A371343 Lexicographically latest sequence of distinct nonnegative integers such that for any n >= 0, the binary expansions of n and of a(n) have the same length (A070939) and the same number of runs of consecutive equals digits (A005811).

0, 1, 2, 3, 6, 5, 4, 7, 14, 13, 10, 11, 12, 9, 8, 15, 30, 29, 26, 27, 22, 21, 20, 25, 28, 23, 18, 19, 24, 17, 16, 31, 62, 61, 58, 59, 54, 53, 52, 57, 50, 45, 42, 43, 46, 41, 44, 55, 60, 51, 40, 49, 38, 37, 36, 47, 56, 39, 34, 35, 48, 33, 32, 63, 126, 125, 122

Offset: 0

Author

Rémy Sigrist, Mar 24 2024

Keywords

• nonn
• base

Comments

This sequence is a self-inverse permutation of the nonnegative integers with infinitely many fixed points (for example, all terms of A000225 are fixed points).

Examples

			The first terms, in decimal and in binary, are:
  n   a(n)  bin(n)  bin(a(n))
  --  ----  ------  ---------
   0     0
   1     1       1          1
   2     2      10         10
   3     3      11         11
   4     6     100        110
   5     5     101        101
   6     4     110        100
   7     7     111        111
   8    14    1000       1110
   9    13    1001       1101
  10    10    1010       1010
  11    11    1011       1011
  12    12    1100       1100
  13     9    1101       1001
  14     8    1110       1000
  15    15    1111       1111
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8191
• Rémy Sigrist, Colored scatterplot of the first 2^20 terms (where the color is function of A005811(n))
• 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

See A331274 and A337242 for similar sequences.

Cf. A000225, A005811, A070939.

Programs

PARI

\\ See Links section.