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

Author

Hugo Pfoertner, Feb 03 2004

Keywords

• frac
• nonn

Comments

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

Links

• Patrice Le Conte, Coincident Birthdays.
• Mathforum at Drexel, The Birthday Problem, Ask Dr. Math: FAQ.
• Eric Weisstein's World of Mathematics, Birthday Problem.

Crossrefs

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

Programs

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 *)

Python

from math import prod
def A091674(n): return 365**(n-1)-prod(365-i for i in range(1,n)) # Chai Wah Wu, Jan 22 2025

Formula

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

Extensions

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