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

Author

Leroy Quet, Jul 25 2008

Keywords

• base
• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A143116.

Programs

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 *)

Formula

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