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A050255 Diaconis-Mosteller approximation to the Birthday problem function. 3
1, 23, 88, 187, 313, 459, 622, 797, 983, 1179, 1382, 1592, 1809, 2031, 2257, 2489, 2724, 2963, 3205, 3450, 3698, 3949, 4203, 4459, 4717, 4977, 5239, 5503, 5768, 6036, 6305, 6575, 6847, 7121, 7395, 7671, 7948, 8227, 8506, 8787, 9068, 9351 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..42.

P. Diaconis and F. Mosteller, Methods of studying coincidences, J. Amer. Statist. Assoc. 84 (1989), pp. 853-861.

Eric Weisstein's World of Mathematics, Birthday Problem

FORMULA

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

MATHEMATICA

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 *)

CROSSREFS

Cf. A014088, A050256.

Sequence in context: A193018 A044210 A044591 * A014088 A244453 A158537

Adjacent sequences:  A050252 A050253 A050254 * A050256 A050257 A050258

KEYWORD

nonn

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified October 15 01:40 EDT 2019. Contains 328025 sequences. (Running on oeis4.)