A371974 For any positive integer n with binary expansion (b_1, ..., b_w) (where b_1 = 1), the binary expansion of a(n) is (c_1, ..., c_w) with c_k = (Sum_{i = 1 mod (w+1-k)} b_i) mod 2 for k = 1..w; a(0) = 0.

0, 1, 3, 2, 7, 4, 6, 5, 15, 10, 12, 9, 14, 11, 13, 8, 31, 20, 26, 17, 28, 23, 25, 18, 30, 21, 27, 16, 29, 22, 24, 19, 63, 46, 52, 37, 58, 43, 49, 32, 60, 45, 55, 38, 57, 40, 50, 35, 62, 47, 53, 36, 59, 42, 48, 33, 61, 44, 54, 39, 56, 41, 51, 34, 127, 88, 110

Offset

0,3

Comments

This sequence is a permutation of the nonnegative integers with inverse A371975.

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

A070939(a(n)) = A070939(n).

a(n) mod 2 = A010060(n).

Example

For n = 42: the binary expansion of 42 is "101010":
          b_1 b_2 b_3 b_4 b_5 b_6
           1   0   1   0   1   0
     c_1 = 1                      = 1 mod 2
     c_2 = 1                 + 0  = 1 mod 2
     c_3 = 1             + 1      = 0 mod 2
     c_4 = 1         + 0          = 1 mod 2
     c_5 = 1     + 1     + 1      = 1 mod 2
     c_6 = 1 + 0 + 1 + 0 + 1 + 0  = 1 mod 2
- so the binary expansion of a(42) is "110111", and a(42) = 55.

Prog

(PARI) a(n) = { my (b = binary(n), c = vector(#b)); for (k = 1, #c, forstep (i = 1, #b, #b+1-k, c[k] += b[i]; ); ); fromdigits(c % 2, 2); }

Crossrefs

See A341335 and A371976 for similar sequences.

Cf. A010060, A070939, A371975 (inverse).

Sequence in context: A341911 A341916 A360960 * A344878 A344875 A178910

Adjacent sequences: A371971 A371972 A371973 * A371975 A371976 A371977

Keyword

nonn,base

Author

Rémy Sigrist, Apr 14 2024

Status

approved