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A190183 Continued fraction of (1+x+sqrt(8+2x))/4, where x=sqrt(15).

%I A190183 #12 Sep 08 2022 08:45:56
%S A190183 2,4,1,3,10,1,3,1,1,2,66,1,4,2,1,1,48,5,1,1,2,1,1,1,8,2,1,1,4,16,2,2,
%T A190183 1,4,1,3,1,3,1,11,1,1,8,16,1,1,1,10,1,2,4,1,1,1,3,1,1,1,1,30,1,1,2,1,
%U A190183 1,8,13,1,1,6,6,1,6,1,1,2,2,10,1,2,7,9,2,4,7,3,1,2,2,1,2,5,4,2,3,2,3,2,1,3
%N A190183 Continued fraction of (1+x+sqrt(8+2x))/4, where x=sqrt(15).
%C A190183 Equivalent to the periodic continued fraction [r,1,1,r,1,1,...] where r=(1+sqrt(5))/2, the golden ratio. For geometric interpretations of both continued fractions, see A190182 and A188635.
%H A190183 G. C. Greubel, <a href="/A190183/b190183.txt">Table of n, a(n) for n = 1..10000</a>
%t A190183 r = (1 + 5^(1/2))/2;
%t A190183 FromContinuedFraction[{r, 1, 1, {r, 1, 1}}]
%t A190183 FullSimplify[%]
%t A190183 ContinuedFraction[%, 100] (* A190183 *)
%t A190183 RealDigits[N[%%, 120]]    (* A190182 *)
%t A190183 N[%%%, 40]
%t A190183 ContinuedFraction[(1+Sqrt[15]+Sqrt[8+2Sqrt[15]])/4,100] (* _Harvey P. Dale_, Apr 29 2013 *)
%o A190183 (PARI) contfrac((1+sqrt(15)+sqrt(8+2*sqrt(15)))/4) \\ _G. C. Greubel_, Dec 28 2017
%o A190183 (Magma) ContinuedFraction((1+Sqrt(15)+Sqrt(8+2*Sqrt(15)))/4); // _G. C. Greubel_, Dec 28 2017
%Y A190183 Cf. A190182, A188635.
%K A190183 nonn,cofr
%O A190183 1,1
%A A190183 _Clark Kimberling_, May 05 2011