A265158 a(1) = 1, a(2*n) = 2*a(n), a(2*n+1) = floor(a(n)/2).

1, 2, 0, 4, 1, 0, 0, 8, 2, 2, 0, 0, 0, 0, 0, 16, 4, 4, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 8, 8, 2, 8, 2, 2, 0, 8, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 16, 16, 4, 16, 4, 4, 1, 16, 4, 4, 1, 4, 1, 0, 0, 16, 4, 4, 1, 4, 1, 0

Offset: 1

Author

Reinhard Zumkeller, Dec 04 2015

Keywords

• nonn

Comments

All terms are either zero or a power of 2;

a(2^k) = 2^k; for k > 1: a(2^k+1) = 2^(k-2); a(2^k-1) = 0;

A264784 gives lengths of runs of zeros.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..2047

Crossrefs

Cf. A000051, A000079, A000225, A131577, A264784.

Programs

Haskell

import Data.List (transpose)
a265158 n = a265158_list !! (n-1)
a265158_list = 1 : concat
   (transpose [map (* 2) a265158_list, map (flip div 2) a265158_list])

PARI

a(n) = if (n==1, 1, if (n%2, a(n\2)\2, 2*a(n\2))); \\ Michel Marcus, Jan 22 2022