", "2", "3", "4", "3", "4", "2", "4", "2", "3", "4", "1", "4", "1", "3", "4", "1", "2", "4", "1", "2", "3", "4", "5", "4", "5", "3", "5", "3", "4", "5", "2", "5", "2", "4", "5", "2", "3", "5", "2", "3", "4", "5", "1", "5", "1", "4", "5", "1", "3", "5", "1", "3", "4", "5", "1", "2", "5", "1", "2", "4", "5", "1", "2", "3", "5", "1", "2", "3", "4", "5", "6", "5", "6", "4", "6", "4", "5" ]
[ "nonn", "tabf" ]
9
1
2
[ "A000120", "A001511", "A011782", "A029837", "A029931", "A048896", "A065120", "A066099", "A070939", "A133494", "A242628", "A253565", "A253566", "A351014", "A355536", "A357135", "A358133", "A358134", "A358135", "A358136", "A358137", "A359042" ]
null
Gus Wiseman, Oct 31 2022
2023-01-02T15:25:50
oeisdata/seq/A358/A358134.seq
79ae131cf4effb1b9e193763362bbba2
A358135
Difference of first and last parts of the n-th composition in standard order.
[ "0", "0", "0", "0", "-1", "1", "0", "0", "-2", "0", "-1", "2", "0", "1", "0", "0", "-3", "-1", "-2", "1", "-1", "0", "-1", "3", "0", "1", "0", "2", "0", "1", "0", "0", "-4", "-2", "-3", "0", "-2", "-1", "-2", "2", "-1", "0", "-1", "1", "-1", "0", "-1", "4", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "0", "0", "-5", "-3", "-4", "-1", "-3", "-2", "-3", "1", "-2", "-1", "-2", "0", "-2" ]
[ "sign" ]
7
1
9
[ "A000120", "A001511", "A011782", "A029837", "A029931", "A048896", "A058891", "A065120", "A066099", "A070939", "A133494", "A242628", "A243055", "A329395", "A333766", "A333768", "A351014", "A357187", "A358133", "A358134", "A358135", "A358138" ]
null
Gus Wiseman, Oct 31 2022
2022-10-31T15:23:26
oeisdata/seq/A358/A358135.seq
9c87605756a82f3b13b8dfcd01f6d226
A358136
Irregular triangle read by rows whose n-th row lists the partial sums of the prime indices of n (row n of A112798).
[ "1", "2", "1", "2", "3", "1", "3", "4", "1", "2", "3", "2", "4", "1", "4", "5", "1", "2", "4", "6", "1", "5", "2", "5", "1", "2", "3", "4", "7", "1", "3", "5", "8", "1", "2", "5", "2", "6", "1", "6", "9", "1", "2", "3", "5", "3", "6", "1", "7", "2", "4", "6", "1", "2", "6", "10", "1", "3", "6", "11", "1", "2", "3", "4", "5", "2", "7", "1", "8", "3", "7", "1", "2", "4", "6", "12", "1", "9", "2", "8", "1", "2", "3", "6", "13" ]
[ "nonn", "tabf" ]
6
2
2
[ "A000009", "A000041", "A000720", "A001221", "A001222", "A003963", "A055396", "A056239", "A112798", "A318283", "A325362", "A355536", "A358133", "A358134", "A358136", "A358137" ]
null
Gus Wiseman, Oct 31 2022
2022-10-31T22:05:44
oeisdata/seq/A358/A358136.seq
504ac23feb1cc5a73d465394f11f7dfa
A358137
Heinz number of the partial sums of the prime indices of n.
[ "1", "2", "3", "6", "5", "10", "7", "30", "21", "14", "11", "42", "13", "22", "33", "210", "17", "110", "19", "66", "39", "26", "23", "330", "65", "34", "273", "78", "29", "130", "31", "2310", "51", "38", "85", "546", "37", "46", "57", "390", "41", "170", "43", "102", "357", "58", "47", "2730", "133", "238", "69", "114", "53", "1870", "95", "510", "87", "62", "59", "714", "61" ]
[ "nonn" ]
9
1
2
[ "A000009", "A000040", "A000041", "A000720", "A001221", "A001222", "A003963", "A056239", "A112798", "A215366", "A296150", "A318283", "A325362", "A355536", "A358134", "A358136", "A358137" ]
null
Gus Wiseman, Oct 31 2022
2023-01-02T15:26:06
oeisdata/seq/A358/A358137.seq
1abe17ed4f47ca235732a8ef8cc57f96
A358138
Difference between maximum and minimum part in the n-th composition in standard order.
[ "0", "0", "0", "0", "1", "1", "0", "0", "2", "0", "1", "2", "1", "1", "0", "0", "3", "1", "2", "1", "1", "1", "1", "3", "2", "1", "1", "2", "1", "1", "0", "0", "4", "2", "3", "0", "2", "2", "2", "2", "2", "0", "1", "2", "1", "1", "1", "4", "3", "2", "2", "2", "1", "1", "1", "3", "2", "1", "1", "2", "1", "1", "0", "0", "5", "3", "4", "1", "3", "3", "3", "1", "2", "1", "2", "2", "2", "2", "2", "3", "3", "1", "2", "1", "1", "1", "1" ]
[ "nonn" ]
6
1
9
[ "A000120", "A001511", "A011782", "A029837", "A029931", "A048896", "A058891", "A065120", "A066099", "A070939", "A133494", "A242628", "A243055", "A329395", "A333766", "A333768", "A351014", "A357187", "A358133", "A358134", "A358135", "A358138" ]
null
Gus Wiseman, Oct 31 2022
2022-10-31T22:05:28
oeisdata/seq/A358/A358138.seq
50f09e171b8803ce824e38d3e7a26562
A358139
Numbers k > 0 sorted by k/A000120(k) in increasing order. A000120 is the binary weight of k. If k/A000120(k) yields equal values, the smaller k will appear first.
[ "1", "3", "2", "7", "5", "6", "11", "15", "4", "13", "9", "14", "10", "23", "12", "31", "19", "27", "21", "29", "22", "30", "8", "25", "17", "26", "18", "28", "47", "39", "20", "63", "43", "55", "45", "46", "35", "59", "24", "61", "37", "62", "38", "51", "53", "54", "41", "42", "57", "58", "44", "60", "79", "95", "16", "49", "33", "50", "34", "52", "87", "71", "36", "127", "91", "111", "93", "56" ]
[ "nonn", "easy", "base" ]
25
1
2
[ "A000120", "A049445", "A161764", "A199238", "A235602", "A348416", "A358139" ]
null
Thomas Scheuerle, Oct 31 2022
2022-11-17T14:12:15
oeisdata/seq/A358/A358139.seq
998c5366c4b1baf0e651cee8a553e7b8
A358140
Inverse permutation to A358121.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "24", "21", "22", "23", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "40", "48", "37", "38", "39", "41", "42", "49", "50", "43", "44", "45", "46", "47", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67" ]
[ "nonn", "base" ]
12
1
2
[ "A358121", "A358140" ]
null
Rémy Sigrist, Oct 31 2022
2022-11-03T10:07:22
oeisdata/seq/A358/A358140.seq
db64f0f548ee7b6da86e89d3cf8d1193
A358141
Inverse permutation to A358122.
