This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A091715 #31 Feb 16 2025 08:32:52 %S A091715 1,1457,1326781,966556865,616113172585,359063094171965, %T A091715 196176047915944825,102076077386001384485,51120278427593115164425, %U A091715 24824896058243745467563925,11753675337747799989826426225 %N A091715 Numerator Q of probability P = Q(n)/365^(n-1) that three or more out of n people share the same birthday. %C A091715 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. %H A091715 Patrice Le Conte, <a href="/A225852/a225852.pdf">Coincident Birthdays.</a> %H A091715 The Math Forum at Drexel, <a href="https://web.archive.org/web/20180805132402/http://mathforum.org:80/library/drmath/view/56650.html">Three Share a Birthday</a>, Ask Dr. Math. %H A091715 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BirthdayProblem.html">Birthday Problem</a>. %F A091715 a(n) = A091674(n) - A091673(n). %e A091715 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. %e A091715 The probability exceeds 50% for n > A014088(3) = 88. %Y A091715 Cf. A014088, A091673 (probabilities for exactly two), A091674 (probabilities for two or more). %K A091715 frac,nonn %O A091715 3,2 %A A091715 _Hugo Pfoertner_, Feb 04 2004