OFFSET
1,2
COMMENTS
Comment from Stig Blücher Brink, May 18 2023: (Start)
Maximum relative approximation error for a(1) to a(10000) is 0.27%.
Maximum absolute approximation error for a(1) to a(10000) is 2126.
(End)
LINKS
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(43)-a(45) from Alois P. Heinz, May 17 2023
STATUS
approved