cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A190185 Continued fraction of sqrt(1+x+sqrt(1+2*x)), where x=sqrt(2/3).

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%I A190185 #15 Sep 08 2022 08:45:56
%S A190185 1,1,5,1,6,1,5,1,1,40,1,1,1,1,1,1,1,13,1,1,1,5,1,15,1,3,1,2,2,5,1,1,1,
%T A190185 1,4,5,65,1,13,1,3,4,1,1,1,4,13,1,1,2,1,3,2,2,1,10,1,20,4,15,6,1,3,10,
%U A190185 1,78,1,1,11,15,1,11,179,2,1,2,1,1,1,6,1,1,1,2,3,2,6,1,1,7,5,1,4,1,9,1,1,2,10,3
%N A190185 Continued fraction of sqrt(1+x+sqrt(1+2*x)), where x=sqrt(2/3).
%C A190185 Equivalent to the periodic continued fraction [sqrt(2), sqrt(3), sqrt(2), sqrt(3),...].  For geometric interpretations of both continued fractions, see A190184 and A188635.
%H A190185 G. C. Greubel, <a href="/A190185/b190185.txt">Table of n, a(n) for n = 1..10000</a>
%t A190185 FromContinuedFraction[{2^(1/2), 3^(1/2), {2^(1/2), 3^(1/2)}}]
%t A190185 FullSimplify[%]
%t A190185 ContinuedFraction[%, 100]  (* A190185 *)
%t A190185 RealDigits[N[%%, 120]]      (* A190186 *)
%t A190185 N[%%%, 40]
%t A190185 ContinuedFraction[Sqrt[1 + Sqrt[2/3] + Sqrt[1 + 2*Sqrt[2/3]]], 100] (* _G. C. Greubel_, Dec 28 2017 *)
%o A190185 (PARI) contfrac(sqrt(1 + sqrt(2/3) + sqrt(1 + 2*sqrt(2/3)))) \\ _G. C. Greubel_, Dec 28 2017
%o A190185 (Magma) ContinuedFraction(Sqrt(1 + Sqrt(2/3) + Sqrt(1 + 2*Sqrt(2/3)))); // _G. C. Greubel_, Dec 28 2017
%Y A190185 Cf. A188635, A190184.
%K A190185 nonn,cofr
%O A190185 1,3
%A A190185 _Clark Kimberling_, May 05 2011
%E A190185 Definition corrected by _Bruno Berselli_, May 13 2011