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 A275322 Decimal expansion of AGM(1, sqrt(2))^2/Pi. 1
 4, 5, 6, 9, 4, 6, 5, 8, 1, 0, 4, 4, 4, 6, 3, 6, 2, 5, 3, 7, 4, 9, 6, 6, 6, 2, 2, 5, 4, 7, 6, 8, 3, 3, 3, 6, 6, 1, 1, 7, 6, 7, 7, 3, 0, 0, 1, 4, 8, 3, 1, 5, 0, 8, 3, 9, 4, 3, 6, 2, 2, 4, 7, 2, 6, 7, 4, 8, 4, 3, 5, 8, 0, 7, 0, 8, 0, 5, 3, 8, 5, 5 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Conjecture: Equals Product_{n odd} (n/(n+2) if n == 1 (mod 4), (n+2)/n otherwise) = (1/3) * (5/3) * (5/7) * (9/7) * (9/11) * (13/11) * (13/15) * (17/15) * (17/19) * (21/19) * (21/23) * (25/23) * (25/27) * ... LINKS G. C. Greubel, Table of n, a(n) for n = 0..10000 FORMULA Equals 8*Pi^2/Gamma(1/4)^4 = 4*Gamma(3/4)^2/Gamma(1/4)^2. - Vaclav Kotesovec, Sep 22 2016 EXAMPLE 0.45694658104446362537496662254768... MAPLE evalf(GaussAGM(1, sqrt(2))^2/Pi, 100); # Muniru A Asiru, Oct 08 2018 MATHEMATICA First@ RealDigits@ N[ArithmeticGeometricMean[1, Sqrt[2]]^2/Pi, 120] (* Michael De Vlieger, Jul 26 2016 *) PROG (PARI) agm(1, sqrt(2)) ^ 2 / Pi (PARI) 8*Pi^2/gamma(1/4)^4 \\ Altug Alkan, Oct 08 2018 (MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); 8*Pi(R)^2/Gamma(1/4)^4; // G. C. Greubel, Oct 07 2018 CROSSREFS Cf. A053004 (AGM(1, sqrt(2))). Sequence in context: A242955 A086726 A078885 * A195355 A049466 A196551 Adjacent sequences:  A275319 A275320 A275321 * A275323 A275324 A275325 KEYWORD nonn,cons AUTHOR Dimitris Valianatos, Jul 23 2016 STATUS approved

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Last modified July 15 22:48 EDT 2019. Contains 325061 sequences. (Running on oeis4.)