[ "1", "2", "3", "4", "5", "6", "8", "7", "9", "10", "13", "11", "15", "14", "12", "16", "17", "18", "22", "19", "25", "23", "20", "29", "26", "24", "32", "27", "30", "28", "31", "21", "33", "34", "39", "35", "43", "40", "36", "49", "44", "41", "55", "57", "50", "45", "60", "37", "46", "51", "47", "58", "52", "53", "54", "59", "61", "38", "48", "56", "42", "63", "64", "62", "65", "66", "72" ]
[ "nonn" ]
9
1
2
[ "A358122", "A358141" ]
null
Rémy Sigrist, Oct 31 2022
2022-11-03T12:20:24
oeisdata/seq/A358/A358141.seq
8e3e34f618b3ddd03f23add72dcef511
A358142
Inverse permutation to A358123.
[ "1", "2", "3", "4", "5", "6", "7", "8", "11", "9", "10", "12", "13", "18", "14", "16", "15", "19", "17", "20", "21", "23", "30", "22", "26", "24", "29", "25", "27", "32", "28", "31", "33", "34", "47", "35", "49", "38", "41", "36", "46", "37", "43", "39", "50", "40", "42", "52", "44", "48", "45", "53", "51", "54", "55", "74", "60", "78", "56", "80", "62", "66", "57", "75", "59", "68", "58" ]
[ "nonn" ]
9
1
2
[ "A358123", "A358142" ]
null
Rémy Sigrist, Oct 31 2022
2022-11-03T10:07:14
oeisdata/seq/A358/A358142.seq
ecfbbf14b57ac0c0abb020ca67956660
A358143
Inverse permutation to A358124.
[ "1", "2", "3", "4", "5", "6", "8", "7", "9", "12", "11", "13", "10", "14", "19", "18", "21", "16", "20", "15", "17", "22", "30", "28", "34", "26", "32", "29", "31", "24", "33", "23", "27", "25", "35", "48", "45", "54", "43", "52", "47", "55", "39", "50", "46", "49", "37", "53", "41", "51", "36", "42", "40", "44", "38", "56", "77", "72", "87", "68", "85", "76", "89", "64", "81", "74", "88" ]
[ "nonn" ]
9
1
2
[ "A358124", "A358143" ]
null
Rémy Sigrist, Oct 31 2022
2022-11-03T10:07:18
oeisdata/seq/A358/A358143.seq
828cc2c78e455dd6e7f27cdc1df1a27a
A358144
Number of strict closure operators on a set of n elements such that all pairs of distinct points can be separated by clopen sets.
[ "1", "1", "1", "4", "167", "165791", "19194240969" ]
[ "nonn", "hard", "more" ]
26
0
4
[ "A334255", "A356544", "A358144", "A358152" ]
null
Tian Vlasic, Oct 31 2022
2024-06-13T11:36:17
oeisdata/seq/A358/A358144.seq
6016f738034d47da3e4229f07b644113
A358145
a(n) = Sum_{k=0..n} binomial(n*k,k) * binomial(n*(n-k),n-k).
[ "1", "2", "16", "258", "6184", "195660", "7674144", "358788696", "19464910000", "1201543131276", "83134800597280", "6371436086078382", "535715287899894216", "49025879014213908144", "4850781409411286177248", "515964243167132532702480", "58710263012322890445554400" ]
[ "nonn" ]
13
0
2
[ "A358050", "A358145" ]
null
Seiichi Manyama, Oct 31 2022
2022-11-01T10:36:43
oeisdata/seq/A358/A358145.seq
633b1a2d3cc605bf4ce0d8c954871960
A358146
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} binomial(k*j,j).
[ "1", "1", "1", "1", "2", "1", "1", "3", "3", "1", "1", "4", "9", "4", "1", "1", "5", "19", "29", "5", "1", "1", "6", "33", "103", "99", "6", "1", "1", "7", "51", "253", "598", "351", "7", "1", "1", "8", "73", "506", "2073", "3601", "1275", "8", "1", "1", "9", "99", "889", "5351", "17577", "22165", "4707", "9", "1", "1", "10", "129", "1429", "11515", "58481", "152173", "138445", "17577", "10", "1" ]
[ "nonn", "tabl" ]
17
0
5
[ "A000012", "A001477", "A006134", "A188675", "A225612", "A225615", "A226391", "A358050", "A358146" ]
null
Seiichi Manyama, Oct 31 2022
2023-03-18T08:07:45
oeisdata/seq/A358/A358146.seq
963ff035bbfc564916efaeb7fd2532b2
A358147
Primes p such that the polynomial x^7 - 7*x + 3 (mod p) is the product of seven linear factors.
[ "1879", "5381", "5783", "8819", "8893", "12007", "12917", "13967", "14293", "15727", "18311", "20357", "20441", "22639", "26833", "27791", "28711", "31177", "32233", "33829", "35051", "35963", "38167", "40867", "42667", "43003", "46831", "47269", "49937", "51893", "55717", "58603", "59273", "62591", "63487", "64937", "65543", "68881", "72997", "75323", "75659", "75991", "85517" ]
[ "nonn" ]
13
1
1
null
null
Michel Marcus, Oct 31 2022
2022-11-01T07:12:49
oeisdata/seq/A358/A358147.seq
2ed29335605958ab2421b998db6feef4
A358148
Aliquot sequence starting at 326.
[ "326", "166", "86", "46", "26", "16", "15", "9", "4", "3", "1", "0" ]
[ "nonn", "easy", "fini", "full" ]
4
0
1
[ "A143759", "A358148" ]
null
Michal Paulovic, Oct 31 2022
2022-12-01T17:29:07
oeisdata/seq/A358/A358148.seq
1d8070ef1d4e5768bf97ecd7c391c4ce
A358149
First of four consecutive primes p,q,r,s such that (2*p+q)/5 and (r+2*s)/5 are prime.
[ "11", "1151", "33071", "33637", "55331", "57637", "75997", "90821", "97007", "100151", "112237", "118219", "123581", "141629", "154459", "160553", "165961", "199247", "212777", "222823", "288361", "289511", "293677", "319993", "329471", "331697", "336101", "361799", "364537", "375371", "381467", "437279", "437693", "442571", "444461", "457837", "475751", "490877", "540781" ]
[ "nonn" ]
14
1
1
[ "A358149", "A358155" ]
null
J. M. Bergot and Robert Israel, Nov 01 2022
2022-11-10T07:43:17
oeisdata/seq/A358/A358149.seq
b31fbfa5b63ca8aecf24f2c43adaa1e5
A358150
Squares visited by a knight moving on a square-spiral numbered board where the knight moves to the smallest numbered unvisited square and where the square number is more than the number of currently visited squares.
[ "1", "10", "3", "6", "9", "12", "15", "18", "35", "14", "11", "24", "27", "48", "23", "20", "39", "36", "61", "32", "29", "52", "25", "28", "51", "80", "47", "76", "43", "70", "105", "38", "63", "34", "59", "56", "87", "126", "53", "84", "49", "78", "45", "74", "71", "106", "67", "64", "97", "60", "93", "90", "55", "58", "89", "92", "131", "88", "127", "174", "83", "120", "79", "116", "75", "72", "107", "68", "103", "100", "141" ]
[ "nonn", "fini", "walk" ]
9
1
2
[ "A316588", "A316667", "A326918", "A326922", "A358150" ]
null
Scott R. Shannon, Nov 01 2022
2022-11-01T07:50:28
oeisdata/seq/A358/A358150.seq
75212af531fe9b5128650e17108c6d46
A358151
Earliest infinite sequence of distinct integers on a square spiral such that every number equals the sum of its eight adjacent neighbors. See the Comments.
