A375110 Lexicographically earliest sequence of positive integers such that the pairs (a(n) mod a(n+1), a(n+1)) are all distinct.

1, 1, 2, 2, 3, 3, 4, 3, 5, 4, 4, 5, 5, 6, 4, 6, 5, 7, 5, 8, 6, 6, 7, 6, 8, 7, 7, 8, 8, 9, 6, 9, 7, 9, 8, 10, 7, 10, 8, 11, 7, 11, 8, 12, 8, 13, 9, 9, 10, 9, 11, 9, 12, 9, 13, 10, 10, 11, 10, 12, 10, 13, 11, 11, 12, 11, 13, 12, 12, 13, 13, 14, 9, 14, 10, 14, 11

Offset: 1

Author

Rémy Sigrist, Jul 30 2024

Keywords

• nonn

Comments

The value 1 appears twice; for any v > 1, v appears v times.

This sequence shares graphical features with A335943.

Examples

			The first terms, alongside the corresponding pairs, are:
  n   a(n)  (a(n) mod a(n+1), a(n+1))
  --  ----  -------------------------
   1     1  (0, 1)
   2     1  (1, 2)
   3     2  (0, 2)
   4     2  (2, 3)
   5     3  (0, 3)
   6     3  (3, 4)
   7     4  (1, 3)
   8     3  (3, 5)
   9     5  (1, 4)
  10     4  (0, 4)
  11     4  (4, 5)
  12     5  (0, 5)
  13     5  (5, 6)
  14     6  (2, 4)
  15     4  (4, 6)
		

Links

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

Crossrefs

See A375114 and A375115 for similar sequences.

Cf. A335943, A375111, A375112.

Programs

PARI

\\ See Links section.