A340402 For any number n >= 0 with binary expansion Sum_{k = 0..w} b(k)*2^k, a(n) = (b(0)*A340400(0)) XOR ... XOR (b(w)*A340400(w)) (where XOR denotes the bitwise XOR operator).

0, 1, 3, 2, 5, 4, 6, 7, 13, 12, 14, 15, 8, 9, 11, 10, 21, 20, 22, 23, 16, 17, 19, 18, 24, 25, 27, 26, 29, 28, 30, 31, 55, 54, 52, 53, 50, 51, 49, 48, 58, 59, 57, 56, 63, 62, 60, 61, 34, 35, 33, 32, 39, 38, 36, 37, 47, 46, 44, 45, 42, 43, 41, 40, 89, 88, 90, 91

Offset

0,3

Comments

This sequence is a permutation of the nonnegative integers (with inverse A340478) that preserves the number of binary digits.

Links

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

Rémy Sigrist, Scatterplot of the first 2^16 terms

Rémy Sigrist, PARI program for A340402

Index entries for sequences that are permutations of the natural numbers

Example

For n = 41:
- 41 = 2^5 + 2^3 + 2^0,
- so a(41) = A340400(5) XOR A340400(3) XOR A340400(0) = 55 XOR 13 XOR 1 = 59.

Prog

(PARI) See Links section.

Crossrefs

Cf. A340400, A340401, A340478 (inverse).

Sequence in context: A371977 A371976 A340478 * A193231 A191672 A273876

Adjacent sequences: A340399 A340400 A340401 * A340403 A340404 A340405

Keyword

nonn,base

Author

Rémy Sigrist, Jan 06 2021

Status

approved