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%I #24 Sep 08 2022 08:45:56
%S 5,4,15,6,1,13,2,1,1,21,3,2,16,1,4,1,1,157,1,9,1,3,1,5,1,2,1,3,1,1,1,
%T 1,11,1,1,22,1,9,1,1,1,1,12,1,7,6,1,3,2,8,1,1,1,1,4,2,3,1,10,17,1,2,1,
%U 5,8,1,2,1,6,1,12,1,39,16,14,1,46,72,16,3,1,1,5,2,1,5,2,1,10,4,2,2,3,2,1,3,2,2,27,10,4,2,8,1,2,6,3,945,1,1,106,1,1,3,1,2,6,1,1,2
%N Continued fraction of e+sqrt(e^2-1).
%H G. C. Greubel, <a href="/A188627/b188627.txt">Table of n, a(n) for n = 1..10000</a>
%F e+sqrt(e^2-1)) = 5.2459400... = A188739.
%t r = 2 E; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
%t N[t, 130]
%t RealDigits[N[t, 130]][[1]] (* A188739 *)
%t ContinuedFraction[t, 120] (* A188627 *)
%o (PARI) default(realprecision, 100); contfrac(exp(1) + sqrt(exp(2) - 1)) \\ _G. C. Greubel_, Nov 01 2018
%o (Magma) SetDefaultRealField(RealField(100)); ContinuedFraction(Exp(1) + Sqrt(Exp(2) - 1)); // _G. C. Greubel_, Nov 01 2018
%Y Cf. A188739.
%K nonn,cofr
%O 1,1
%A _Clark Kimberling_, Apr 11 2011
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