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A096199 Numbers such that in binary representation the length is a multiple of the number of ones. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 28 07:30 EDT 2022. Contains 354112 sequences. (Running on oeis4.)