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A014088 Minimal number of people to give a 50% probability of having at least n coincident birthdays in one year. 11
1, 23, 88, 187, 313, 460, 623, 798, 985, 1181, 1385, 1596, 1813, 2035, 2263 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..15.

P. 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

I. Peterson, Mathtrek, Birthday Surprises

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-Fran├žois Alcover, Jun 12 2013, after Eric Weisstein *)

CROSSREFS

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

AUTHOR

Steven Finch

EXTENSIONS

Broken links corrected by Steven Finch, Jan 27 2009

STATUS

approved

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Last modified November 22 16:20 EST 2014. Contains 249807 sequences.