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

%I #30 Sep 23 2020 03:34:10

%S 1,2,4,8,13,16,26,32,52,64,104,128,169,208,256,338,416,512,676,832,

%T 1024,1352,1664,2048,2197,2704,3328,4096,4394,5408,6656,8192,8788,

%U 10816,13312,16384,17576,21632,26624,28561,32768,35152,43264,53248,57122

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

%C A204455(13*a(n)) = 13, and only for these numbers. - _Wolfdieter Lang_, Feb 04 2012

%H Amiram Eldar, <a href="/A107326/b107326.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..100 from Vincenzo Librandi)

%F Sum_{n>=1} 1/a(n) = (2*13)/((2-1)*(13-1)) = 13/6. - _Amiram Eldar_, Sep 23 2020

%F a(n) ~ exp(sqrt(2*log(2)*log(13)*n)) / sqrt(26). - _Vaclav Kotesovec_, Sep 23 2020

%t fQ[n_] := PowerMod[26,n,n]==0; Select[Range[60000],fQ] (* _Vincenzo Librandi_, Feb 04 2012 *)

%t 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 *)

%o (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

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

%K nonn,easy

%O 1,2

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

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Last modified April 19 16:21 EDT 2024. Contains 371794 sequences. (Running on oeis4.)