A160323 Continued fraction for (Gamma(1/6)*Gamma(1/3))/(3*sqrt(Pi)).

2, 1, 4, 8, 1, 27, 1, 19, 1, 25, 3, 6, 4, 1, 37, 1, 1, 7, 1, 75, 1, 13, 1, 2, 6, 1, 16, 1, 6, 2, 1, 1, 3, 1, 5, 3, 36, 1, 4, 17, 1, 2, 1, 1, 1, 12, 1, 1, 7, 1, 3, 1, 10, 13, 3, 7, 3, 1, 9, 206, 1, 1, 1, 3, 34, 1, 10, 1, 1, 7, 1, 705, 1, 4, 4, 1, 1, 2, 1, 4, 2, 2, 1, 3, 8, 1, 19, 2, 1, 11, 3, 1, 725, 1, 37

Offset: 0

Author

Harry J. Smith, May 09 2009

Keywords

• nonn
• cofr

Comments

gamma(1/6)*gamma(1/3)/(3*sqrt(Pi)) = gamma(1/3)^3/(2^(1/3)*sqrt(3)*Pi).

Examples

			2.804364210650908522350038158... = 2 + 1/(1 + 1/(4 + 1/(8 + 1/(1 + ...)))).
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..3999

Crossrefs

Cf. A118292 (decimal expansion).

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); ContinuedFraction((Gamma(1/6)*Gamma(1/3))/(3*Sqrt(Pi(R)))); // G. C. Greubel, Oct 05 2018

Mathematica

ContinuedFraction[(Gamma[1/6]*Gamma[1/3])/(3*Sqrt[Pi]), 100] (* G. C. Greubel, Oct 05 2018 *)

PARI

{ allocatemem(932245000); default(realprecision, 4100); x=gamma(1/3)^3/(2^(1/3)*sqrt(3)*Pi); x=contfrac(x); for (n=1, 4000, write("b160323.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Jun 20 2009

Extensions

Offset changed by Andrew Howroyd, Aug 09 2024