A335615 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, n AND a(n) is a square (where AND denotes the bitwise AND operator).

0, 1, 4, 5, 2, 3, 8, 9, 6, 7, 16, 13, 17, 11, 20, 25, 10, 12, 21, 24, 14, 18, 32, 33, 19, 15, 36, 29, 34, 27, 37, 41, 22, 23, 28, 64, 26, 30, 44, 52, 65, 31, 68, 69, 38, 54, 53, 73, 66, 49, 72, 57, 39, 46, 45, 76, 67, 51, 80, 77, 70, 75, 81, 89, 35, 40, 48, 56

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..10000

Index entries for sequences that are permutations of the natural numbers

Rémy Sigrist, Scatterplot of (n, a(n)) such that n, a(n) <= 2^18

Rémy Sigrist, PARI program for A335615

Example

The first terms, alongside the corresponding squares, are:
  n   a(n)  n AND a(n)
  --  ----  ----------
   0     0         0^2
   1     1         1^2
   2     4         0^2
   3     5         1^2
   4     2         0^2
   5     3         1^2
   6     8         0^2
   7     9         1^2
   8     6         0^2
   9     7         1^2
  10    16         0^2
  11    13         3^2
  12    17         0^2

Prog

(PARI) See Links section.

Crossrefs

Cf. A338498, A338499 (fixed points), A338500.

Sequence in context: A213171 A261098 A216252 * A328622 A338248 A328623

Adjacent sequences: A335612 A335613 A335614 * A335616 A335617 A335618

Keyword

nonn,base

Author

Rémy Sigrist, Oct 30 2020

Status

approved