

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
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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)^((p1)/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} ((2n3)!!/(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



