LINKS
Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/BirthdayProblem.html">Birthday Problem</a>
The OEIS is supported by the many generous donors to the OEIS Foundation.
Eric Weisstein's World of Mathematics, <a href="httphttps://mathworld.wolfram.com/BirthdayProblem.html">Birthday Problem</a>
editing
approved
A Diaconis-Mosteller approximation for modest n to the Birthday problem function.
a(n) = floor(47*(n-3/2)^(3/2)).
From Stig Blücher Brink, May 18 2023: (Start)
Curve-fit of A014088 for n=2 to n=13.
From Mentioned in the original Diaconis-Mosteller reference:article.
"We fit a curve to these numbers and find for modest k (say, smaller than 20) that N = 47*(k-1.5)^(3/2) gives a good fit".
Note that for a(20) to a(10000) the approximation error grows from 9% to 1225%
(End)
a(n) = floor(47*(n-3/2)^(3/2)). - Derek Orr, Sep 05 2015
Entry revised by N. J. A. Sloane, Jun 21 2023
proposed
editing
editing
proposed
Comment from _From _Stig Blücher Brink_, May 18 2023: (Start)
"...We fit a curve to these numbers and find for modest k (say, smaller than 20) that N = 47*(k-1.5)^(3/2) gives a good fit".
a(n) = floor(47*(n-1.53/2)^(3/2)). - Derek Orr, Sep 05 2015
proposed
editing
editing
proposed
Curve-fit of A014088 for n=2 to n=13.
proposed
editing
editing
proposed
A Diaconis-Mosteller approximation for modest k n to the Birthday problem function.
"Levin gave an algorithm ...We fit a curve to these numbers and find for modest k (say, smaller than 20) that allows exact computationN = 47*(k-1.5)^(3/2) gives a good fit"
..Thus in an audience of 1,000 people Note that for a(20) to a(10000) the probabilityapproximation error grows from 9% to 1225%
exceeds 1/2 that at least 9 people have the same birthday.
We fit a curve to these numbers and find for
modest k (say, smaller than 20) that
N = 47*(k-1.5)^(3/2)
gives a good fit"
Note that for a(20) to a(10000) the approximation
error grows from 9% to 1225%
proposed
editing
editing
proposed