A371976 For any nonnegative integer n with binary expansion Sum_{i >= 0} b_i * 2^i, the binary expansion of a(n) is Sum_{i >= 0} c_i * 2^i with c_i = (Sum_{k > 0} b_{k*(i+1)-1}) mod 2 for any i >= 0.

0, 1, 3, 2, 5, 4, 6, 7, 11, 10, 8, 9, 14, 15, 13, 12, 17, 16, 18, 19, 20, 21, 23, 22, 26, 27, 25, 24, 31, 30, 28, 29, 39, 38, 36, 37, 34, 35, 33, 32, 44, 45, 47, 46, 41, 40, 42, 43, 54, 55, 53, 52, 51, 50, 48, 49, 61, 60, 62, 63, 56, 57, 59, 58, 65, 64, 66, 67

Offset

0,3

Comments

This sequence is a permutation of the nonnegative integers with inverse A371977.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Rémy Sigrist, Scatterplot of (n, a(n)-n) for n < 2^20

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_5 b_4 b_3 b_2 b_1 b_0
           1   0   1   0   1   0
     c_5 = 1                     = 1 mod 2
     c_4 =     0                 = 0 mod 2
     c_3 =         1             = 1 mod 2
     c_2 = 1         + 0         = 1 mod 2
     c_1 = 1     + 1     + 1     = 1 mod 2
     c_0 = 1 + 0 + 1 + 0 + 1 + 0 = 1 mod 2
- so the binary expansion of a(42) is "101111", and a(42) = 47.

Prog

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

Crossrefs

See A371974 for a similar sequence.

Cf. A010060, A070939, A371977 (inverse).

Sequence in context: A266154 A266089 A371977 * A340478 A340402 A379472

Adjacent sequences: A371973 A371974 A371975 * A371977 A371978 A371979

Keyword

nonn

Author

Rémy Sigrist, Apr 14 2024

Status

approved