A014088 Minimal number of people to give a 50% probability of having at least n coincident birthdays in one year.

1, 23, 88, 187, 313, 460, 623, 798, 985, 1181, 1385, 1596, 1813, 2035, 2263, 2494, 2730, 2970, 3213, 3459, 3707, 3959, 4213, 4470, 4728, 4989, 5252, 5516, 5783, 6051, 6320, 6592, 6864, 7138, 7413, 7690, 7968, 8247, 8527, 8808, 9090, 9373, 9657, 9942, 10228

Offset

1,2

Links

Stig Blücher Brink, Table of n, a(n) for n = 1..10000 (terms 1..61 from Hiroaki Yamanouchi, terms 62..250 from Rob Cook)

Patrice Le Conte, Coincident Birthdays.

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

Bruce Levin, Exact Solutions of the Generalized Birthday Problem.

B. Martin, Coincidence:Remarkable or Random, Skeptical Inquirer Volume 22.5, September / October 1998.

I. Peterson, Mathtrek, Birthday Surprises [Archived version from Jun 28 2013]

Eric Weisstein's World of Mathematics, Birthday Problem.

Mathematica

q[1][n_, d_] := q[1][n, d] = d!/((d-n)!*d^n) // N; q[k_][n_, d_] := q[k][n, d] = Sum[ n!*d!/(d^(i* k)*i!*(k!)^i*(n-i*k)!*(d-i)!)*Sum[ q[j][n-i*k, d-i]*(d-i)^(n-i* k)/d^(n-i*k), {j, 1, k-1}], {i, 1, Floor[n/k]}] // N; p[k_][n_, d_] := 1 - Sum[q[i][n, d], {i, 1, k-1}]; a[1] = 1; a[k_] := a[k] = For[n = a[k-1], True, n++, If[p[k][n, 365] >= 1/2, Return[n]]]; Table[ Print["a(", k, ") = ", a[k]]; a[k], {k, 1, 15}] (* Jean-François Alcover, Jun 12 2013, after Eric W. Weisstein *)

Crossrefs

Cf. A033810 (2 people on n days), A225852 (3 people on n days), A225871 (4 people on n days).

Cf. A088141, A182008, A182009, A182010.

Sequence in context: A044210 A044591 A050255 * A244453 A158537 A117049

Adjacent sequences: A014085 A014086 A014087 * A014089 A014090 A014091

Keyword

nonn

Author

Steven Finch

Extensions

Broken links corrected by Steven Finch, Jan 27 2009

a(16)-a(45) from Hiroaki Yamanouchi, Mar 19 2015

Status

approved