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

0,3

Comments

Also called the Ubiquitous Constant.

Links

Harry J. Smith, Table of n, a(n) for n = 0..20000

Formula

The Ubiquitous Constant = agm(1, sqrt(1/2)) = BetaC(0.75, 0.75) / 2 = Gam(0.75)*Gam(0.75)/(2*Gam(1.5).

Example

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A242133 A144221 A209575 * A280374 A259975 A028313

Adjacent sequences: A159567 A159568 A159569 * A159571 A159572 A159573

Keyword

nonn

Author

Harry J. Smith, Apr 16 2009

Status

approved