cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 31-36 of 36 results.

A361323 a(n) = k such that A000469(k) = A361321(n).

Original entry on oeis.org

1, 2, 3, 12, 6, 10, 7, 4, 33, 14, 5, 18, 27, 15, 8, 22, 30, 11, 13, 19, 17, 45, 25, 9, 24, 62, 50, 36, 40, 16, 121, 55, 23, 20, 56, 38, 28, 21, 59, 43, 52, 26, 71, 63, 32, 79, 58, 29, 47, 34, 87, 69, 31, 48, 41, 105, 97, 35, 53, 61, 39, 44, 67, 70, 46, 49, 76, 77, 51, 54, 84, 89, 57, 60, 96
Offset: 1

Views

Author

Scott R. Shannon, Rémy Sigrist, and N. J. A. Sloane, Mar 11 2023

Keywords

Comments

Conjectured to be a permutation of the natural numbers (if not then there exists a k such that A000469(k) does not appear in A361321).

Links

Crossrefs

Cf. A361321, A000469, A361324, A336957, A360519, A361102.

A361324 a(n) = k such that A361321(k) = A000469(n), or -1 if A000469(n) never appears in A361321.

Original entry on oeis.org

1, 2, 3, 8, 11, 5, 7, 15, 24, 6, 18, 4, 19, 10, 14, 30, 21, 12, 20, 34, 38, 16, 33, 25, 23, 42, 13, 37, 48, 17, 53, 45, 9, 50, 58, 28, 83, 36, 61, 29, 55, 79, 40, 62, 22, 65, 49, 54, 66, 27, 69, 41, 59, 70, 32, 35, 73, 47, 39, 74, 60, 26, 44, 87, 78, 93, 63, 98, 52, 64, 43, 101, 77, 86, 102
Offset: 1

Views

Author

Scott R. Shannon, Rémy Sigrist, and N. J. A. Sloane, Mar 11 2023

Keywords

Comments

Conjectured to be a permutation of the natural numbers (and if so, -1 will never appear).

Links

Crossrefs

Cf. A361321, A000469, A361323, A336957, A360519, A361102.

A362600 a(1) = 1, a(2) = 6, a(3) = 10; for n > 3, a(n) is the smallest positive number that has not yet appeared that shares a factor with a(n-1) and a(n-2) and also contains as factors the smallest primes that are not factors of both a(n-1) and a(n-2).

Original entry on oeis.org

1, 6, 10, 15, 12, 20, 30, 42, 35, 40, 60, 84, 70, 45, 18, 50, 75, 24, 80, 90, 105, 14, 36, 120, 140, 21, 48, 150, 210, 154, 33, 54, 110, 135, 66, 100, 165, 72, 130, 180, 126, 175, 160, 168, 195, 170, 78, 225, 190, 96, 240, 280, 63, 102, 270, 315, 28, 108, 300, 350, 147, 114, 330, 420, 77, 22
Offset: 1

Views

Author

Scott R. Shannon, May 02 2023

Keywords

Comments

No term can be a prime power as each term must contain at least two distinct prime factors. This make the sequence similar to A362754, A360519 and A361606. Some small composite numbers take many terms to appear, e.g., a(354476) = 65. Such terms are usually preceded by a term that contains all the lower primes as factors. In the first 500000 terms, other than the first term, there are no fixed points, and it is unknown if any exist.

Examples

			a(4) = 15 as a(2) = 6 = 2*3 and a(3) = 10 = 2*5, and 15 is the smallest unused number that shares a factor with 6 and 10 while also containing 5 and 3 as prime factors, the smallest primes not factors of 6 and 10 respectively. This is the first term to differ from A362754.

Links

Crossrefs

Cf. A362754, A337687, A351495, A064413, A360519, A361606, A053669.

Programs

  • Mathematica
    nn = 120; c[_] := False;
f[x_] := If[OddQ[x], 2, y = 3; While[Divisible[x, y], y = NextPrime[y]]; y];
MapIndexed[Set[{a[First[#2]], c[#1]}, {#1, First[#2]}] &, {1, 6, 10}];
i = a[2]; j = a[3]; q = 5; u = 12;
Do[qq = f[j]; k = Ceiling[u/#] &[q*qq];
  While[Or[c[#], CoprimeQ[i, #], CoprimeQ[i, j]] &[k*q*qq], k++];
  k *= q*qq;
  Set[{a[n], c[k], i, j, q}, {k, True, j, k, qq}];
  If[k == u, While[Or[c[u], PrimePowerQ[u]], u++]], {n, 4, nn}];
Array[a, nn] (* Michael De Vlieger, May 09 2023 *)

A361322 The binary expansion of a(n) specifies which primes divide A361321(n).

Original entry on oeis.org

0, 3, 5, 12, 10, 18, 17, 9, 40, 34, 6, 20, 24, 11, 33, 36, 68, 65, 129, 130, 66, 72, 13, 7, 258, 264, 136, 132, 21, 257, 288, 48, 19, 513, 516, 14, 35, 1025, 1028, 260, 259, 2049, 2052, 22, 514, 520, 25, 4097, 4098, 1026, 1032, 41, 8193, 8194, 2050, 2056, 73
Offset: 1

Views

Author

Scott R. Shannon, Rémy Sigrist and N. J. A. Sloane, Mar 09 2023

Keywords

Comments

Conjecture: The sequence is a permutation of A057716.

Links

Crossrefs

Cf. A057716, A087207, A361321.

Programs

  • PARI
    \\ See Links section.

Formula

a(n) = A087207(A360519(n)).

A361325 Records in A361321.

Original entry on oeis.org

1, 6, 10, 35, 91, 119, 161, 299, 445, 623, 1067, 1351, 1379, 1561, 1589, 1603, 1631, 2051, 2681, 3199, 3829, 4207, 4963, 5089, 6139, 7427, 7441, 8953, 15037, 21769, 26389, 35519, 42647, 49423, 53471, 70279, 77297, 95843, 102839, 111661, 116677, 146707, 158059, 172051, 181247, 206503, 227491
Offset: 1

Views

Author

Scott R. Shannon, Rémy Sigrist and N. J. A. Sloane, Mar 11 2023

Keywords

Crossrefs

Cf. A361321, A000469, A361326, A360519, A361107.

A361326 Indices of records in A361321.

Original entry on oeis.org

1, 2, 3, 4, 9, 22, 26, 31, 95, 99, 132, 216, 222, 287, 293, 298, 303, 321, 406, 490, 581, 643, 764, 791, 932, 1131, 1138, 1346, 1439, 2077, 2541, 3434, 4123, 4813, 5216, 6883, 7525, 9404, 10107, 10975, 11457, 14462, 15565, 16977, 17908, 20456, 22557, 22779, 23929, 29033, 35776, 38811, 43493
Offset: 1

Views

Author

Scott R. Shannon, Rémy Sigrist and N. J. A. Sloane, Mar 11 2023

Keywords

Crossrefs

Cf. A361321, A000469, A361325, A360519, A361107.
Previous Showing 31-36 of 36 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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