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A050255
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A Diaconis-Mosteller approximation to the Birthday problem function.
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4
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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, 9634, 9919, 10204
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OFFSET
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1,2
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COMMENTS
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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)
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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