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A088538 Decimal expansion of 4/Pi. 30
1, 2, 7, 3, 2, 3, 9, 5, 4, 4, 7, 3, 5, 1, 6, 2, 6, 8, 6, 1, 5, 1, 0, 7, 0, 1, 0, 6, 9, 8, 0, 1, 1, 4, 8, 9, 6, 2, 7, 5, 6, 7, 7, 1, 6, 5, 9, 2, 3, 6, 5, 1, 5, 8, 9, 9, 8, 1, 3, 3, 8, 7, 5, 2, 4, 7, 1, 1, 7, 4, 3, 8, 1, 0, 7, 3, 8, 1, 2, 2, 8, 0, 7, 2, 0, 9, 1, 0, 4, 2, 2, 1, 3, 0, 0, 2, 4, 6, 8, 7, 6, 4, 8, 5, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Average length of chord formed from two randomly chosen points on the circumference of a unit circle (see Weisstein/MathWorld link). - Rick L. Shepherd, Jun 19 2006

Suppose u(0) = 1 + i where i^2 = -1 and u(n+1) = (1/2)*(u(n) + |u(n)|). Conjecture: limit(Real(u(n)), n = +infinity) = 4/Pi. - Yalcin Aktar, Jul 18 2007

REFERENCES

S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, p. 86

L. B. W. Jolley, Summation of Series, Dover (1961).

LINKS

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Circle Line Picking.

R. J. Mathar, Chebyshev Series Expansion of Inverse Polynomials, arXiv:0403344 [math.CA]

FORMULA

4/Pi = prod(1-(-1)^((p-1)/2)/p) where p runs through the odd primes.

arcsin x = (4/Pi) sum_{n = 1, 3, 5, 7, ...} T_n(x)/n^2 (Chebyshev series of arcsin; App C of math.CA/0403344). - R. J. Mathar, Jun 26 2006

Equals 1 + sum_{n >= 1} ((2n-3)!!/(2n)!!)^2. [Jolley eq 274]. - R. J. Mathar, Nov 03 2011

EXAMPLE

4/Pi = 1.2732395.... = 1/0.78539816...

MATHEMATICA

RealDigits[N[4/Pi, 6!]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jun 18 2009 *)

PROG

(PARI) 4/Pi \\ Charles R Greathouse IV, Jun 21 2013

CROSSREFS

Cf. A079097 for terms of a generalized continued fraction for 4/Pi.

Sequence in context: A124910 A090388 A021370 * A210516 A226626 A011049

Adjacent sequences:  A088535 A088536 A088537 * A088539 A088540 A088541

KEYWORD

cons,nonn

AUTHOR

Benoit Cloitre, Nov 16 2003

STATUS

approved

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Last modified April 17 11:46 EDT 2014. Contains 240635 sequences.