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%I #8 Mar 23 2017 04:38:00
%S 1,2,2,4,2,5,7,6,10,8,8,5,8,13,7,10,13,10,11,10,14,19,15,13,12,13,16,
%T 17,15,11,17,24,21,29,23,18,23,24,26,31,28,26,29,31,24,31,28,26,20,18,
%U 18,23,30,33,36,36,31,33,38,37,35,37,29,40,43,45,39,37,40,39,42,47,41,33
%N Number of terms in simple continued fraction for (3/2)^n.
%D S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 156.
%H G. C. Greubel, <a href="/A090397/b090397.txt">Table of n, a(n) for n = 0..10000</a>
%F Conjecture : a(n) is asymptotic to c*n where c=12*(log(2)/Pi)^2=log(2)*Levy's constant=0.58416081665664902187922697....
%t Table[Length[ContinuedFraction[(3/2)^n]], {n,0,100}] (* _G. C. Greubel_, Mar 23 2017 *)
%o (PARI) a(n)=length(contfrac((3/2)^n))
%Y Cf. A089729.
%K nonn
%O 0,2
%A _Benoit Cloitre_, Jan 31 2004
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