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

0,3

Comments

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

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

Formula

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

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

Example

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}

Prog

(PARI) See Links section.

Crossrefs

See A342115, A342116 and A342117 for similar sequences.

Cf. A000120, A080791, A331274, A337242.

Sequence in context: A056539 A105726 A336962 * A284460 A336963 A175949

Adjacent sequences: A342099 A342100 A342101 * A342103 A342104 A342105

Keyword

nonn,base

Author

Rémy Sigrist, Feb 28 2021

Status

approved