A352725 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of a(n) and a(n+1) have no common runs of consecutive 1's.

0, 1, 2, 3, 4, 6, 5, 7, 8, 12, 9, 14, 10, 13, 11, 15, 16, 24, 17, 26, 19, 25, 18, 27, 20, 28, 21, 30, 22, 29, 23, 31, 32, 48, 33, 50, 35, 49, 34, 51, 36, 54, 37, 55, 38, 52, 39, 53, 40, 56, 41, 58, 43, 57, 42, 59, 44, 60, 45, 62, 46, 61, 47, 63, 64, 96, 65, 98

Offset: 0

Author

Rémy Sigrist, Mar 30 2022

Keywords

• nonn
• base

Comments

This sequence is a variant of A109812; here we consider runs of consecutive 1's, there individual 1's in binary expansions.

The binary expansions of two consecutive terms may share some 1's, but cannot have a common run of consecutive 1's (as given by A352724).

Examples

			The first terms, alongside the corresponding partitions into runs of 1's, are:
  n   a(n)  runs in a(n)
  --  ----  ------------
   0     0  []
   1     1  [1]
   2     2  [2]
   3     3  [3]
   4     4  [4]
   5     6  [6]
   6     5  [1, 4]
   7     7  [7]
   8     8  [8]
   9    12  [12]
  10     9  [1, 8]
  11    14  [14]
  12    10  [2, 8]
  13    13  [1, 12]
  14    11  [3, 8]
  15    15  [15]
  16    16  [16]
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Rémy Sigrist, Scatterplot of the first 32769 terms
• Rémy Sigrist, PARI program

Crossrefs

Cf. A109812, A332565, A352724.

Programs

PARI

See Links section.