A392223 Let P(m,k) = 1-(m-1)*...*(m-k+1)/m^(k-1) be the probability that at least two out of k people share a birthday out of m possible days. Sequence gives values of m for which P(m,k(m)) sets a new maximum, where k(m) = A033810(m)-1 is the largest k such that P(m,k) < 1/2.

1, 3, 6, 10, 43, 253, 870, 1317, 14084, 581349, 1564557, 3352229

Offset

1,2

Comments

For n >= 2, a(n)-1 is a term of A072829.

Links

Table of n, a(n) for n=1..12.

Wikipedia, Birthday problem.

Example

   n |   a(n)  | k(a(n)) |  probability P(a(n),k(a(n)))
  ---+---------+---------+------------------------------
   1 |       1 |      1  |          0.000000000000000...
   2 |       3 |      2  |    1/3 = 0.333333333333333...
   3 |       6 |      3  |    4/9 = 0.444444444444444...
   4 |      10 |      4  | 62/125 = 0.496000000000000...
   5 |      43 |      8  |          0.499773865497106...
   6 |     253 |     19  |          0.499922998453490...
   7 |     870 |     35  |          0.499992307369813...
   8 |    1317 |     43  |          0.499999366829696...
   9 |   14084 |    140  |          0.499999996652907...
  10 |  581349 |    898  |          0.499999999702956...
  11 | 1564557 |   1473  |          0.499999999922048...
  12 | 3352229 |   2156  |          0.499999999954675...

Crossrefs

Cf. A033810, A072829, A392222.

Sequence in context: A317361 A384898 A048089 * A081975 A160965 A069708

Adjacent sequences: A392220 A392221 A392222 * A392224 A392225 A392226

Keyword

nonn,more

Author

Pontus von Brömssen, Jan 04 2026

Status

approved