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Numbers of the form (11^i)*(13^j).
20

%I #20 Sep 08 2022 08:45:19

%S 1,11,13,121,143,169,1331,1573,1859,2197,14641,17303,20449,24167,

%T 28561,161051,190333,224939,265837,314171,371293,1771561,2093663,

%U 2474329,2924207,3455881,4084223,4826809,19487171,23030293,27217619

%N Numbers of the form (11^i)*(13^j).

%H Reinhard Zumkeller, <a href="/A108090/b108090.txt">Table of n, a(n) for n = 1..10000</a>

%F Sum_{n>=1} 1/a(n) = (11*13)/((11-1)*(13-1)) = 143/120. - _Amiram Eldar_, Sep 23 2020

%F a(n) ~ exp(sqrt(2*log(11)*log(13)*n)) / sqrt(143). - _Vaclav Kotesovec_, Sep 23 2020

%t mx = 3*10^7; Sort@ Flatten@ Table[ 11^i*13^j, {i, 0, Log[11, mx]}, {j, 0, Log[13, mx/11^i]}] (* _Robert G. Wilson v_, Aug 17 2012 *)

%t fQ[n_]:=PowerMod[143, n, n] == 0; Select[Range[2 10^7], fQ] (* _Vincenzo Librandi_, Jun 27 2016 *)

%o (Haskell)

%o import Data.Set (singleton, deleteFindMin, insert)

%o a108090 n = a108090_list !! (n-1)

%o a108090_list = f $ singleton (1,0,0) where

%o f s = y : f (insert (11 * y, i + 1, j) $ insert (13 * y, i, j + 1) s')

%o where ((y, i, j), s') = deleteFindMin s

%o -- _Reinhard Zumkeller_, May 15 2015

%o (Magma) [n: n in [1..10^7] | PrimeDivisors(n) subset [11, 13]]; // _Vincenzo Librandi_, Jun 27 2016

%o (PARI) list(lim)=my(v=List(),t); for(j=0,logint(lim\=1,13), t=13^j; while(t<=lim, listput(v,t); t*=11)); Set(v) \\ _Charles R Greathouse IV_, Aug 29 2016

%Y Cf. A003586, A003592, A003593, A003591, A003594, A003595, A003596, A003597, A003598, A003599, A107326, A107364, A107466, A108056.

%K nonn,easy

%O 1,2

%A Douglas Winston (douglas.winston(AT)srupc.com), Jun 03 2005