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

0,1

Links

Harry J. Smith, Table of n, a(n) for n = 0..4999

Simon Plouffe, Lemniscate or Gauss constant

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A062539 (decimal expansion).

Sequence in context: A173441 A326851 A129192 * A173636 A115878 A127125

Adjacent sequences: A062537 A062538 A062539 * A062541 A062542 A062543

Keyword

easy,nonn,cofr

Author

Jason Earls, Jun 25 2001

Extensions

Offset changed by Andrew Howroyd, Aug 04 2024

Status

approved