A096199 Numbers such that in binary representation the length is a multiple of the number of ones.

1, 2, 3, 4, 7, 8, 9, 10, 12, 15, 16, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 44, 48, 49, 50, 52, 56, 63, 64, 127, 128, 129, 130, 132, 135, 136, 139, 141, 142, 144, 147, 149, 150, 153, 154, 156, 160, 163, 165, 166, 169, 170, 172, 177, 178, 180, 184, 192, 195, 197

Offset

1,2

Comments

A070939(a(n)) mod A000120(a(n)) = 0;

A000079 and A000225 (> 0) are subsequences.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10674 (all terms up to 2^16)

Index entries for sequences related to binary expansion of n

Example

400 -> '110010000' with 3 binary ones and length = 9 = 3*3, therefore 400 is a term.

Maple

q:= n-> (l-> irem(nops(l), add(i, i=l))=0)(Bits[Split](n)):
select(q, [$1..200])[];  # Alois P. Heinz, Feb 04 2022

Mathematica

lmnQ[n_]:=Module[{idn2=IntegerDigits[n, 2]}, Divisible[Length[idn2], Count[ idn2, 1]]]; Select[Range[200], lmnQ] (* Harvey P. Dale, Jul 27 2019 *)

Prog

(Perl)
$cnt=1; foreach $n(1..100_000){$_=sprintf ("%b", $n); print $cnt++, " $n\n" unless (length)%s/1//g; }

Crossrefs

Cf. A007088, A049445.

Sequence in context: A330217 A231003 A171551 * A104576 A332485 A031477

Adjacent sequences: A096196 A096197 A096198 * A096200 A096201 A096202

Keyword

nonn,base

Author

Reinhard Zumkeller, Jul 26 2004

Status

approved