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A190261 Continued fraction of (1 + sqrt(1 + 2x))/2, where x=sqrt(2).

%I A190261 #16 Sep 08 2022 08:45:57
%S A190261 1,2,11,32,1,4,10,2,1,1,3,1,1,5,2,3,2,1,4,2,3,2,41,1,2,1,1,3,4,1,35,1,
%T A190261 5,1,29661,2,1,1,2,1,1,1,1,1,2,5,2,2,2,1,1,1,5,15,2,1,1,1,2,7,1,1,1,
%U A190261 13,1,1,1,1,20,2,1,2,1,1,1,1,1,4,1,1,1,1,3,14,1,8,2,1,1,1,1,2,1,3,2,3,1,8,2
%N A190261 Continued fraction of (1 + sqrt(1 + 2x))/2, where x=sqrt(2).
%C A190261 1 followed by A190259.
%H A190261 G. C. Greubel, <a href="/A190261/b190261.txt">Table of n, a(n) for n = 1..10000</a>
%t A190261 r=2^(1/2);
%t A190261 FromContinuedFraction[{1, r, {1, r}}]
%t A190261 FullSimplify[%]
%t A190261 ContinuedFraction[%, 100]  (* A190261 *)
%t A190261 RealDigits[N[%%, 120]]     (* A190260 *)
%t A190261 N[%%%, 40]
%t A190261 ContinuedFraction[(1+Sqrt[1+2Sqrt[2]])/2,100] (* _Harvey P. Dale_, Jan 27 2013 *)
%o A190261 (PARI) contfrac((1+sqrt(1+2*sqrt(2)))/2) \\ _G. C. Greubel_, Dec 26 2017
%o A190261 (Magma) ContinuedFraction((1+Sqrt(1+2*Sqrt(2)))/2) // _G. C. Greubel_, Dec 26 2017
%Y A190261 Cf. A190260, A190259.
%K A190261 nonn,cofr
%O A190261 1,2
%A A190261 _Clark Kimberling_, May 06 2011