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A062540 Continued fraction for the Lemniscate constant or Gauss's constant. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..5000

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, " ", 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.

Sequence in context: A132068 A173441 A129192 * A173636 A115878 A127125

Adjacent sequences:  A062537 A062538 A062539 * A062541 A062542 A062543

KEYWORD

easy,nonn,cofr

AUTHOR

Jason Earls, Jun 25 2001

STATUS

approved

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Last modified June 19 17:16 EDT 2019. Contains 324222 sequences. (Running on oeis4.)