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

1,2

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

Prog

(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

Crossrefs

Cf. A000120, A036563, A263017.

Sequence in context: A073281 A130922 A353170 * A215622 A195820 A006921

Adjacent sequences: A263015 A263016 A263017 * A263019 A263020 A263021

Keyword

nonn,base

Author

Paul Tek, Oct 07 2015

Status

approved