

A049541


Decimal expansion of 1/Pi.


73



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
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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


LINKS

Table of n, a(n) for n=0..98.
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. 6264. [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 WenChin Liaw, The RogersRamanujan continued fraction and a quintic iteration for 1/Pi, Proc. Amer. Math. Soc. 135 (2007), 34173424.
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 ForsythGlaisher type series for 1/π and Catalan’s constant by an elementary method, The Mathematics Student, Indian Math. Soc., Vol. 84, Nos. 12, Jan.June (2015), 6986.
Eric W. Weisstein, Octahedron


FORMULA

Equals 1/(1216*A002162)*Sum_{n>=0} A002894(n)*H(n)/(A001025(n)*A016754(n1)), where H(n) denotes the nth harmonic number.  John M. Campbell, Aug 28 2016


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


CROSSREFS

Cf. A000796, A165922, A165952, A165953, A165954, A063723, A010503.  Rick L. Shepherd, Oct 01 2009
Sequence in context: A273927 A185452 A179449 * A249757 A207609 A130300
Adjacent sequences: A049538 A049539 A049540 * A049542 A049543 A049544


KEYWORD

nonn,cons


AUTHOR

N. J. A. Sloane, Dec 11 1999


STATUS

approved



