A180020 Numbers k such that the relation 1 - d!/((d-i)!d^i) > 1/2 holds for integers d > 2 between i-1 and n+i-1.

0, 0, 3, 4, 7, 7, 9, 10, 12, 14, 14, 17, 17, 19, 21, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 36, 38, 39, 41, 42, 44, 45, 46, 48, 49, 51, 53, 53, 55, 57, 58, 60, 60, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 77, 78, 80, 81, 83, 84, 85, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101

Offset

1,3

Comments

The expression is the "birthday problem" probability out of d equally possible birthdays, while i is the smallest integer for which the relation holds given d, and k is the number of values of d for which the relation holds given i.

Links

Table of n, a(n) for n=1..71.

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

Crossrefs

Equals the first order difference of A180005 plus one.

Sequence in context: A021746 A023849 A197034 * A162431 A024605 A215630

Adjacent sequences: A180017 A180018 A180019 * A180021 A180022 A180023

Keyword

nonn

Author

Mario O. Bourgoin (mob(AT)brandeis.edu), Aug 06 2010

Status

approved