A396027 Decimal expansion of the probability that Buffon's needle will land on exactly two lines when dropped on a hexagonal tiling in which the inradius of each hexagon equals the length of the needle.

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

Offset

0,2

Links

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

Colin P. D. Birch, Diagonal and orthogonal neighbours in grid-based simulations: Buffon's stick after 200 years, Ecological Modelling, Vol. 192, No. 3-4 (2006), pp. 637-644.

Christoforos Vlachos and Vasilis Friderikos, MOCA: Multiobjective cell association for device-to-device communications, IEEE Transactions on Vehicular Technology, Vol. 66, No. 10 (2017), pp. 9313-9327; alternative link.

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

Wikipedia, Buffon's needle problem.

Wikipedia, Hexagonal tiling.

G. R. Wood and J. M. Robertson, Buffon got it straight, Statistics & Probability Letters, Vol. 37, No. 4 (1998), pp. 415-421.

Formula

Equals sqrt(3)/(4*Pi) - 1/12 (Wood and Robertson, 1998).

Equals 1 - A396025 - A396026.

Equals A240935/3 - 1/12.

Example

0.0544988905221146790444982912449090270160132867583268...

Mathematica

RealDigits[Sqrt[3]/(4*Pi) - 1/12, 10, 120, -1][[1]]

Prog

(PARI) sqrt(3)/(4*Pi) - 1/12

Crossrefs

Cf. A060294, A089491, A240935, A396025 (0 lines), A396026 (1 line).

Sequence in context: A303270 A340918 A244046 * A255332 A071419 A291069

Adjacent sequences: A396024 A396025 A396026 * A396028 A396029 A396030

Keyword

nonn,cons

Author

Amiram Eldar, May 14 2026

Status

approved