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

1,3

Comments

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

This sequence shares graphical features with A335943.

Links

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

Rémy Sigrist, PARI program

Example

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)

Prog

(PARI) \\ See Links section.

Crossrefs

See A375114 and A375115 for similar sequences.

Cf. A335943, A375111, A375112.

Sequence in context: A205561 A323636 A375115 * A283367 A322528 A258756

Adjacent sequences: A375107 A375108 A375109 * A375111 A375112 A375113

Keyword

nonn

Author

Rémy Sigrist, Jul 30 2024

Status

approved