A263018 If n is the i-th positive integer with binary weight j, then a(n) is the j-th positive integer with binary weight i.

1, 3, 2, 7, 5, 11, 4, 15, 23, 47, 6, 95, 13, 27, 8, 31, 191, 383, 55, 767, 111, 223, 9, 1535, 447, 895, 14, 1791, 29, 59, 16, 63, 3071, 6143, 3583, 12287, 7167, 14335, 119, 24575, 28671, 57343, 239, 114687, 479, 959, 10, 49151, 229375, 458751, 1919, 917503

Offset: 1

Author

Paul Tek, Oct 07 2015

Keywords

• nonn
• base

Comments

Binary weight is given by A000120.

This is a self-inverse permutation of the natural numbers.

The positive terms in the sequence A036563 give the fixed points.

A000120(n) = A263017(a(n)) for any n>0.

A263017(n) = A000120(a(n)) for any n>0.

a(2^(n+1)-1) = 2^n for any n>0.

a(2^n) = 2^(n+1)-1 for any n>0.

Links

• Paul Tek, Table of n, a(n) for n = 1..10000
• Paul Tek, PERL program for this sequence

Crossrefs

Cf. A000120, A036563, A263017.

Programs

PARI

a(n) = {j = hammingweight(n); v = vector(n, k, hammingweight(k)); i = #select(x->x==j, v); nb = 0; k = 0; while(nb != j, k++; if (hammingweight(k) == i, nb++)); k;} \\ Michel Marcus, Oct 16 2015