A394807 Decimal expansion of 1/4 + 5 * arcsin(1/4) / (2*Pi).

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

Offset

0,1

Comments

The probability that in a sample of 5 independent variables distributed according to the same normal distribution the mean lies between 2nd and 3rd variable when they are arranged in increasing order of magnitude (David, 1963).

It is also the probability that it lies between the 3rd and 4th. The probability that it lies between 1st and 2nd and the probability that it lies between 4th and 5th are both 5*arccos(1/4)/(2*Pi) - 1 = 0.048923441... .

Links

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

Herbert T. David, The sample mean among the extreme normal order statistics, The Annals of Mathematical Statistics, Vol. 34, No. 1 (1963), pp. 33-55.

Florian Frick, Andrew Newman, and Wesley Pegden, Youden's demon is Sylvester's problem, Mathematika, Vol. 71, No. 2 (2025), Article e70015; arXiv preprint, arXiv:2407.02589 [math.PR], 2024.

Index entries for transcendental numbers.

Formula

Equals 1/4 + A132715 * A195621 / 10.

Equals A394806 / 2.

Example

0.451076558137915609427375483321210638960161078118841...

Mathematica

RealDigits[1/4 + 5 * ArcSin[1/4] / (2*Pi), 10, 120][[1]]

Prog

(PARI) 1/4 + 5 * asin(1/4) / (2*Pi)

Crossrefs

Cf. A132715, A195621, A394805, A394806.

Sequence in context: A360220 A375943 A122753 * A016714 A211799 A113950

Adjacent sequences: A394804 A394805 A394806 * A394808 A394809 A394810

Keyword

nonn,cons

Author

Amiram Eldar, Apr 02 2026

Status

approved