A394833 Decimal expansion of the mean distance between two points chosen independently and uniformly at random from a half-disk, one from each of the two sides of the radius that divides it into two quadrants.

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

Offset

0,1

References

Stanley Rabinowitz, Problems and Solutions from the Mathematical Visitor 1877-1896, MathPro Press, 1991, page 59.

Links

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

Enoch Beery Seitz, Problem 32, The Mathematical Visitor, Vol. 1, No. 1 (1878), p. 5; Solution, by the proposer, ibid., Vol. 1, No. 2 (1878), pp. 35-36.

Formula

Equals (32/(135*Pi^2))*(94*sqrt(2) - 95 + 6*log((1 + sqrt(2))/2)).

Equals 2 * A130203 - A130204.

Example

0.938229556537378409840810962672826514330266236871159...

Mathematica

RealDigits[(32/(135*Pi^2))*(94*Sqrt[2] - 95 + 6*Log[(1 + Sqrt[2])/2]), 10, 120][[1]]

Prog

(PARI) (32/(135*Pi^2))*(94*sqrt(2) - 95 + 6*log((1 + sqrt(2))/2))

Crossrefs

Cf. A091648, A130203, A130204, A394832.

Sequence in context: A021520 A248313 A010539 * A284832 A380599 A394059

Adjacent sequences: A394830 A394831 A394832 * A394834 A394835 A394836

Keyword

nonn,cons

Author

Amiram Eldar, Apr 04 2026

Status

approved