A095377 Values of k such that the total number of 1's in the binary expansions of the first k primes is a multiple of k.

1, 4, 14, 43, 46, 141, 4900, 10264541, 10281244, 10281247, 10281248, 10281249, 10281266, 10281271, 10368575, 531439030, 1997778943, 412276655628

Offset

1,2

Comments

Integer solutions to {A095375(x)/x is an integer}.

a(18) > pi(10^12). - Donovan Johnson, May 03 2010

a(20) > 6.2*10^11. The first 19 ratios between the total number of 1's and k are 1, 2, 3, 4, 4, 5, 8, 14, 14, 14, 14, 14, 14, 14, 14, 17, 18, 22. - Giovanni Resta, May 08 2017

Links

Table of n, a(n) for n=1..18.

Formula

Integer solutions to {A095375(x)/x is an integer}.

Example

n=14: the relevant list = {2,3,5...,41,43} = {10,11,101,...,11001,11011} contains 42 digits "1", and 42/14 = 3, so 14 is in the sequence.

Mathematica

s=0; Reap[Do[s += DigitCount[Prime@n, 2][[1]]; If[Mod[s, n] == 0, Sow@ n], {n, 10^4}]][[2, 1]] (* Giovanni Resta, May 08 2017 *)

Crossrefs

Cf. A000120, A000788, A014499, A095375.

Sequence in context: A189426 A007076 A135483 * A296253 A247470 A049539

Adjacent sequences: A095374 A095375 A095376 * A095378 A095379 A095380

Keyword

nonn,base,more,changed

Author

Labos Elemer, Jun 07 2004

Extensions

a(16)-a(17) from Donovan Johnson, May 03 2010

a(18) from Giovanni Resta, May 08 2017

Status

approved