A180059 Smallest k such that binary weight of k*n is less than binary weight of k, or zero if no such k exists (for n = powers of 2).

0, 0, 11, 0, 13, 11, 23, 0, 29, 13, 47, 11, 79, 23, 47, 0, 61, 29, 27, 13, 55, 47, 23, 11, 41, 79, 19, 23, 53, 47, 95, 0, 125, 61, 59, 29, 111, 27, 55, 13, 25, 55, 143, 47, 47, 23, 47, 11, 209, 41, 91, 79, 29, 19, 149, 23, 575, 53, 139, 47, 277, 95, 191, 0, 253, 125, 107, 61

Offset: 1

Author

Zak Seidov, Aug 08 2010

Keywords

• base
• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A180054, A180055.

Programs

Mathematica

s={};Do[Do[If[Count[IntegerDigits[k x,2],1]Zak Seidov, Oct 24 2013 *)

PARI

a(n)=if((n<=1)||((n>>valuation(n, 2))==1), 0, my(k=3); while(hammingweight(k*n)>=hammingweight(k), k+=2); k ) \\ Charles R Greathouse IV, Oct 19 2013

Formula

A000120(n) > A000120(k*n).