login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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