A306869 Lexicographically earliest sequence of distinct positive terms such that the binary representation of the bitwise-OR of two consecutive terms has exactly one run of consecutive ones.

1, 2, 3, 4, 6, 5, 7, 8, 12, 10, 13, 11, 14, 9, 15, 16, 24, 20, 26, 21, 27, 22, 25, 23, 28, 18, 29, 19, 30, 17, 31, 32, 48, 40, 52, 42, 53, 43, 54, 41, 55, 44, 50, 45, 51, 46, 49, 47, 56, 36, 58, 37, 59, 38, 57, 39, 60, 34, 61, 35, 62, 33, 63, 64, 96, 80, 104

Offset: 1

Author

Rémy Sigrist, Mar 14 2019

Keywords

• nonn
• base

Comments

This sequence has similarities with A175343; in both sequences, the binary representation of the bitwise OR of two consecutive terms has exactly one run of consecutive ones.

Examples

			The first terms, alongside the binary representation of a(n) OR a(n+1), are:
  a   a(n)  bin(a(n) OR a(n+1))
  --  ----  -------------------
   1     1                 11
   2     2                 11
   3     3                111
   4     4                110
   5     6                111
   6     5                111
   7     7               1111
   8     8               1100
   9    12               1110
  10    10               1111
  11    13               1111
  12    11               1111
  13    14               1111
  14     9               1111
  15    15              11111
  16    16              11000
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8192
• Rémy Sigrist, PARI program for A306869

Crossrefs

Cf. A069010, A175343.

Programs

PARI

See Links section.

Formula

A069010(a(n) OR a(n+1)) = 1.