A352726 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of n and a(n) have no common runs of consecutive 1's.

0, 2, 1, 4, 3, 6, 5, 8, 7, 12, 13, 14, 9, 10, 11, 16, 15, 24, 25, 26, 27, 28, 29, 30, 17, 18, 19, 20, 21, 22, 23, 32, 31, 48, 49, 50, 51, 54, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 33, 34, 35, 36, 38, 39, 37, 40, 41, 42, 43, 44, 45, 46, 47, 64, 63, 96, 97, 98

Offset: 0

Author

Rémy Sigrist, Mar 30 2022

Keywords

• nonn
• base

Comments

This sequence is a self-inverse permutation of the nonnegative integers.

This sequence has similarities with A238757; here we consider runs of consecutive 1's, there individual 1's in binary expansions.

The binary expansion of n and a(n) 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 n  runs in a(n)
  --  ----  ---------  ------------
   0     0  []         []
   1     2  [1]        [2]
   2     1  [2]        [1]
   3     4  [3]        [4]
   4     3  [4]        [3]
   5     6  [1, 4]     [6]
   6     5  [6]        [1, 4]
   7     8  [7]        [8]
   8     7  [8]        [7]
   9    12  [1, 8]     [12]
  10    13  [2, 8]     [1, 12]
  11    14  [3, 8]     [14]
  12     9  [12]       [1, 8]
  13    10  [1, 12]    [2, 8]
  14    11  [14]       [3, 8]
  15    16  [15]       [16]
  16    15  [16]       [15]
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Rémy Sigrist, Scatterplot of the first 32769 terms
• Rémy Sigrist, Scatterplot of (x, y) such that x, y < 2^10 and the binary expansions of x and y have no common runs of consecutive 1's
• Rémy Sigrist, PARI program
• Index entries for sequences related to binary expansion of n
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A238757, A332022, A352724.

Programs

PARI

See Links section.