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%I #39 Oct 19 2016 07:57:04
%S 2,1,3,5,8,12,19,28,41,60,87,127,183,266,384,555,802,1158,1671,2412,
%T 3480,5022,7246,10455,15084,21763,31398,45298,65353,94285,136025,
%U 196244,283121,408458,589281,850154,1226514,1769486,2552829,3682955,5313382
%N 3rd term of continued fraction for sqrt(2)^sqrt(2)^...^sqrt(2) with n sqrt(2)'s.
%C 1st terms are 1,1,1,1,1,... and 2nd terms are 2,1,1,1,1,...
%H G. C. Greubel, <a href="/A198094/b198094.txt">Table of n, a(n) for n = 1..251</a>
%F a(n) ~ c / log(2)^n, where c = 1/A277435 = 1.582031511247872306827383... - _Vladimir Reshetnikov_, Oct 18 2016
%t ContinuedFraction[#, 3][[3]] & /@ NestList[Sqrt[2]^# &, Sqrt[2], 40]
%o (PARI) a(n) = {my(c = sqrt(2)); for (k=1, n-1, c = sqrt(2)^c); contfrac(c)[3];} \\ _Michel Marcus_, Oct 19 2016
%Y Cf. A002193, A078333, A194348.
%Y Cf. A260691, A277435.
%K nonn,easy
%O 1,1
%A _Vladimir Reshetnikov_, Oct 30 2011
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