A159570 Continued fraction for 1/(sqrt(2)*G), where G is Gauss's constant A014549.

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, 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, 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

Offset: 0

Author

Harry J. Smith, Apr 16 2009

Keywords

• nonn

Comments

Continued fraction for A096427.

Also called the Ubiquitous Constant.

Examples

			0.847213084793979086606499123... = 0 + 1/(1 + 1/(5 + 1/(1 + 1/(1 + ...))))
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20000
• Eric Weisstein's World of Mathematics, Ubiquitous Constant.

Crossrefs

Cf. A096427.

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); ContinuedFraction(2*Pi(R)^(3/2)/Gamma(1/4)^2); // G. C. Greubel, Sep 28 2018

Mathematica

ContinuedFraction[2*Pi^(3/2)/Gamma[1/4]^2, 100] (* G. C. Greubel, Sep 28 2018 *)

PARI

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(agm(1, sqrt(1/2))); for (n=0, 20000, write("b159570.txt", n, " ", x[n+1])); }

PARI

default(realprecision, 100); contfrac(2*Pi^(3/2)/gamma(1/4)^2) \\ G. C. Greubel, Sep 28 2018