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

Author

Rémy Sigrist, Mar 23 2025

Keywords

• nonn

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

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

Crossrefs

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

Programs

PARI

\\ See Links section.