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A050255 A Diaconis-Mosteller approximation to the Birthday problem function. 3


%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

%N A Diaconis-Mosteller approximation to the Birthday problem function.

%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_

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Last modified August 4 20:28 EDT 2021. Contains 346455 sequences. (Running on oeis4.)