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A159570 Continued fraction for 1/(sqrt(2)G), where G is Gauss's constant A014549. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)