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A049541 Decimal expansion of 1/Pi. 76
3, 1, 8, 3, 0, 9, 8, 8, 6, 1, 8, 3, 7, 9, 0, 6, 7, 1, 5, 3, 7, 7, 6, 7, 5, 2, 6, 7, 4, 5, 0, 2, 8, 7, 2, 4, 0, 6, 8, 9, 1, 9, 2, 9, 1, 4, 8, 0, 9, 1, 2, 8, 9, 7, 4, 9, 5, 3, 3, 4, 6, 8, 8, 1, 1, 7, 7, 9, 3, 5, 9, 5, 2, 6, 8, 4, 5, 3, 0, 7, 0, 1, 8, 0, 2, 2, 7, 6, 0, 5, 5, 3, 2, 5, 0, 6, 1, 7, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The ratio of the volume of a regular octahedron to the volume of the circumscribed sphere (which has circumradius a*sqrt(2)/2 = a*A010503, where a is the octahedron's edge length; see MathWorld link). For similar ratios for other Platonic solids, see A165922, A165952, A165953 and A165954. - Rick L. Shepherd, Oct 01 2009

REFERENCES

J.-P. Delahaye, Pi - die Story (German translation), Birkhäuser, 1999 Baasel, p. 245. French original: Le fascinant nombre Pi, Pour la Science, Paris, 1997.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

Mohammad K. Azarian, An Expression for Pi, Problem #870, College Mathematics Journal, Vol. 39, No. 1, January 2008, p. 66. Solution appeared in Vol. 40, No. 1, January 2009, pp. 62-64. [From Mohammad K. Azarian, Feb 08 2009]

J. Bohr, Ramanujan's Method of Approximating Pi

J. Borwein, Ramanujan's Sum

Heng Huat Chan, Shaun Cooper and Wen-Chin Liaw, The Rogers-Ramanujan continued fraction and a quintic iteration for 1/Pi, Proc. Amer. Math. Soc. 135 (2007), 3417-3424.

J. Guillera, A New Method to Obtain Series for 1/Pi and 1/Pi^2, Experimental Mathematics, Volume 15, Issue 1, 2006.

R. Matsumoto, Ramanujan Type Series [Broken link]

A. S. Nimbran, Deriving Forsyth-Glaisher type series for 1/π and Catalan’s constant by an elementary method, The Mathematics Student, Indian Math. Soc., Vol. 84, Nos. 1-2, Jan.-June (2015), 69-86.

Eric W. Weisstein, Octahedron

FORMULA

Equals 1/(12-16*A002162)*Sum_{n>=0} A002894(n)*H(n)/(A001025(n) * A016754(n-1)), where H(n) denotes the n-th harmonic number. - John M. Campbell, Aug 28 2016

1/Pi = Sum_{m>=0} binomial(2*m, m)^2*(42*m+5)/(2^(12*m+4)), Ramanujan, from the J.-P. Delahaye reference. - Wolfdieter Lang, Sep 18 2018

EXAMPLE

0.3183098861837906715377675267450287240689192914809128974953...

MAPLE

Digits:=100: evalf(1/Pi); # Wesley Ivan Hurt, Aug 29 2016

MATHEMATICA

RealDigits[N[1/Pi, 6! ]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jun 18 2009 *)

PROG

(PARI) 1/Pi \\ Charles R Greathouse IV, Jun 16 2011

(MATLAB) 1/pi \\ Altug Alkan, Apr 10 2016

(MAGMA) R:= RealField(100); 1/Pi(R); // G. C. Greubel, Aug 21 2018

CROSSREFS

Cf. A000796, A165922, A165952, A165953, A165954, A063723, A010503. - Rick L. Shepherd, Oct 01 2009

Cf. A088538 (4/Pi).

Sequence in context: A293975 A185452 A179449 * A249757 A207609 A130300

Adjacent sequences:  A049538 A049539 A049540 * A049542 A049543 A049544

KEYWORD

nonn,cons,changed

AUTHOR

N. J. A. Sloane, Dec 11 1999

STATUS

approved

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Last modified September 25 21:12 EDT 2018. Contains 315425 sequences. (Running on oeis4.)