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%I #30 Jun 21 2023 12:36:22
%S 1,23,88,187,313,459,622,797,983,1179,1382,1592,1809,2031,2257,2489,
%T 2724,2963,3205,3450,3698,3949,4203,4459,4717,4977,5239,5503,5768,
%U 6036,6305,6575,6847,7121,7395,7671,7948,8227,8506,8787,9068,9351,9634,9919,10204
%N A Diaconis-Mosteller approximation to the Birthday problem function.
%C Comment from _Stig Blücher Brink_, May 18 2023: (Start)
%C Maximum relative approximation error for a(1) to a(10000) is 0.27%.
%C Maximum absolute approximation error for a(1) to a(10000) is 2126.
%C (End)
%H _Stig Blücher Brink_, <a href="/A050255/b050255.txt">Table of n, a(n) for n = 1..10000</a>
%H P. Diaconis and F. Mosteller, <a href="https://www.stat.berkeley.edu/~aldous/157/Papers/diaconis_mosteller.pdf">Methods of studying coincidences</a>, J. Amer. Statist. Assoc. 84 (1989), pp. 853-861.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BirthdayProblem.html">Birthday Problem</a>
%F a(n) is ceiling(x), where x is the real solution to x*exp(-x/(365*n)) = (log(2)*365^(n-1)*n!*(1 - x/(365*(n+1))))^(1/n). - _Iain Fox_, Oct 26 2018
%t a[n_]:=Ceiling[x /. N[Solve[x Exp[-x/(365 n)]==(365^(n-1) n! Log[2] (1-x/(365 (n+1))))^(1/n), x, Reals]]]; Flatten[Table[a[n], {n, 15}]] (* _Iain Fox_, Oct 26 2018 *)
%Y Cf. A014088, A050256.
%K nonn
%O 1,2
%A _Eric W. Weisstein_
%E a(43)-a(45) from _Alois P. Heinz_, May 17 2023
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