[ "0", "1", "-1", "2", "-2", "3", "-3", "4", "-4", "-5", "-6", "11", "5", "6", "-20", "15", "8", "7", "-17", "12", "9", "18", "-32", "21", "13", "-8", "16", "-38", "14", "30", "-7", "-11", "-37", "57", "-60", "23", "-9", "10", "24", "-34", "-24", "60", "-10", "-13", "-31", "72", "-109", "82", "20", "-12", "-14", "-108", "182", "-142", "-28", "188", "-15", "-16", "-160", "168", "-82", "67", "-128", "120", "-21", "22", "-43", "-22" ]
[ "sign" ]
41
0
4
[ "A344659", "A354435", "A354441", "A358048", "A358151", "A358254" ]
null
Scott R. Shannon, Nov 01 2022
2022-11-10T07:42:59
oeisdata/seq/A358/A358151.seq
8f7821613aa2256ac5eb31cd6678eaae
A358152
Number of strict closure operators on a set of n elements such that every point and every closed set not containing that point can be separated by clopen sets.
[ "1", "1", "2", "8", "121", "18460", "159273237" ]
[ "nonn", "hard", "more" ]
31
0
3
[ "A334255", "A356544", "A358144", "A358152" ]
null
Tian Vlasic, Nov 01 2022
2024-07-20T08:10:25
oeisdata/seq/A358/A358152.seq
5bfa831e4720dffbb1b36d6795846170
A358153
Lexicographically earliest infinite sequence of distinct positive integers on a square spiral such that each number shares a factor with its four orthogonally nearest neighbors but shares no factor with its four diagonal next-nearest neighbors.
[ "6", "10", "35", "21", "77", "22", "143", "39", "65", "117", "12", "63", "18", "20", "24", "44", "26", "273", "30", "195", "36", "88", "42", "40", "48", "14", "455", "50", "175", "80", "55", "33", "385", "147", "539", "91", "105", "110", "847", "176", "1001", "28", "119", "51", "187", "153", "85", "459", "595", "15", "54", "351", "66", "189", "72", "99", "57", "95", "114", "100", "78", "220", "52", "60", "34", "833" ]
[ "nonn" ]
16
1
1
[ "A253279", "A257112", "A335710", "A336799", "A336946", "A336957", "A346294", "A358153" ]
null
Scott R. Shannon, Nov 01 2022
2024-04-28T16:24:24
oeisdata/seq/A358/A358153.seq
5b1c523c056404e24d6289b28b840346
A358154
a(n) is the smallest composite number obtained by appending one or more 1's to n.
[ "111", "21", "3111", "411", "51", "611", "711", "81", "91", "1011", "111", "121", "1311", "141", "15111", "161", "171", "18111", "1911", "201", "21111", "221", "231", "24111", "2511", "261", "27111", "2811", "291", "301", "3111", "321", "3311", "341", "351", "361", "371", "381", "391", "4011", "411", "42111", "4311", "441", "451", "4611", "471", "481", "4911", "501", "511", "5211", "531", "5411" ]
[ "nonn", "base" ]
21
1
1
[ "A002808", "A069568", "A112386", "A153275", "A358154" ]
null
Gleb Ivanov, Nov 01 2022
2022-12-22T14:40:21
oeisdata/seq/A358/A358154.seq
ee7831bc2e0c8272a0eaa41774a70b78
A358155
First of four consecutive primes p,q,r,s such that (2*p+q)/5, (q+r)/10 and (r+2*s)/5 are prime.
[ "11", "2696717", "3500381", "3989903", "4515113", "8164073", "12451013", "18793013", "23567267", "24057713", "30312409", "36391853", "44569853", "45657881", "53442343", "54721253", "54944761", "56652203", "63993803", "76763081", "90662303", "92889127", "94670143", "105790973", "106339481", "108988223", "117213871", "118802533", "130741007", "145543523" ]
[ "nonn" ]
12
1
1
[ "A007530", "A358149", "A358155" ]
null
J. M. Bergot and Robert Israel, Nov 01 2022
2022-11-10T07:43:13
oeisdata/seq/A358/A358155.seq
3801542eee84821446cbfedb4212f4d0
A358156
a(n) is the smallest number k such that the sum of k consecutive prime numbers starting with the n-th prime is a square.
[ "9", "23", "4", "1862", "14", "3", "2", "211", "331", "163", "366", "3", "124", "48", "2", "449", "8403", "121", "35", "2", "4", "105", "77", "43", "190769", "1726", "234", "248", "200", "295", "293", "73", "4", "873", "32", "64", "2456139382", "8", "4519", "14", "123", "5", "9395", "296", "26", "5", "3479", "810", "9", "7091", "1669", "157", "1189", "12559", "269", "4930", "21", "376", "3" ]
[ "nonn" ]
41
1
1
[ "A000040", "A000290", "A064397", "A072849", "A076305", "A105720", "A166255", "A166261", "A230327", "A287027", "A358156" ]
null
Todor Szimeonov, Nov 01 2022
2022-12-14T16:25:39
oeisdata/seq/A358/A358156.seq
d5a93f3cbf936f92abfe13b2e5714a6f
A358157
a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = floor(i*j/3).
[ "1", "0", "0", "1", "32", "1422", "146720", "18258864", "3217515264", "910849979232", "316878962588928", "143616562358849280", "90359341652805156864", "68004478547050644357120", "63187026071337208000512000", "75392341069747600992153600000", "104962910849766568886449582080000", "174017685915978467201007058206720000" ]
[ "nonn" ]
11
0
5
[ "A000212", "A143974", "A181286", "A358157", "A358158" ]
null
Stefano Spezia, Nov 01 2022
2022-11-02T11:53:15
oeisdata/seq/A358/A358157.seq
c128271e130f4b79f175c5a312abac47
A358158
a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = floor(i*j/3).
[ "1", "0", "4", "238", "31992", "9390096", "4755878928", "3802500283680", "4720879431568800", "8379987002639042400", "20346893722025317036800" ]
[ "nonn", "hard", "more" ]
13
0
3
[ "A000212", "A143974", "A181286", "A358157", "A358158" ]
null
Stefano Spezia, Nov 01 2022
2023-10-15T09:26:50
oeisdata/seq/A358/A358158.seq
1a1f54e5cffdbd7f518320a1e0653655
A358159
a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = i*j - floor(i*j/3).
[ "1", "1", "7", "102", "4396", "374216", "49857920", "11344877568", "3879729283968", "1804571320405248", "1195546731955854336", "1058730877124859138048", "1184751018265831288602624", "1725335046543668616765112320", "3147123030650561978295975936000", "6934187745940804400441946931200000", "18840570649600136750602236509552640000" ]
[ "nonn" ]
10
0
3
[ "A071619", "A143976", "A358042", "A358159", "A358160" ]
null
Stefano Spezia, Nov 01 2022
2022-11-02T11:53:28
oeisdata/seq/A358/A358159.seq
31f4a3ba1ec1ebac0c94766e2ee8fa9b
A358160
a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = i*j - floor(i*j/3).
[ "1", "2", "40", "3884", "1016376", "534983256", "510252517152", "802452895865280", "1901953775079849600", "6537796866589765507200", "31381746234057256630521600" ]
[ "nonn", "hard", "more" ]
13
0
2
[ "A071619", "A143976", "A358042", "A358159", "A358160" ]
null
Stefano Spezia, Nov 01 2022
2023-10-15T09:26:55
oeisdata/seq/A358/A358160.seq
982852be9f2e28d9076f956476b63f6a
A358161
a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = ceiling(i*j/3).
