A348485 Lexicographically earliest sequence of positive integers in which, for all positive k, there are exactly k contiguous pairs whose product is k, and a(k) * a(k+1) <> a(k+1) * a(k+2).

1, 1, 2, 2, 1, 3, 2, 2, 3, 1, 4, 2, 2, 3, 1, 5, 2, 3, 3, 2, 4, 3, 2, 4, 3, 3, 4, 2, 5, 1, 7, 2, 4, 3, 3, 4, 2, 5, 1, 7, 2, 4, 3, 3, 4, 2, 5, 1, 7, 2, 5, 1, 7, 2, 5, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 4, 4, 5, 2, 7, 1, 9, 2, 5, 3, 3, 5, 2, 7, 1, 10, 2, 7, 1, 11, 2

Offset: 1

Author

Rémy Sigrist, Oct 21 2021

Keywords

• nonn

Comments

This sequence is a variant of A307720 where we don't allow consecutive equal products of contiguous pairs.

Examples

			The first terms, alongside a(n)*a(n+1), are:
  n   a(n)  a(n)*a(n+1)
  --  ----  -----------
   1     1            1
   2     1            2
   3     2            4
   4     2            2
   5     1            3
   6     3            6
   7     2            4
   8     2            6
   9     3            3
  10     1            4
  11     4            8
  12     2            4
  13     2            6
  14     3            3
  15     1            5
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A348485

Crossrefs

Cf. A307720, A348486 (the products).

Programs

PARI

See Links section.