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%I #10 Sep 08 2022 08:45:56
%S 3,5,1,2,1,1,1,2,1,12,1,5,1,1,2,1,14,2,9,11,1,12,1,2,1,832,1,2,2,5,1,
%T 1,17,1,2,1,9,1,12,1,1,1,6,3,2,1,1,6,3,1,1,1,2,2,1,3,1,3,3,1,2,1,45,1,
%U 1,1,1,62,9,1,1,2,3,1,6,1,3,5,1,4
%N Continued fraction of (1+sqrt(2)+sqrt(7+6*sqrt(2)))/2.
%C Equivalent to the periodic continued fraction [r,1,r,1,...] where r=1+sqrt(2), the silver ratio. For geometric interpretations of both continued fractions, see A189977 and A188635.
%H G. C. Greubel, <a href="/A190178/b190178.txt">Table of n, a(n) for n = 1..10000</a>
%t r = 1 + 2^(1/2));
%t FromContinuedFraction[{r, 1, {r, 1}}]
%t FullSimplify[%]
%t ContinuedFraction[%, 100] (* A190178 *)
%t RealDigits[N[%%, 120]] (* A190177 *)
%t N[%%%, 40]
%t ContinuedFraction[(1 + Sqrt[2] + Sqrt[7 + 6*Sqrt[2]])/2, 100] (* _G. C. Greubel_, Dec 28 2017 *)
%o (PARI) contfrac((1+sqrt(2)+sqrt(7+6*sqrt(2)))/2) \\ _G. C. Greubel_, Dec 28 2017
%o (Magma) ContinuedFraction((1+Sqrt(2)+Sqrt(7+6*Sqrt(2)))/2); // _G. C. Greubel_, Dec 28 2017
%Y Cf. A188635, A190177, A190180.
%K nonn,cofr
%O 1,1
%A _Clark Kimberling_, May 05 2011
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