A143116 a(n) = the smallest positive multiple of n that has exactly n (nonleading) 0's in its binary representation.

2, 4, 18, 16, 65, 132, 518, 256, 1026, 2050, 4224, 8196, 16640, 65548, 262155, 65536, 262208, 524304, 1050624, 2097160, 8388618, 8388864, 33554562, 33554448, 67174400, 134218240, 268435458, 1073741844, 1073807360, 8589934620

Offset: 1

Author

Leroy Quet, Jul 25 2008

Keywords

• base
• nonn

Examples

			For n = 3, checking: 3*1=3 (11 in binary, zero 0's). 3*2=6 (110 in binary, one 0). 3*3=9 (1001 in binary, two 0's). 3*4=12 (1100 in binary, two 0's). 3*5=15 (1111 in binary, zero 0's). 3*6=18 (10010 in binary, three 0's). So a(3) = 18.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..2046

Crossrefs

Cf. A143115.

Programs

Mathematica

a[n_]:=Module[{m=1},Until[DigitCount[n*m,2][[2]]==n,m++];n*m];Array[a,20] (* James C. McMahon, Aug 16 2025 *)

Extensions

a(6)-a(27) from Owen Whitby, Oct 22 2008

a(28)-a(30) from Ray Chandler, Nov 11 2008