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%I #11 Sep 08 2022 08:45:44
%S 0,1,5,1,1,5,20,1,13,2,1,1,61,1,1,2,4,1,3,1,2,1,5,1,13,1,11,7,6,2,77,
%T 7,1,5,4,8,1,1,6,4,2,1,1,2,4,1,1,2,1,3,1,1,6,6,1,7,1,10,1,1,4,1,4,2,1,
%U 7,1,4,1,2,17,2,2,1,5,2,1,2,1,1,1,3,3,1,1,6,1,1,16,3,1320,2,2,7,5,9,1,217,3
%N Continued fraction for 1/(sqrt(2)G), where G is Gauss's constant A014549.
%C Also called the Ubiquitous Constant.
%H Harry J. Smith, <a href="/A159570/b159570.txt">Table of n, a(n) for n = 0..20000</a>
%F The Ubiquitous Constant = agm(1, sqrt(1/2)) = BetaC(0.75, 0.75) / 2 = Gam(0.75)*Gam(0.75)/(2*Gam(1.5).
%e 0.847213084793979086606499123... = 0 + 1/(1 + 1/(5 + 1/(1 + 1/(1 + ...))))
%t ContinuedFraction[2*Pi^(3/2)/Gamma[1/4]^2, 100] (* _G. C. Greubel_, Sep 28 2018 *)
%o (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(agm(1, sqrt(1/2))); for (n=0, 20000, write("b159570.txt", n, " ", x[n+1])); }
%o (PARI) default(realprecision, 100); contfrac(2*Pi^(3/2)/gamma(1/4)^2) \\ _G. C. Greubel_, Sep 28 2018
%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); ContinuedFraction(2*Pi(R)^(3/2)/Gamma(1/4)^2); // _G. C. Greubel_, Sep 28 2018
%K nonn
%O 0,3
%A _Harry J. Smith_, Apr 16 2009
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