A382376 -id:A382376 - cp's OEIS frontend

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.

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

Rémy Sigrist, Mar 23 2025

nonn

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.

			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

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program

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

PARI
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A382377 Lexicographically earliest sequence of distinct positive integers such that the number of distinct prime factors of n and a(n) differ exactly by one.

Original entry on oeis.org

2, 1, 6, 10, 12, 3, 14, 15, 18, 4, 20, 5, 21, 7, 8, 22, 24, 9, 26, 11, 13, 16, 28, 17, 33, 19, 34, 23, 35, 36, 38, 39, 25, 27, 29, 30, 40, 31, 32, 37, 44, 45, 46, 41, 42, 43, 48, 47, 50, 49, 53, 59, 51, 60, 61, 64, 66, 67, 52, 54, 55, 70, 71, 56, 73, 57, 58

Offset: 1

Rémy Sigrist, Mar 23 2025

nonn

A self-inverse permutation of the positive integers.

			The initial terms are:
  n   a(n)  A001221(n)  A001221(a(n))
  --  ----  ----------  -------------
   1     2           0              1
   2     1           1              0
   3     6           1              2
   4    10           1              2
   5    12           1              2
   6     3           2              1
   7    14           1              2
   8    15           1              2
   9    18           1              2
  10     4           2              1
  11    20           1              2
  12     5           2              1
  13    21           1              2
  14     7           2              1
  15     8           2              1

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program
Index entries for sequences that are permutations of the natural numbers

Cf. A001221, A382375, A382376.

PARI
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cp's OEIS Frontend

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.

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