A159570 - OEIS

%I #19 Feb 16 2025 08:33:10

%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 Continued fraction for A096427.

%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>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UbiquitousConstant.html">Ubiquitous Constant</a>.

%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

%Y Cf. A096427.

%K nonn

%O 0,3

%A _Harry J. Smith_, Apr 16 2009