A091674 Numerator Q of probability P = Q(n)/365^(n-1) that two or more out of n people share the same birthday.

1, 1093, 795341, 481626601, 262130079485, 132974790903865, 64157156143943045, 29808728817823292065, 13447118719710220490765, 5923562823392985950002825, 2558600264156303883127171925, 1087010123072386037371040127025

Offset

2,2

Comments

A 365-day year and a uniform distribution of birthdays throughout the year are assumed.

Links

Table of n, a(n) for n=2..13.

Patrice Le Conte, Coincident Birthdays.

Mathforum at Drexel, The Birthday Problem, Ask Dr. Math: FAQ.

Eric Weisstein's World of Mathematics, Birthday Problem.

Formula

Q(n) = (1 - Product_{i=1..n-1} (1-i/365))*365^(n-1).

Mathematica

Q[n_] := (1 - Product[(1 - i/365), {i, 1, n - 1}])365^(n - 1); Table[ Q[n], {n, 2, 13}] (* Robert G. Wilson v, Feb 05 2004 *)

Crossrefs

Cf. A014088, A091673 (probabilities for exactly two), A091715 (probabilities for three or more).

Sequence in context: A203858 A115192 A307220 * A022197 A259909 A124122

Adjacent sequences: A091671 A091672 A091673 * A091675 A091676 A091677

Keyword

frac,nonn

Author

Hugo Pfoertner, Feb 03 2004

Extensions

More terms from Robert G. Wilson v, Feb 05 2004

Status

approved