A340401 For any number n >= 0 with binary expansion Sum_{k = 0..w} b(k)*2^k, a(n) = (b(0)*A340399(0)) XOR ... XOR (b(w)*A340399(w)) (where XOR denotes the bitwise XOR operator).

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

Offset

0,3

Comments

This sequence is a permutation of the nonnegative integers (with inverse A340477) 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 A340401

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) = A340399(5) XOR A340399(3) XOR A340399(0) = 34 XOR 8 XOR 1 = 43.

Prog

(PARI) See Links section.

Crossrefs

Cf. A340399, A340402, A340477 (inverse).

Sequence in context: A057756 A378785 A340477 * A160051 A351298 A082746

Adjacent sequences: A340398 A340399 A340400 * A340402 A340403 A340404

Keyword

nonn,base

Author

Rémy Sigrist, Jan 06 2021

Status

approved