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

0,3

Comments

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

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

Formula

a(n) >= A370427(n).

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A006995, A370427.

Sequence in context: A004442 A065190 A152208 * A282650 A270671 A282664

Adjacent sequences: A370426 A370427 A370428 * A370430 A370431 A370432

Keyword

nonn,base

Author

Rémy Sigrist, Feb 18 2024

Status

approved