A091673 -id:A091673 - cp's OEIS frontend

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

Hugo Pfoertner, Feb 03 2004

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

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

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

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 *)

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

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

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

A091715 Numerator Q of probability P = Q(n)/365^(n-1) that three or more out of n people share the same birthday.

Original entry on oeis.org

1, 1457, 1326781, 966556865, 616113172585, 359063094171965, 196176047915944825, 102076077386001384485, 51120278427593115164425, 24824896058243745467563925, 11753675337747799989826426225

Offset: 3

Hugo Pfoertner, Feb 04 2004

A 365-day year and a uniform distribution of birthdays throughout the year are assumed. The probability that 3 or more out of n people share a birthday equals the probability A091674(n)/365^(n-1) that 2 or more share a birthday minus the probability A091673(n)/365^(n-1) that exactly 2 share a birthday.

			The probability that 3 or more people in a group of 10 share the same birthday is a(10)/365^9 = 102076077386001384485/114983567789585767578125 ~= 8.87744913*10^-4.
The probability exceeds 50% for n > A014088(3) = 88.

Patrice Le Conte, Coincident Birthdays.
The Math Forum at Drexel, Three Share a Birthday, Ask Dr. Math.
Eric Weisstein's World of Mathematics, Birthday Problem.

Cf. A014088, A091673 (probabilities for exactly two), A091674 (probabilities for two or more).

a(n) = A091674(n) - A091673(n).

cp's OEIS Frontend

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

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