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

Author

Rémy Sigrist, Jul 30 2024

Keywords

• nonn
• base

Comments

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

Examples

			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)
		

Links

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

Crossrefs

See A375110 for similar sequences.

Cf. A001316.

Programs

PARI

\\ See Links section.