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 A343015 #6 Apr 02 2021 21:20:18 %S A343015 5,0,6,8,7,6,0,9,3,1,6,5,2,7,8,4,5,5,2,2,2,4,3,9,3,1,3,1,6,0,5,1,1,2, %T A343015 3,7,7,7,3,5,2,6,9,9,8,2,5,4,8,5,2,6,1,0,5,6,1,9,4,1,2,1,4,3,8,1,4,1, %U A343015 3,7,2,5,8,4,6,7,8,6,3,3,5,4,8,4,9,5,1 %N A343015 Decimal expansion of the probability that at least 2 of 23 randomly selected people share a birthday, considering leap years. %C A343015 The usual solution of the Birthday Problem, 1 - ((365!)/((365 - 23)! * 365^23)) = 0.507297... (A333507), is based on the assumption that all the years have 365 days. %C A343015 The solution given by Nandor (2004) includes leap years, i.e., 97 years of 366 days in each cycle of 400 years of the Gregorian calendar. %C A343015 With the addition of leap-year days, i.e., the possibility of having a birthday on February 29, the probability is reduced to 0.506876... %C A343015 This constant is a rational number: its numerator and denominator have 111 and 112 digits, respectively. %C A343015 The sequence has a period of 7.983424...*10^108. %H A343015 M. J. Nandor, <a href="http://www.jstor.org/stable/20871519">Including Leap Year in the Canonical Birthday Problem</a>, The Mathematics Teacher, Vol. 97, No. 2 (2004), pp. 87-89. %H A343015 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BirthdayProblem.html">Birthday Problem</a>. %H A343015 Wikipedia, <a href="https://en.wikipedia.org/wiki/Birthday_problem">Birthday problem</a>. %H A343015 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gregorian_calendar">Gregorian calendar</a>. %F A343015 Equals 1 - (365!/((365 - 23)! * 365^23)) * (146000/146097)^23 * (1 + 97 * 365 * 23/146000/(366 - 23)). %e A343015 0.50687609316527845522243931316051123777352699825485... %t A343015 RealDigits[1 - (365!/((365 - 23)! * 365^23)) * (146000/146097)^23 * (1 + 97 * 365 * 23/146000/(366 - 23)), 10, 100][[1]] %Y A343015 Cf. A011763, A014088, A333507. %K A343015 nonn,cons %O A343015 0,1 %A A343015 _Amiram Eldar_, Apr 02 2021