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

Author

Labos Elemer, Jun 07 2004

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000120, A000788, A014499, A095375.

Programs

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}]

Formula

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