cp's OEIS Frontend

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

%I A096199 #17 Feb 04 2022 09:39:48
%S A096199 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,
%T A096199 50,52,56,63,64,127,128,129,130,132,135,136,139,141,142,144,147,149,
%U A096199 150,153,154,156,160,163,165,166,169,170,172,177,178,180,184,192,195,197
%N A096199 Numbers such that in binary representation the length is a multiple of the number of ones.
%C A096199 A070939(a(n)) mod A000120(a(n)) = 0;
%C A096199 A000079 and A000225 (> 0) are subsequences.
%H A096199 Ivan Neretin, <a href="/A096199/b096199.txt">Table of n, a(n) for n = 1..10674 (all terms up to 2^16)</a>
%H A096199 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%e A096199 400 -> '110010000' with 3 binary ones and length = 9 = 3*3, therefore 400 is a term.
%p A096199 q:= n-> (l-> irem(nops(l), add(i, i=l))=0)(Bits[Split](n)):
%p A096199 select(q, [$1..200])[];  # _Alois P. Heinz_, Feb 04 2022
%t A096199 lmnQ[n_]:=Module[{idn2=IntegerDigits[n,2]},Divisible[Length[idn2],Count[ idn2,1]]]; Select[Range[200],lmnQ] (* _Harvey P. Dale_, Jul 27 2019 *)
%o A096199 (Perl)
%o A096199 $cnt=1;foreach $n(1..100_000){$_=sprintf ("%b",$n); print $cnt++," $n\n" unless (length)%s/1//g;}
%Y A096199 Cf. A007088, A049445.
%K A096199 nonn,base
%O A096199 1,2
%A A096199 _Reinhard Zumkeller_, Jul 26 2004