[ "1", "1", "3", "19", "434", "18142", "1138592", "131646240", "22247821152", "4990553682336", "1661493079305216", "729074911776673536", "397903630707426852864", "290086114501734871449600", "262660633302518916820992000", "284075108357948520100761600000", "385808192325346588875691868160000", "626209817056857125529475382231040000" ]
[ "nonn" ]
11
0
3
[ "A008810", "A070333", "A143977", "A358161", "A358162" ]
null
Stefano Spezia, Nov 01 2022
2022-11-02T11:53:33
oeisdata/seq/A358/A358161.seq
ba567e59d6d072c9e433138105917fc4
A358162
a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = ceiling(i*j/3).
[ "1", "1", "11", "530", "71196", "18680148", "8825763888", "6969574132560", "8223753750015600", "14043461354695317600", "33726601900489760438400" ]
[ "nonn", "hard", "more" ]
16
0
3
[ "A008810", "A070333", "A143977", "A358161", "A358162" ]
null
Stefano Spezia, Nov 01 2022
2023-10-15T09:26:59
oeisdata/seq/A358/A358162.seq
a9458c143619fac6eb2b58b28aa6fe14
A358163
a(n) is the permanent of the n X n matrix M(n) that is defined by M[i,j] = i*j - ceiling(i*j/3).
[ "1", "0", "1", "30", "1272", "113224", "18615680", "4299553536", "1507609286784", "781464165813504", "525599814806986752", "473934337123421786112", "567876971785035135320064", "837723761443461191423754240", "1549608938859438129393893376000", "3582000047767392376356107059200000", "9838495669776145718724862743674880000" ]
[ "nonn" ]
10
0
4
[ "A030511", "A143979", "A358163", "A358164" ]
null
Stefano Spezia, Nov 01 2022
2022-11-02T11:53:20
oeisdata/seq/A358/A358163.seq
36db2a594ffcbfafc75548291cab634b
A358164
a(n) is the hafnian of the 2n X 2n symmetric matrix defined by M[i,j] = i*j - ceiling(i*j/3).
[ "1", "1", "26", "2704", "698568", "384890688", "378771904512", "597991783196160", "1450380828625459200", "5077825865646165964800", "24487520383436615392204800" ]
[ "nonn", "hard", "more" ]
15
0
3
[ "A030511", "A143979", "A358163", "A358164" ]
null
Stefano Spezia, Nov 01 2022
2023-10-15T09:27:07
oeisdata/seq/A358/A358164.seq
61fad32ce4284318155148ea9c6d4188
A358165
Irregular triangular array read by rows. T(n,k) is the number of direct sum decompositions V_1 + V_2 + ... + V_m = GF(2)^n with the dimensions of the V_i corresponding to the k-th partition of n in canonical ordering, n >= 0, 1 <= k <= A000041(n).
[ "1", "1", "1", "3", "1", "28", "28", "1", "120", "280", "1680", "840", "1", "496", "9920", "29760", "138880", "277760", "83328", "1", "2016", "166656", "499968", "357120", "19998720", "19998720", "15554560", "139991040", "139991040", "27998208", "1", "8128", "2731008", "8193024", "48377856", "1354579968", "1354579968", "2902671360", "13545799680", "81274798080", "40637399040", "126427463680", "379282391040", "227569434624", "32509919232" ]
[ "nonn", "tabf" ]
10
0
4
[ "A000041", "A002884", "A053601", "A080575", "A270880", "A270881", "A279038", "A358165" ]
null
Geoffrey Critzer, Nov 01 2022
2024-04-19T17:49:30
oeisdata/seq/A358/A358165.seq
2da8c63b6b0c3f362f62fc069f311dc7
A358166
a(1) = 13; for n > 1, if a(n-1) is even, then a(n) = a(n-1)/2; otherwise, a(n) = a(n-1) + prime(a(n-1)).
[ "13", "54", "27", "130", "65", "378", "189", "1318", "659", "5592", "2796", "1398", "699", "5972", "2986", "1493", "13996", "6998", "3499", "36102", "18051", "218932", "109466", "54733", "730334", "365167", "5622764", "2811382", "1405691", "23685544", "11842772", "5921386", "2960693", "52246474", "26123237", "521463688", "260731844", "130365922", "65182961", "1364229390" ]
[ "nonn", "look", "hard" ]
30
1
1
[ "A014688", "A293981", "A350877", "A358166" ]
null
Sander G. Huisman, Nov 01 2022
2022-12-06T07:59:13
oeisdata/seq/A358/A358166.seq
ea7bef86655265a496afe946d2407b8f
A358167
Irregular triangle read by rows: T(n, k) = k-th fixed point in Zhegalkin permutation n (row n of A197819).
[ "0", "1", "0", "2", "0", "6", "8", "14", "0", "30", "40", "54", "72", "86", "96", "126", "128", "158", "168", "182", "200", "214", "224", "254", "0", "510", "680", "854", "1224", "1334", "1632", "1950", "2176", "2430", "2600", "3030", "3144", "3510", "3808", "3870", "4320", "4382", "4680", "5046", "5160" ]
[ "nonn", "tabf" ]
49
0
4
[ "A000225", "A001146", "A058891", "A147537", "A197819", "A358167" ]
null
Tilman Piesk, Nov 01 2022
2022-12-25T14:06:57
oeisdata/seq/A358/A358167.seq
8ad2067b35f42d5228627364ec1fd224
A358168
First n-digit number to occur in Van Eck's Sequence (A181391).
[ "0", "14", "131", "1024", "10381", "100881", "1014748", "10001558", "100246289", "1000943528", "10010107437" ]
[ "nonn", "base", "hard", "more" ]
30
1
2
[ "A181391", "A358168", "A358180" ]
null
G. L. Honaker, Jr., Nov 01 2022
2022-11-06T01:40:20
oeisdata/seq/A358/A358168.seq
977d9f5ac122dac94f995b29a0f5146e
A358169
Row n lists the first differences plus one of the prime indices of n with 1 prepended.
[ "1", "2", "1", "1", "3", "1", "2", "4", "1", "1", "1", "2", "1", "1", "3", "5", "1", "1", "2", "6", "1", "4", "2", "2", "1", "1", "1", "1", "7", "1", "2", "1", "8", "1", "1", "3", "2", "3", "1", "5", "9", "1", "1", "1", "2", "3", "1", "1", "6", "2", "1", "1", "1", "1", "4", "10", "1", "2", "2", "11", "1", "1", "1", "1", "1", "2", "4", "1", "7", "3", "2", "1", "1", "2", "1", "12", "1", "8", "2", "5", "1", "1", "1", "3" ]
[ "nonn", "tabf" ]
8
2
2
[ "A001222", "A055396", "A056239", "A112798", "A124010", "A243055", "A243056", "A252464", "A253566", "A286470", "A287352", "A307824", "A325351", "A325352", "A325366", "A325390", "A355523", "A355524", "A355525", "A355526", "A355528", "A355531", "A355532", "A355533", "A355534", "A355536", "A358169" ]
null
Gus Wiseman, Nov 01 2022
2022-11-02T11:08:01
oeisdata/seq/A358/A358169.seq
67e0cf2dc1e3962f1a1d34f1e48875b6
A358170
Heinz number of the partial sums of the n-th composition in standard order (A066099).
