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%I #12 Sep 08 2022 08:45:56
%S 1,3,5,1,2,1,1,1,2,1,12,1,5,1,1,2,1,14,2,9,11,1,12,1,2,1,832,1,2,2,5,
%T 1,1,17,1,2,1,9,1,12,1,1,1,6,3,2,1,1,6,3,1,1,1,2,2,1,3,1,3,3,1,2,1,45,
%U 1,1,1,1,62,9,1,1,2,3,1,6,1,3,5,1
%N Continued fraction of (1+sqrt(-3+4*sqrt(2)))/2.
%C Equivalent to the periodic continued fraction [1,r,1,r,...] where r=1+sqrt(2), the silver ratio. For geometric interpretations of both continued fractions, see A189979 and A188635.
%C 1 followed by A190178.
%H G. C. Greubel, <a href="/A190180/b190180.txt">Table of n, a(n) for n = 1..10000</a>
%t r = 1 + 2^(1/2));
%t FromContinuedFraction[{1, r, {1, r}}]
%t FullSimplify[%]
%t ContinuedFraction[%, 100] (* A190180 *)
%t RealDigits[N[%%, 120]] (* A190179 *)
%t N[%%%, 40]
%t ContinuedFraction[(1 + Sqrt[-3 + 4*Sqrt[2]])/2, 100] (* _G. C. Greubel_, Dec 28 2017 *)
%o (PARI) contfrac((1+sqrt(-3+4*sqrt(2)))/2) \\ _G. C. Greubel_, Dec 28 2017
%o (Magma) ContinuedFraction((1+Sqrt(-3+4*Sqrt(2)))/2); // _G. C. Greubel_, Dec 28 2017
%Y Cf. A190179, A188635, A190177, A190178.
%K nonn,cofr
%O 1,2
%A _Clark Kimberling_, May 05 2011
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