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

1,2

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.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..8192

Rémy Sigrist, PARI program for A306869

Formula

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A069010, A175343.

Sequence in context: A367307 A139706 A333777 * A139708 A333776 A305410

Adjacent sequences: A306866 A306867 A306868 * A306870 A306871 A306872

Keyword

nonn,base

Author

Rémy Sigrist, Mar 14 2019

Status

approved