[ "1", "2", "3", "6", "5", "15", "10", "30", "7", "35", "21", "105", "14", "70", "42", "210", "11", "77", "55", "385", "33", "231", "165", "1155", "22", "154", "110", "770", "66", "462", "330", "2310", "13", "143", "91", "1001", "65", "715", "455", "5005", "39", "429", "273", "3003", "195", "2145", "1365", "15015", "26", "286", "182", "2002", "130", "1430", "910", "10010" ]
[ "nonn" ]
6
0
2
[ "A000120", "A000720", "A001221", "A001222", "A001511", "A005117", "A005940", "A019565", "A029837", "A029931", "A048793", "A056239", "A059893", "A061395", "A065120", "A066099", "A070939", "A112798", "A241916", "A242628", "A253565", "A253566", "A355536", "A358133", "A358134", "A358135", "A358137", "A358170", "A359042" ]
null
Gus Wiseman, Dec 20 2022
2022-12-21T13:18:17
oeisdata/seq/A358/A358170.seq
4ea725ac140c46ff5911a59040476e1c
A358171
The a(n)-th composition in standard order (A066099) is the first differences plus one of the prime indices of n (A112798).
[ "0", "0", "0", "1", "0", "2", "0", "3", "1", "4", "0", "6", "0", "8", "2", "7", "0", "5", "0", "12", "4", "16", "0", "14", "1", "32", "3", "24", "0", "10", "0", "15", "8", "64", "2", "13", "0", "128", "16", "28", "0", "20", "0", "48", "6", "256", "0", "30", "1", "9", "32", "96", "0", "11", "4", "56", "64", "512", "0", "26", "0", "1024", "12", "31", "8", "40", "0", "192", "128", "18", "0", "29", "0" ]
[ "nonn" ]
12
1
6
[ "A000120", "A000720", "A001221", "A001222", "A005940", "A055932", "A056239", "A057335", "A066099", "A066312", "A070939", "A112798", "A242628", "A243055", "A253565", "A253566", "A286470", "A287352", "A325351", "A325352", "A325390", "A355534", "A355536", "A358169", "A358171" ]
null
Gus Wiseman, Dec 21 2022
2023-07-15T10:36:27
oeisdata/seq/A358/A358171.seq
9d7af9ced14a9a9a96d78a62f9c976fb
A358172
Triangle read by rows: if n has weakly increasing prime indices (a,b,...,y,z) then row n is (z-a+1, z-b+1, ..., z-y+1).
[ "1", "2", "1", "1", "1", "3", "2", "2", "4", "2", "1", "1", "1", "2", "1", "3", "3", "3", "5", "2", "2", "2", "1", "6", "1", "1", "4", "4", "3", "2", "1", "1", "1", "1", "4", "7", "2", "2", "2", "1", "8", "5", "3", "3", "3", "4", "3", "5", "5", "2", "2", "9", "2", "2", "2", "2", "1", "3", "1", "6", "6", "6", "2", "1", "1", "3", "4", "4", "4", "7", "10", "3", "3", "2", "11", "3", "3", "1", "1", "1", "1", "1", "4", "5", "4" ]
[ "nonn", "tabf" ]
9
1
2
[ "A001222", "A008578", "A055396", "A056239", "A112798", "A124010", "A241916", "A243055", "A243503", "A246277", "A253565", "A325351", "A325352", "A326844", "A355534", "A355536", "A356958", "A358137", "A358172", "A358195" ]
null
Gus Wiseman, Dec 20 2022
2022-12-28T09:04:58
oeisdata/seq/A358/A358172.seq
3dc7268ccfd8011b335ff3b99239480b
A358173
First differences of A286708.
[ "36", "28", "8", "36", "52", "4", "16", "9", "63", "36", "68", "8", "32", "9", "43", "16", "76", "72", "27", "1", "108", "16", "64", "36", "68", "4", "28", "89", "36", "27", "4", "69", "71", "27", "29", "20", "72", "77", "47", "32", "128", "36", "36", "136", "8", "56", "25", "91", "188", "8", "188", "92", "9", "99", "4", "40", "144", "28", "109", "62", "49", "64", "49", "18", "97", "11", "81" ]
[ "nonn" ]
14
1
1
[ "A001694", "A053707", "A076446", "A246547", "A286708", "A358173" ]
null
Michael De Vlieger, Nov 01 2022
2024-09-11T00:34:35
oeisdata/seq/A358/A358173.seq
db2c376b400912c91b0e9d46ade490c0
A358174
Smaller of a pair of numbers (m, m+1) such that both are products P of composite prime powers with omega(P) > 1.
[ "675", "9800", "235224", "465124", "1825200", "11309768", "384199200", "592192224", "4931691075", "5425069447", "13051463048", "221322261600", "865363202000", "8192480787000", "11968683934831", "13325427460800", "15061377048200", "28821995554247", "48689748233307", "511643454094368", "1558709801289000" ]
[ "nonn" ]
7
1
1
[ "A286708", "A358173", "A358174" ]
null
Michael De Vlieger, Nov 01 2022
2022-11-05T21:02:47
oeisdata/seq/A358/A358174.seq
6858bfabc76ced241db7099cd2aa9690
A358175
a(1) = 1, a(2) = 2; a(3) = 3; for n > 3, a(n) is the smallest positive number not occurring earlier that shares a factor with Sum_{k=1..n-1} A001065(a(k)), where A001065(m) is the sum of the proper divisors of m.
[ "1", "2", "3", "4", "5", "6", "8", "19", "10", "7", "29", "9", "12", "14", "15", "18", "16", "20", "127", "22", "24", "26", "28", "21", "233", "13", "25", "241", "11", "27", "30", "32", "35", "33", "17", "34", "36", "433", "31", "39", "38", "40", "42", "44", "45", "48", "727", "46", "50", "797", "49", "52", "51", "54", "57", "37", "60", "56", "55", "58", "62", "63", "1259", "64", "66", "69", "68", "70", "65", "1579", "72", "78", "77", "74" ]
[ "nonn" ]
9
1
2
[ "A001065", "A027751", "A064413", "A354960", "A356430", "A356851", "A358082", "A358175" ]
null
Scott R. Shannon, Nov 02 2022
2023-01-16T09:10:46
oeisdata/seq/A358/A358175.seq
d16b9ed910664f7f439fc974cd297b3c
A358176
a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier that shares a factor with sigma(a(n-1)).
[ "1", "2", "3", "4", "7", "6", "8", "5", "9", "13", "10", "12", "14", "15", "16", "31", "18", "21", "20", "22", "24", "25", "62", "26", "27", "28", "30", "32", "33", "34", "36", "35", "38", "39", "40", "42", "44", "45", "46", "48", "50", "51", "52", "49", "19", "54", "55", "56", "57", "58", "60", "63", "64", "127", "66", "68", "69", "70", "72", "65", "74", "75", "76", "77", "78", "80", "81", "11", "82", "84", "86", "87", "85", "88", "90", "91", "92" ]
[ "nonn" ]
13
1
2
[ "A000203", "A064413", "A354960", "A356430", "A356851", "A358082", "A358176", "A358201" ]
null
Scott R. Shannon, Nov 02 2022
2023-01-16T09:10:46
oeisdata/seq/A358/A358176.seq
940f290cb1422145388354bd5655601c
A358177
Number of Eulerian orientations of a (labeled) 2n-dimensional hypercube graph, Q_2n. Q_2n is also the n-dimensional torus grid graph (C_4)^n.
