A062540 Continued fraction for the Lemniscate constant or Gauss's constant.

2, 1, 1, 1, 1, 1, 4, 1, 2, 5, 1, 1, 1, 14, 9, 2, 6, 2, 9, 4, 1, 10, 2, 4, 1, 8, 2, 1, 5, 3, 11, 3, 17, 2, 338, 2, 3, 1, 1, 6, 3, 1, 2, 1, 1, 1, 2, 1, 2, 3, 9, 1, 1, 1, 2, 21, 1, 1, 2, 5, 3, 1, 1, 3, 1, 1, 10, 1, 1, 1, 40, 1, 2, 7, 1, 1, 2, 2, 2, 1, 1, 2, 81, 1, 2, 2, 1, 1, 4, 8, 3, 5, 1, 1, 3, 180, 2, 1

Offset: 0

Author

Jason Earls, Jun 25 2001

Keywords

• easy
• nonn
• cofr

Examples

			2.622057554292119810464839589891119413682754951431623162816821703...
2.622057554292119810464839589... = 2 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 20 2009
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..4999
• Simon Plouffe, Lemniscate or Gauss constant

Crossrefs

Cf. A062539 (decimal expansion).

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); ContinuedFraction(Sqrt(2*Pi(R)^3)/(2*Gamma(3/4)^2)); // G. C. Greubel, Oct 07 2018

Mathematica

ContinuedFraction[Sqrt[2*Pi^3]/(2*Gamma[3/4]^2), 100] (* G. C. Greubel, Oct 07 2018 *)

PARI

contfrac(1/2*Pi^(3/2)/gamma(3/4)^2*2^(1/2))

PARI

{ allocatemem(932245000); default(realprecision, 5200); x=contfrac(Pi^(3/2)*sqrt(2)/(2*gamma(3/4)^2)); for (n=1, 5000, write("b062540.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Jun 20 2009

Extensions

Offset changed by Andrew Howroyd, Aug 04 2024