A107326 Numbers of the form (2^i)*(13^j).

1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 169, 208, 256, 338, 416, 512, 676, 832, 1024, 1352, 1664, 2048, 2197, 2704, 3328, 4096, 4394, 5408, 6656, 8192, 8788, 10816, 13312, 16384, 17576, 21632, 26624, 28561, 32768, 35152, 43264, 53248, 57122

Offset: 1

Author

Douglas Winston (douglas.winston(AT)srupc.com), May 21 2005

Keywords

• nonn
• easy

Comments

A204455(13*a(n)) = 13, and only for these numbers. - Wolfdieter Lang, Feb 04 2012

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..100 from Vincenzo Librandi)

Crossrefs

Cf. A003586, A003592, A003593, A003591, A003594, A003595, A003596, A003597, A003598, A003599.

Programs

Mathematica

fQ[n_] := PowerMod[26,n,n]==0; Select[Range[60000],fQ] (* Vincenzo Librandi, Feb 04 2012 *)
mx = 60000; Sort@ Flatten@ Table[2^i*13^j, {i, 0, Log[2, mx]}, {j, 0, Log[13, mx/2^i]}] (* Robert G. Wilson v, Aug 17 2012 *)

PARI

list(lim)=my(v=List(),N); for(n=0,log(lim)\log(13),N=13^n; while(N<=lim,listput(v,N);N<<=1)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jun 28 2011

Formula

Sum_{n>=1} 1/a(n) = (2*13)/((2-1)*(13-1)) = 13/6. - Amiram Eldar, Sep 23 2020

a(n) ~ exp(sqrt(2*log(2)*log(13)*n)) / sqrt(26). - Vaclav Kotesovec, Sep 23 2020