[ "1", "2", "2970", "351135773356461511142023680" ]
[ "nonn", "hard", "more" ]
30
0
2
[ "A007081", "A054759", "A298119", "A307334", "A334553", "A358177" ]
null
Peter Munn and Zachary DeStefano, Nov 02 2022
2025-02-16T08:34:04
oeisdata/seq/A358/A358177.seq
b517449aa3c13d9a71eeac74f9e1e639
A358178
a(n) is the cardinality of the set of distinct pairwise gcd's of {1! + 1, ..., n! + 1}.
[ "0", "1", "1", "1", "1", "2", "2", "2", "3", "4", "4", "4", "4", "4", "4", "5", "6", "8", "8", "8", "8", "8", "8", "8", "8", "8", "8", "9", "9", "9", "9", "9", "10", "10", "11", "12", "12", "12", "13", "14", "14", "15", "15", "15", "15", "16", "16", "16", "16", "16", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "17", "18", "18", "18", "18", "18", "18", "18", "18", "18" ]
[ "nonn" ]
16
1
6
[ "A038507", "A214799", "A356371", "A358127", "A358178" ]
null
Gleb Ivanov, Nov 02 2022
2022-12-16T09:00:57
oeisdata/seq/A358/A358178.seq
0c2d1ee2df72ee20c1074d1a35ab8f0f
A358179
Prime numbers with prime indices in A333244.
[ "31", "709", "1787", "8527", "19577", "27457", "42043", "52711", "72727", "96797", "112129", "137077", "167449", "173867", "239489", "250751", "285191", "352007", "401519", "443419", "464939", "490643", "527623", "683873", "718807", "755387", "839483", "864013", "985151", "1021271", "1080923", "1128889", "1159901", "1278779", "1323503", "1342907", "1656649", "1693031" ]
[ "nonn" ]
34
1
1
[ "A078442", "A262275", "A333242", "A333243", "A333244", "A358179" ]
null
Michael P. May, Nov 11 2022
2022-11-22T11:56:21
oeisdata/seq/A358/A358179.seq
54c353f2ef551e502459c6cb50085f14
A358180
Indices for A358168.
[ "1", "30", "162", "1150", "11603", "104511", "1041245", "10226995", "101514698", "1008495923", "10060201866" ]
[ "nonn", "hard", "more" ]
24
1
2
[ "A181391", "A358168", "A358180" ]
null
G. L. Honaker, Jr., Nov 02 2022
2022-11-06T01:40:29
oeisdata/seq/A358/A358180.seq
147a331f3316889b13f2e9aead46f7b8
A358181
Decimal expansion of the real root of x^3 - 2*x^2 - x - 1.
[ "2", "5", "4", "6", "8", "1", "8", "2", "7", "6", "8", "8", "4", "0", "8", "2", "0", "7", "9", "1", "3", "5", "9", "9", "7", "5", "0", "8", "8", "0", "9", "7", "9", "1", "5", "2", "8", "8", "1", "1", "2", "7", "0", "3", "3", "7", "4", "5", "2", "0", "0", "6", "1", "2", "9", "5", "5", "1", "4", "7", "4", "5", "7", "4", "7", "1", "1", "1", "9", "7", "9", "8", "3", "1", "3", "1" ]
[ "nonn", "cons", "easy" ]
17
1
1
[ "A088559", "A160389", "A231187", "A255240", "A358181" ]
null
Wolfdieter Lang, Nov 07 2022
2025-03-30T18:00:23
oeisdata/seq/A358/A358181.seq
e7bb6a17bf3340111041dfefd2b5d45b
A358182
Decimal expansion of the real root of 2*x^3 - x^2 - x - 1.
[ "1", "2", "3", "3", "7", "5", "1", "9", "2", "8", "5", "2", "8", "2", "5", "8", "7", "8", "8", "1", "9", "0", "9", "4", "3", "3", "7", "7", "6", "7", "9", "3", "9", "3", "0", "3", "5", "1", "9", "1", "1", "2", "7", "2", "3", "7", "5", "3", "1", "1", "8", "6", "4", "9", "4", "2", "3", "2", "0", "0", "9", "8", "8", "7", "0", "2", "7", "5", "3", "7", "5", "9", "6", "7", "9", "5" ]
[ "nonn", "cons", "easy" ]
14
1
2
[ "A358181", "A358182", "A358183" ]
null
Wolfdieter Lang, Nov 07 2022
2022-11-09T19:20:05
oeisdata/seq/A358/A358182.seq
26177eded77d9d2574fc6137908fe2c9
A358183
Decimal expansion of the real root of 2*x^3 + x^2 - x - 1.
[ "8", "2", "9", "4", "8", "3", "5", "4", "0", "9", "5", "8", "4", "9", "7", "0", "3", "9", "6", "7", "3", "3", "8", "7", "5", "7", "8", "3", "9", "2", "0", "0", "7", "8", "0", "7", "6", "2", "1", "9", "9", "6", "6", "7", "2", "2", "8", "1", "3", "8", "8", "5", "5", "0", "1", "7", "6", "1", "0", "7", "7", "4", "4", "4", "9", "2", "0", "8", "4", "0", "1", "0", "3", "9", "0", "1" ]
[ "nonn", "cons", "easy" ]
15
0
1
[ "A358182", "A358183", "A358184" ]
null
Wolfdieter Lang, Nov 07 2022
2022-11-09T19:20:14
oeisdata/seq/A358/A358183.seq
5f5858d7c841a2fcf8189ee900cf765c
A358184
Decimal expansion of the real root of 2*x^3 - x^2 + x - 1.
[ "7", "3", "8", "9", "8", "3", "6", "2", "1", "5", "0", "4", "5", "0", "6", "2", "3", "7", "3", "2", "3", "4", "6", "2", "5", "4", "0", "6", "7", "1", "0", "8", "7", "5", "5", "0", "7", "2", "3", "7", "7", "4", "7", "7", "6", "3", "7", "9", "0", "9", "6", "7", "2", "2", "1", "1", "7", "9", "5", "4", "9", "6", "9", "3", "0", "2", "3", "0", "2", "0", "3", "1", "5", "9", "8", "0" ]
[ "nonn", "cons", "easy" ]
12
0
1
[ "A358182", "A358183", "A358184" ]
null
Wolfdieter Lang, Nov 07 2022
2023-09-09T16:22:14
oeisdata/seq/A358/A358184.seq
96f2bca3d0810e26a45e792aaa162e87
A358185
Coefficients of x^n/n! in the expansion of (1 - x)*log(1 - x).
[ "0", "-1", "1", "1", "2", "6", "24", "120", "720", "5040", "40320", "362880", "3628800", "39916800", "479001600", "6227020800", "87178291200", "1307674368000", "20922789888000", "355687428096000", "6402373705728000", "121645100408832000", "2432902008176640000", "51090942171709440000", "1124000727777607680000", "25852016738884976640000" ]
[ "sign", "easy" ]
19
0
5
[ "A000142", "A000312", "A103505", "A104150", "A159333", "A358185" ]
null
Wolfdieter Lang, Nov 14 2022
2023-09-16T15:20:07
oeisdata/seq/A358/A358185.seq
5e76c666543f4c84893565d8b381d1bb
A358186
Decimal expansion of the positive real root r of 3*x^4 - 1.
