A143115 a(n) = the smallest positive multiple of n that has exactly n 1's in its binary representation.

1, 6, 21, 60, 55, 126, 623, 2040, 1503, 3070, 3839, 16380, 16367, 94206, 96255, 1048560, 483327, 524286, 1040383, 4194300, 5767167, 16515070, 16252927, 134217720, 66584575, 251658238, 402651135, 5234491388, 1073741791

Offset

1,2

Links

Ray Chandler, Table of n, a(n) for n = 1..2024

Formula

a(n) = n*A102032(n). - Vladeta Jovovic, Sep 17 2008

Example

For n = 3, checking: 3*1=3 (11 in binary, two 1's). 3*2=6 (110 in binary, two 1's). 3*3=9 (1001 in binary, two 1's). 3*4=12 (1100 in binary, two 1's). 3*5=15 (1111 in binary, four 1's). 3*6=18 (10010 in binary, two 1's). 3*7=21 (10101 in binary, three 1's). So a(3) = 21.

Maple

a:=proc(n) local k: for k while add(convert(k*n, base, 2)[j], j=1..nops(convert(k*n, base, 2))) <> n do end do: k*n end proc: seq(a(n), n=1..16); # Emeric Deutsch, Aug 16 2008

Mathematica

Fold[Append[#1, SelectFirst[Range[2^#2] #2, Function[k, DigitCount[k, 2, 1] == #2]]] &, {1}, Range[2, 20]] (* Michael De Vlieger, Oct 25 2017 *)

Crossrefs

Cf. A143116.

Sequence in context: A047520 A294836 A341221 * A258142 A321257 A305120

Adjacent sequences: A143112 A143113 A143114 * A143116 A143117 A143118

Keyword

base,nonn

Author

Leroy Quet, Jul 25 2008

Extensions

More terms from Emeric Deutsch, Aug 16 2008

a(17) to a(27) from Owen Whitby, Oct 22 2008. For n=28,29,30 if a(n) exists it is greater than 20000000n.

a(28)-a(29) from Ray Chandler, Nov 11 2008

Status

approved