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A120671

Decimal expansion of arccos(1-8/(Pi^2)) / (2*Pi).

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

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OFFSET

0,1

COMMENTS

The average arc length between two randomly chosen points on a circle of radius r is r*A120669 corresponding to the average chord length r*A088538. (Each arc averaged is no larger than the semicircle.). This sequence is the ratio of that average arc length to the circumference (and is thus also the ratio of the corresponding sector's area to the circle's area).

LINKS

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

FORMULA

Equals A120669/(2*Pi) = A120670/360.

EXAMPLE

0.219667909710056641181661197550...

MATHEMATICA

RealDigits[ArcCos[(1-(8/(Pi^2) ))]/(2Pi), 10, 120][[1]] (* Harvey P. Dale, Jun 17 2018 *)

PROG

(PARI) acos(1-8/Pi^2)/(2*Pi)

CROSSREFS

Cf. A088538, A120669 (2*Pi*A120671), A120670 (360*A120671).