A396023 Decimal expansion of (Pi+2)/Pi^2.

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

Offset

0,1

Comments

The probability that Buffon's needle (see A060294), bent at its midpoint at a uniformly random angle between 0 and 360 degrees, will land on a line when dropped onto a floor with parallel lines spaced at a distance equal to the length of the needle.

Links

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

Uwe Bäsel, Buffon's problem with a pivot needle, Elemente der Mathematik, Vol. 70, No. 2 (2015), pp. 67-70. See Remark 1, p. 70.

Eric Weisstein's World of Mathematics, Buffon's needle problem.

Wikipedia, Buffon's needle problem.

Index entries for transcendental numbers.

Formula

Equals A049541 + A185197.

Equals 1/A197724.

Example

0.520952253468466214425526453164484001877636840825405...

Mathematica

RealDigits[(Pi+2)/Pi^2, 10, 120][[1]]

Prog

(PARI) (Pi+2)/Pi^2

Crossrefs

Cf. A049541, A060294, A089491, A185197, A197724, A396022.

Sequence in context: A021196 A257406 A269980 * A319231 A058512 A111560

Adjacent sequences: A396020 A396021 A396022 * A396024 A396025 A396026

Keyword

nonn,cons

Author

Amiram Eldar, May 14 2026

Status

approved