A095376 Values of k such that the total number of 1's in the binary expansions of the first k integers is a multiple of k.

1, 2, 14, 62, 65, 77, 254, 322, 323, 327, 331, 332, 1022, 1281, 1341, 1348, 1349, 1350, 1352, 1353, 1354, 4094, 16382, 21505, 21757, 21762, 21820, 65534, 87299, 87355, 262142, 348161, 349181, 1048574, 1397762, 1398012, 1398020, 1398074, 4194302

Offset

1,2

Comments

All numbers of the form 4^k-2, with k>0, appear in this sequence. - Paul Tek, Sep 24 2013

Links

Donovan Johnson, Table of n, a(n) for n = 1..100

Formula

Integer solutions to {A000788(x)/x is an integer}.

Example

k=14: {1, 10, 11, 10, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110} includes 28 1's so A000788(14)/14 = 2 is an integer, thus 14 is here.

Mathematica

lib[x_] := Count[IntegerDigits[x, 2], 1]; {s=0, ta=Table[0, {100}], tb=Table[0, {100}], u=1}; Do[s=s+lib[n]; w=n; If[IntegerQ[s/n], Print[{n, s/n}]; ta[[u]]=n; tb[[u]]=s/n; u=u+1], {n, 100000}]

Crossrefs

Cf. A000120, A000788, A014499, A095375.

Sequence in context: A232370 A174704 A058738 * A153332 A331822 A217154

Adjacent sequences: A095373 A095374 A095375 * A095377 A095378 A095379

Keyword

nonn,base

Author

Labos Elemer, Jun 07 2004

Status

approved