A370429 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, n OR a(n) is a binary palindrome (where OR denotes the bitwise OR operator).

0, 1, 3, 2, 5, 4, 7, 6, 9, 8, 13, 12, 11, 10, 15, 14, 17, 16, 25, 24, 21, 20, 27, 26, 19, 18, 23, 22, 31, 30, 29, 28, 33, 32, 49, 48, 41, 40, 57, 56, 37, 36, 53, 52, 45, 44, 51, 50, 35, 34, 47, 46, 43, 42, 59, 58, 39, 38, 55, 54, 63, 62, 61, 60, 65, 64, 97, 96

Offset: 0

Author

Rémy Sigrist, Feb 18 2024

Keywords

• nonn
• base

Comments

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

Examples

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

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Rémy Sigrist, Scatterplot of the first 2^18 terms
• Rémy Sigrist, PARI program
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A006995, A370427.

Programs

PARI

See Links section.

Formula

a(n) >= A370427(n).