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.

Showing 1-3 of 3 results.

A382360 a(n) is the unique k such that A382357(k) = 2^n.

Original entry on oeis.org

1, 2, 5, 6, 27, 28, 87, 88, 371, 372, 1303, 1304, 5717, 5718, 27099, 27100, 100637, 100638, 429041, 429042, 1676037, 1676038, 6566201, 6566202, 26703687, 26703688, 105939329, 105939330, 424972311, 424972312, 1688465121, 1688465122, 6744826613, 6744826614
Offset: 0

Views

Author

Rémy Sigrist, Mar 22 2025

Keywords

Examples

			A382357(27) = 2^4, so a(4) = 27.

Links

Crossrefs

Cf. A382357.

Programs

  • PARI
    \\ See Links section.
(C++) // See Links section.

Formula

Empirically: a(2*n+1) = a(2*n)+1.

A382374 Lexicographically earliest sequence of distinct positive integers such that the number of prime factors counted with multiplicity of adjacent terms differ exactly by one.

Original entry on oeis.org

1, 2, 4, 3, 6, 5, 9, 7, 10, 8, 14, 11, 15, 12, 16, 18, 21, 13, 22, 17, 25, 19, 26, 20, 24, 27, 33, 23, 34, 28, 35, 29, 38, 30, 36, 32, 40, 42, 39, 31, 46, 37, 49, 41, 51, 43, 55, 44, 54, 45, 56, 48, 60, 50, 57, 47, 58, 52, 62, 53, 65, 59, 69, 61, 74, 63, 77
Offset: 1

Views

Author

Rémy Sigrist, Mar 23 2025

Keywords

Comments

All powers of 2 appear in the sequence (we can use similar arguments as for A382357).
Conjecture: this sequence is a permutation of the positive integers.

Examples

			The initial terms are:
  n   a(n)  A001222(a(n))
  --  ----  -------------
   1     1              0
   2     2              1
   3     4              2
   4     3              1
   5     6              2
   6     5              1
   7     9              2
   8     7              1
   9    10              2
  10     8              3
  11    14              2
  12    11              1
  13    15              2
  14    12              3
  15    16              4

Links

Crossrefs

Cf. A001222, A382229, A382357, A382375, A382376.

Programs

  • PARI
    \\ See Links section.

A382376 Lexicographically earliest sequence of distinct positive integers such that the number of distinct prime factors of adjacent terms differ exactly by one.

Original entry on oeis.org

1, 2, 6, 3, 10, 4, 12, 5, 14, 7, 15, 8, 18, 9, 20, 11, 21, 13, 22, 16, 24, 17, 26, 19, 28, 23, 33, 25, 34, 27, 35, 29, 36, 30, 38, 31, 39, 32, 40, 37, 44, 41, 45, 42, 46, 43, 48, 47, 50, 49, 51, 53, 52, 59, 54, 60, 55, 61, 56, 64, 57, 66, 58, 67, 62, 70, 63
Offset: 1

Views

Author

Rémy Sigrist, Mar 23 2025

Keywords

Comments

All primorial numbers appear in the sequence (we can use similar arguments as for A382357).
Conjecture: this sequence is a permutation of the positive integers.

Examples

			The initial terms are:
  n   a(n)  A001221(a(n))
  --  ----  -------------
   1     1              0
   2     2              1
   3     6              2
   4     3              1
   5    10              2
   6     4              1
   7    12              2
   8     5              1
   9    14              2
  10     7              1
  11    15              2
  12     8              1
  13    18              2
  14     9              1
  15    20              2

Links

Crossrefs

Cf. A001221, A382357, A382374, A382377.

Programs

  • PARI
    \\ See Links section.
Showing 1-3 of 3 results.

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

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