%I #51 Nov 03 2023 10:31:38

%S 1,2,4,8,11,16,22,32,44,64,88,121,128,176,242,256,352,484,512,704,968,

%T 1024,1331,1408,1936,2048,2662,2816,3872,4096,5324,5632,7744,8192,

%U 10648,11264,14641,15488,16384,21296,22528,29282,30976,32768

%N Numbers of the form 2^i * 11^j.

%C A204455(11*a(n)) = 11, and only for these numbers. - _Wolfdieter Lang_, Feb 04 2012

%H Charles R Greathouse IV, <a href="/A003596/b003596.txt">Table of n, a(n) for n = 1..10000</a> (first 100 terms from Vincenzo Librandi)

%F The characteristic function of this sequence is given by Sum_{n >= 1} x^a(n) = Sum_{n >= 1} mu(22*n)*x^n/(1 - x^n), where mu(n) is the Möbius function A008683. Cf. with the formula of Hanna in A051037. - _Peter Bala_, Mar 18 2019

%F Sum_{n>=1} 1/a(n) = (2*11)/((2-1)*(11-1)) = 11/5. - _Amiram Eldar_, Sep 23 2020

%F a(n) ~ exp(sqrt(2*log(2)*log(11)*n)) / sqrt(22). - _Vaclav Kotesovec_, Sep 23 2020

%t fQ[n_] := PowerMod[22,n,n]==0; Select[Range[40000], fQ] (* _Vincenzo Librandi_, Feb 04 2012 *)

%o (PARI) list(lim)=my(v=List(),N);for(n=0,log(lim)\log(11),N=11^n;while(N<=lim,listput(v,N);N<<=1));vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jun 28 2011

%o (Haskell)

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

%o a003596 n = a003596_list !! (n-1)

%o a003596_list = f $ singleton (1,0,0) where

%o f s = y : f (insert (2 * y, i + 1, j) $ insert (11 * 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..2*10^5] | PrimeDivisors(n) subset [2, 11]]; // _Vincenzo Librandi_, Jun 27 2016

%o (GAP) Filtered([1..33000],n->PowerMod(22,n,n)=0); # _Muniru A Asiru_, Mar 19 2019

%Y Cf. A025612, A025616, A025621, A025625, A025629, A025632, A025634, A025635, A108761, A003597, A107988, A003598, A108698, A003599, A107788, A108687, A108779, A108090.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_