A396942 Decimal expansion of the probability that an acute triangle is formed by selecting two points independently and uniformly at random in a disk, and a third point uniformly at random on the segment of the radius between the second point and the circumference.

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

Offset

0,2

Links

Table of n, a(n) for n=0..105.

Formula

Equals 2*G/Pi + log(2)/2 - 11/(9*Pi) - 4/9, where G is Catalan's constant (A006752).

Example

0.096205537450310505328113552088620792348314352230686...

Mathematica

RealDigits[2*Catalan/Pi + Log[2]/2 - 11/(9*Pi) - 4/9, 10, 120, -1][[1]]

Prog

(PARI) 2*Catalan/Pi + log(2)/2 - 11/(9*Pi) - 4/9

Crossrefs

Cf. A002162, A006752, A378910.

Cf. A016631, A075549, A093072, A093588, A102519, A102520, A180434, A210958, A262041, A262080, A341942, A348668, A391867, A394106, A394107, A394836, A396941, A396943.

Sequence in context: A355333 A089479 A388877 * A269444 A199431 A154899

Adjacent sequences: A396939 A396940 A396941 * A396943 A396944 A396946

Keyword

nonn,cons

Author

Amiram Eldar, Jun 11 2026

Status

approved