[ "7", "5", "9", "8", "3", "5", "6", "8", "5", "6", "5", "1", "5", "9", "2", "5", "4", "7", "3", "3", "1", "1", "8", "7", "7", "5", "0", "6", "5", "4", "5", "4", "5", "3", "3", "5", "3", "9", "6", "7", "7", "3", "4", "4", "8", "8", "8", "7", "3", "1", "0", "3", "1", "8", "6", "1", "1", "2", "8", "8", "6", "5", "3", "7", "0", "0", "3", "2", "2", "2", "3", "3", "1", "7", "1", "0" ]
[ "nonn", "cons", "easy" ]
16
0
1
[ "A011002", "A011022", "A358186" ]
null
Wolfdieter Lang, Dec 04 2022
2024-07-27T23:54:11
oeisdata/seq/A358/A358186.seq
6972963c620ad7f251fdd6fc71c08aec
A358187
Decimal expansion of the positive real root r of x^4 + 2*x^3 - 1.
[ "7", "1", "6", "6", "7", "2", "7", "4", "9", "2", "8", "2", "2", "8", "6", "6", "3", "8", "4", "2", "4", "7", "3", "9", "3", "0", "1", "4", "3", "2", "5", "5", "6", "1", "8", "3", "9", "2", "1", "5", "5", "1", "3", "7", "6", "0", "2", "9", "8", "6", "1", "6", "4", "6", "6", "7", "8", "9", "4", "5", "6", "8", "0", "2", "4", "2", "1", "4", "7", "4", "9", "0", "0", "7", "3", "3", "8", "7" ]
[ "nonn", "cons", "easy" ]
13
0
1
[ "A358187", "A358188" ]
null
Wolfdieter Lang, Dec 06 2022
2023-01-11T15:59:25
oeisdata/seq/A358/A358187.seq
2af4b92debc3af010a0a542e80a81ad9
A358188
Decimal expansion of the positive real root r of x^4 - 2*x^3 - 1.
[ "2", "1", "0", "6", "9", "1", "9", "3", "4", "0", "3", "7", "6", "2", "1", "7", "2", "1", "7", "0", "9", "7", "1", "0", "6", "1", "2", "9", "5", "3", "7", "9", "7", "3", "0", "4", "6", "6", "2", "9", "2", "7", "6", "5", "4", "4", "0", "9", "2", "8", "1", "4", "9", "3", "8", "3", "6", "7", "3", "5", "4", "6", "6", "4", "4", "1", "4", "2", "2", "4", "2", "7", "2", "9", "4", "2", "3", "7" ]
[ "nonn", "cons", "easy" ]
10
1
1
[ "A358187", "A358188" ]
null
Wolfdieter Lang, Dec 06 2022
2022-12-11T10:29:50
oeisdata/seq/A358/A358188.seq
cd90e05513699670c3830e4e7814ef68
A358189
Decimal expansion of the positive real root r of x^4 + 2*x - 1.
[ "4", "7", "4", "6", "2", "6", "6", "1", "7", "5", "6", "2", "6", "0", "5", "5", "5", "0", "3", "2", "9", "4", "1", "3", "2", "0", "9", "8", "9", "4", "9", "3", "1", "4", "1", "2", "6", "6", "7", "3", "6", "1", "3", "6", "5", "9", "1", "9", "4", "7", "8", "5", "2", "2", "3", "4", "9", "5", "6", "5", "6", "3", "2", "6", "1", "1", "4", "3", "1", "1", "1", "3", "0", "2", "5", "7", "8", "6" ]
[ "nonn", "cons", "easy" ]
9
0
1
[ "A358189", "A358190" ]
null
Wolfdieter Lang, Dec 07 2022
2022-12-08T16:37:23
oeisdata/seq/A358/A358189.seq
0d95a23be4be18225834cbef3909ec59
A358190
Decimal expansion of the positive real root r of x^4 - 2*x - 1.
[ "1", "3", "9", "5", "3", "3", "6", "9", "9", "4", "4", "6", "7", "0", "7", "3", "0", "1", "8", "7", "9", "3", "1", "4", "3", "6", "1", "3", "0", "7", "1", "0", "5", "5", "3", "4", "2", "8", "4", "1", "8", "3", "4", "9", "1", "2", "4", "0", "9", "7", "5", "6", "6", "2", "0", "7", "9", "3", "3", "0", "9", "0", "1", "1", "3", "5", "2", "1", "3", "0", "8", "9", "1", "5", "1", "0", "5", "4" ]
[ "nonn", "cons", "easy" ]
10
1
2
[ "A358189", "A358190" ]
null
Wolfdieter Lang, Dec 07 2022
2022-12-11T10:30:42
oeisdata/seq/A358/A358190.seq
52bd912719ff92b371d99ea1c52c1dd0
A358191
Decimal expansion of Sum_{n >= 2} (n-1)/(n^n).
[ "3", "3", "7", "1", "8", "7", "7", "1", "5", "8", "3", "8", "9", "2", "0", "9", "0", "6", "6", "4", "8", "6", "0", "6", "5", "5", "2", "6", "6", "6", "2", "8", "2", "4", "9", "0", "1", "5", "1", "9", "2", "0", "9", "4", "2", "6", "8", "0", "0", "9", "9", "0", "9", "9", "1", "6", "4", "1", "3", "3", "9", "8", "4", "9", "5", "5", "4", "4", "1", "4", "3", "1", "7", "5", "2", "8", "8", "5", "3", "4", "9", "3", "0", "5", "5", "0", "9", "3", "9", "9", "1", "8", "3", "5", "3", "2", "3", "4", "4", "4" ]
[ "cons", "nonn" ]
13
0
1
[ "A073009", "A098686", "A358191" ]
null
Peter Bala, Nov 02 2022
2025-02-16T08:34:04
oeisdata/seq/A358/A358191.seq
423736116c30df72402c915c57537c26
A358192
Numerator of the quotient of the prime indices of the n-th semiprime.
[ "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "3", "1", "1", "1", "1", "2", "3", "1", "1", "1", "1", "2", "1", "4", "1", "3", "1", "1", "2", "2", "1", "3", "1", "1", "1", "1", "4", "1", "1", "2", "1", "1", "1", "2", "1", "5", "3", "1", "3", "1", "1", "4", "1", "1", "2", "1", "1", "1", "5", "1", "2", "1", "2", "3", "1", "5", "1", "1", "3", "4", "1", "2", "6", "1", "1", "1", "3", "2", "5", "1", "1", "1", "3", "1", "1" ]
[ "nonn", "frac" ]
10
1
6
[ "A000040", "A000720", "A001221", "A001222", "A001358", "A003963", "A006881", "A027751", "A056239", "A128301", "A215366", "A289508", "A289509", "A296150", "A300912", "A318990", "A318991", "A338912", "A338913", "A339005", "A358103", "A358104", "A358105", "A358106", "A358192", "A358193" ]
null
Gus Wiseman, Nov 03 2022
2023-07-15T10:36:08
oeisdata/seq/A358/A358192.seq
ec2550207a9f218c156845680def4679
A358193
Denominator of the quotient of the prime indices of the n-th semiprime.
