A375115 Lexicographically earliest sequence of positive integers such that the pairs (a(n) AND a(n+1), a(n+1)) are all distinct (where AND denotes the bitwise AND operator).

0, 0, 1, 1, 2, 2, 3, 3, 4, 3, 5, 3, 6, 4, 5, 5, 6, 6, 7, 7, 8, 5, 7, 9, 6, 9, 7, 10, 7, 11, 7, 12, 7, 13, 8, 7, 14, 9, 9, 10, 10, 11, 11, 12, 11, 13, 11, 14, 12, 13, 13, 14, 14, 15, 15, 16, 10, 13, 15, 17, 11, 15, 18, 11, 19, 12, 15, 20, 11, 20, 13, 18, 13, 19

Offset

0,5

Comments

The value 0 appears twice; for any v > 0, the value v appears A001316(v) times.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, PARI program

Example

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

Prog

(PARI) \\ See Links section.

Crossrefs

See A375110 for similar sequences.

Cf. A001316.

Sequence in context: A309067 A205561 A323636 * A375110 A283367 A322528

Adjacent sequences: A375112 A375113 A375114 * A375116 A375117 A375118

Keyword

nonn,base

Author

Rémy Sigrist, Jul 30 2024

Status

approved