A395137 Decimal expansion of the probability that the line that passes through two points selected independently and uniformly at random in the interior of a quadrant (quarter of a disk) does not intersect the arc.

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

Offset

0,2

References

Stanley Rabinowitz, Problems and Solutions from the Mathematical Visitor 1877-1896, MathPro Press, 1991, page 80.

Links

Table of n, a(n) for n=0..104.

Enoch Beery Seitz, Problem 77, The Mathematical Visitor, Vol. 1, No. 2 (1878), p. 46; Solution by Henry Heaton, ibid., Vol. 1, No. 3 (1879), p. 71.

George B. McClellan Zerr, Solution to Problem 11135, Mathematical questions and solutions from the "Educational Times", Vol. 55 (1891), p. 162.

Index entries for transcendental numbers.

Formula

Equals 4/(3*Pi^2).

Equals 1 - A217739 - A395136.

Example

0.135094911523117028591839284279636851872478366229662...

Mathematica

RealDigits[4/(3*Pi^2), 10, 120, -1][[1]]

Prog

(PARI) 4/(3*Pi^2)

Crossrefs

Cf. A217739, A395134, A395135, A395136.

Sequence in context: A248192 A323987 A124222 * A200615 A349605 A318204

Adjacent sequences: A395134 A395135 A395136 * A395138 A395139 A395140

Keyword

nonn,cons

Author

Amiram Eldar, Apr 13 2026

Status

approved