[ "1", "2", "1", "3", "4", "3", "2", "5", "1", "6", "5", "7", "4", "8", "3", "9", "1", "7", "5", "4", "10", "11", "2", "9", "12", "5", "13", "7", "14", "5", "3", "11", "15", "8", "16", "6", "3", "17", "7", "1", "18", "13", "7", "2", "19", "15", "20", "6", "10", "21", "11", "22", "8", "9", "23", "1", "17", "24", "9", "4", "7", "25", "19", "26", "5", "13", "27", "8", "10", "28", "14", "11", "29", "21", "7", "30" ]
[ "nonn", "frac" ]
6
1
2
[ "A000040", "A000720", "A001221", "A001222", "A001358", "A003963", "A006881", "A027751", "A032741", "A056239", "A128301", "A215366", "A289508", "A289509", "A296150", "A300912", "A318990", "A318991", "A338912", "A338913", "A339005", "A358103", "A358104", "A358105", "A358106", "A358192", "A358193" ]
null
Gus Wiseman, Nov 03 2022
2022-11-04T14:44:56
oeisdata/seq/A358/A358193.seq
581a2d8db86991c73661e92fa0a4fd16
A358194
Irregular triangle read by rows where T(n,k) is the number of integer partitions of n with partial sums summing to k, where k ranges from n to n(n+1)/2.
[ "1", "1", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "0", "0", "1", "1", "0", "1", "1", "0", "1", "1", "1", "0", "0", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "1", "0", "0", "0", "1", "1", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "1", "0", "0", "0", "1", "1", "1", "1", "0", "1", "1", "1", "2", "1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "0", "1", "1" ]
[ "nonn", "tabf" ]
6
0
77
[ "A000009", "A000041", "A029931", "A048793", "A053632", "A152947", "A264034", "A304818", "A318283", "A325362", "A358134", "A358136", "A358137", "A358194", "A359042", "A359361", "A359397" ]
null
Gus Wiseman, Dec 31 2022
2023-01-01T19:30:53
oeisdata/seq/A358/A358194.seq
e50c68288875b232c5223796ba035fa6
A358195
Heinz number of the partial sums plus one of the reversed first differences of the prime indices of n.
[ "1", "1", "1", "2", "1", "3", "1", "4", "2", "5", "1", "9", "1", "7", "3", "8", "1", "6", "1", "25", "5", "11", "1", "27", "2", "13", "4", "49", "1", "15", "1", "16", "7", "17", "3", "18", "1", "19", "11", "125", "1", "35", "1", "121", "9", "23", "1", "81", "2", "10", "13", "169", "1", "12", "5", "343", "17", "29", "1", "75", "1", "31", "25", "32", "7", "77", "1", "289", "19", "21", "1", "54", "1", "37" ]
[ "nonn" ]
5
1
4
[ "A001222", "A005940", "A019565", "A048793", "A056239", "A112798", "A161511", "A241916", "A246277", "A253565", "A326844", "A358137", "A358170", "A358195" ]
null
Gus Wiseman, Dec 23 2022
2022-12-24T11:15:30
oeisdata/seq/A358/A358195.seq
bcfda490739abf28251577398a07235a
A358196
Numbers k such that 5^k and 8^k have the same leading digit.
[ "0", "5", "9", "15", "19", "29", "34", "39", "44", "49", "54", "59", "98", "102", "108", "112", "118", "122", "132", "137", "142", "147", "152", "162", "191", "195", "201", "205", "211", "215", "225", "230", "235", "240", "245", "250", "255", "284", "294", "298", "304", "308", "318", "328", "333", "338", "343", "348", "387", "391", "397", "401", "407", "411", "421", "426", "431", "436", "441", "446", "451", "480", "490", "494", "500" ]
[ "nonn", "base" ]
31
1
2
[ "A000351", "A001018", "A088935", "A111395", "A358196" ]
null
Nicolay Avilov, Nov 02 2022
2022-12-26T09:47:37
oeisdata/seq/A358/A358196.seq
1e19a18d58b89f800225b77113b3f746
A358197
Numbers k such that 2^k, 5^k and 8^k have the same first digit.
[ "0", "5", "15", "98", "108", "118", "191", "201", "211", "284", "294", "304", "387", "397", "407", "480", "490", "500", "583", "593", "603", "676", "686", "696", "779", "789", "872", "882", "892", "965", "975", "985", "1068", "1078", "1088", "1161", "1171", "1181", "1264", "1274", "1284", "1357", "1367", "1377", "1450", "1460", "1470", "1553", "1563", "1573", "1646", "1656", "1666" ]
[ "nonn", "base" ]
42
1
2
[ "A008952", "A088935", "A111395", "A358196", "A358197" ]
null
Alexander M. Domashenko, Nov 02 2022
2022-12-26T11:30:24
oeisdata/seq/A358/A358197.seq
8b385ab358d5a2257651aa7a0e4a999b
A358198
a(n) is the first member p of A007530 such that, with q = p+2, r = p+6 and s = p+8, (2*p+q)/5 is a prime and (r+2*s)/5^n is a prime.
[ "11", "101", "243701", "6758951", "3257480201", "5493848951", "58634348951", "218007942701", "21840280598951", "213065296223951", "186522444661451", "383378987630201", "7794174397786451", "110420241292317701", "67327687581380201", "91455128987630201", "3987035878499348951", "80659241994222005201", "4289429982503255201" ]
[ "nonn" ]
8
1
1
[ "A007530", "A358149", "A358198" ]
null
J. M. Bergot and Robert Israel, Nov 02 2022
2023-01-31T08:26:14
oeisdata/seq/A358/A358198.seq
d7ca3d469e54f47e14e27cfdeac02284
A358199
a(n) is the least integer whose sum of the i-th powers of the proper divisors is a prime for 1 <= i <= n, or -1 if no such number exists.
[ "4", "4", "981", "8829", "8829", "122029105", "2282761881" ]
[ "nonn", "more" ]
30
1
1
[ "A000203", "A001065", "A001157", "A001158", "A037020", "A057709", "A180852", "A357324", "A358199" ]
null
Jean-Marc Rebert, Nov 02 2022
2022-11-16T06:58:01
oeisdata/seq/A358/A358199.seq
7e43368a51971a7b80f61a3c569db59b
A358200
Frequency ranking position of the ratio r(n) between consecutive prime gaps, among all previous ratios {r(i) : 2 < i < n, r(i) = (prime(i) - prime(i-1))/(prime(i-1) - prime(i-2))}. If the ratio r(n) is not among previous ratios, then a(n)=n.
[ "4", "2", "6", "1", "2", "1", "10", "11", "12", "13", "2", "1", "6", "6", "5", "7", "7", "2", "7", "5", "7", "25", "2", "1", "2", "1", "2", "31", "32", "4", "6", "35", "36", "6", "7", "6", "4", "7", "7", "12", "9", "2", "2", "47", "6", "5", "1", "2", "5", "4", "9", "55", "5", "4", "4", "7", "7", "1", "8", "63", "10", "1", "2", "14", "68", "69", "9", "2", "5", "14", "74", "4", "6", "5", "11", "1", "2", "81", "9", "9", "9", "8", "6", "4", "10", "1", "1", "2", "7", "6", "1", "2", "1", "3", "2", "99", "100", "6", "19", "16" ]
[ "nonn" ]
37
4
1
[ "A001223", "A272863", "A274225", "A275785", "A276812", "A358200" ]
null
Andres Cicuttin, Feb 22 2023
2025-03-24T05:53:32
oeisdata/seq/A358/A358200.seq
6b70aaf230a75f657904a07de2f109e1