A342102 Lexicographically latest sequence of distinct nonnegative integers such that for any n >= 0, {A000120(n), A080791(n)} = {A000120(a(n)), A080791(a(n))}.

0, 1, 2, 3, 6, 5, 4, 7, 14, 12, 10, 13, 9, 11, 8, 15, 30, 28, 26, 25, 24, 22, 21, 29, 20, 19, 18, 27, 17, 23, 16, 31, 62, 60, 58, 56, 57, 52, 50, 54, 53, 49, 44, 51, 42, 48, 46, 61, 45, 41, 38, 43, 37, 40, 39, 59, 35, 36, 34, 55, 33, 47, 32, 63, 126, 124, 122

Offset: 0

Author

Rémy Sigrist, Feb 28 2021

Keywords

• nonn
• base

Comments

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

Examples

			The first terms, in decimal and in binary, alongside {A000120(n), A080791(n)}, are:
  n   a(n)  bin(n)  bin(a(n))  {A000120(n), A080791(n)}
  --  ----  ------  ---------  ------------------------
   0     0       0          0  {0}
   1     1       1          1  {0, 1}
   2     2      10         10  {1}
   3     3      11         11  {0, 2}
   4     6     100        110  {1, 2}
   5     5     101        101  {1, 2}
   6     4     110        100  {1, 2}
   7     7     111        111  {0, 3}
   8    14    1000       1110  {1, 3}
   9    12    1001       1100  {2}
  10    10    1010       1010  {2}
  11    13    1011       1101  {1, 3}
  12     9    1100       1001  {2}
  13    11    1101       1011  {1, 3}
  14     8    1110       1000  {1, 3}
  15    15    1111       1111  {0, 4}
		

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 min(A000120(n), A080791(n)))
• Rémy Sigrist, PARI program for A342102
• Index entries for sequences related to binary expansion of n
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A342115, A342116 and A342117 for similar sequences.

Cf. A000120, A080791, A331274, A337242.

Programs

PARI

\\ See Links section.

Formula

a(2^k-1) = 2^k-1 for any k >= 0.

a(n) < 2^k for any n < 2^k.