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

1,3

Links

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

Formula

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

Mathematica

s={}; Do[Do[If[Count[IntegerDigits[k x, 2], 1]<Count[IntegerDigits[x, 2], 1],
AppendTo[s, {k, x}]; Break[]], {x, 10000}], {k, 2, 200}]; s (* Zak Seidov, Oct 24 2013 *)

Prog

(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

Crossrefs

Cf. A000120, A180054, A180055.

Sequence in context: A088623 A167166 A271572 * A147765 A087556 A082268

Adjacent sequences: A180056 A180057 A180058 * A180060 A180061 A180062

Keyword

base,nonn

Author

Zak Seidov, Aug 08 2010

Status

approved