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

1,1

Links

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

Example

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.

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 *)

Crossrefs

Cf. A143115.

Sequence in context: A275725 A242528 A137933 * A387889 A304856 A115987

Adjacent sequences: A143113 A143114 A143115 * A143117 A143118 A143119

Keyword

base,nonn

Author

Leroy Quet, Jul 25 2008

Extensions

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

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

Status

approved