A375183 In the binary expansion of n, complement bits at even positions and to the right of a 1 (the most significant bit corresponding to position 1).

0, 1, 3, 2, 6, 7, 4, 5, 12, 13, 15, 14, 8, 9, 11, 10, 24, 25, 26, 27, 30, 31, 28, 29, 16, 17, 18, 19, 22, 23, 20, 21, 48, 49, 51, 50, 52, 53, 55, 54, 60, 61, 63, 62, 56, 57, 59, 58, 32, 33, 35, 34, 36, 37, 39, 38, 44, 45, 47, 46, 40, 41, 43, 42, 96, 97, 98, 99

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

Index entries for sequences related to binary expansion of n

Index entries for sequences that are permutations of the natural numbers

Formula

a(floor(n/2)) = floor(a(n)/2).

Example

For n = 9: the binary expansion of 9 is "1001": the bit at position 2 (0) sits to the right of a 1 so we complement it, the bit at position 4 (1) sits to the right of a 0 so we keep it; the binary expansion of a(9) is "1101" and a(9) = 13.

Prog

(PARI) a(n) = { my (b = binary(n)); forstep (k = 2, #b, 2, if (b[k-1], b[k] = 1-b[k]; ); ); fromdigits(b, 2); }

Crossrefs

Cf. A063946, A165199, A375184.

Sequence in context: A154441 A154446 A154442 * A371961 A354225 A154445

Adjacent sequences: A375179 A375180 A375182 * A375184 A375185 A375186

Keyword

nonn,base

Author

Rémy Sigrist, Aug 03 2024

Status

approved