A324559 Decimal expansion of the probability that the length of a chord drawn through 2 points taken at random within a circle on each side of a given diameter will be less than the radius.

3, 4, 1, 8, 0, 0, 5, 0, 8, 4, 0, 5, 4, 4, 4, 7, 0, 1, 2, 9, 7, 8, 0, 5, 2, 1, 4, 0, 3, 5, 4, 1, 1, 5, 1, 7, 0, 9, 4, 5, 0, 2, 3, 0, 9, 4, 1, 7, 6, 2, 9, 4, 1, 8, 2, 7, 1, 9, 6, 9, 2, 7, 6, 8, 4, 2, 6, 0, 0, 5, 2, 0, 4, 1, 2, 3, 5, 9, 6, 0, 0, 8, 2, 6, 1, 1, 1

Offset

-2,1

Links

Table of n, a(n) for n=-2..84.

J. J. Sylvester, Problem 1849, solved by Stephen Watson, Mathematical Questions with Their Solutions: From the "Educational Times", Vol. 8 (1868), pp. 92-93.

Formula

Equals 13/144 - 13*sqrt(3)/(48*Pi) + 3*(3 + log(4/3))/(16*Pi^2).

Example

0.0034180050840544470129780521403541151709450230941762...

Mathematica

RealDigits[13/144-13*Sqrt[3]/(48*Pi)+3*(3+Log[4/3])/(16*Pi^2), 10, 100][[1]]

Crossrefs

Cf. A102519, A240935, A324558.

Sequence in context: A111516 A210636 A116392 * A174607 A326503 A105578

Adjacent sequences: A324556 A324557 A324558 * A324560 A324561 A324562

Keyword

nonn,cons

Author

Amiram Eldar, Mar 06 2019

Status

approved