A072829 Greatest m such that Product_{k=1..n-1} (1 - k/m) <= 1/2.

2, 5, 9, 16, 23, 32, 42, 54, 68, 82, 99, 116, 135, 156, 178, 201, 226, 252, 280, 309, 340, 372, 406, 441, 477, 515, 554, 595, 637, 681, 726, 772, 820, 869, 920, 973, 1026, 1081, 1138, 1196, 1256, 1316, 1379, 1443, 1508, 1575, 1643, 1712, 1783, 1856, 1930, 2005

Offset

2,1

Comments

Among n randomly selected dates over an interval of m days (or less), the odds are even (or better than even) for two or more of them to coincide.

Halley's Comet appeared in exactly one year between each of the last 9 given entries of this sequence, i.e. a(45) to a(53). - David Terr, Jan 03 2005

Links

Table of n, a(n) for n=2..53.

Formula

Corresponds to the ultimate occurrence of n in A033810. For large n, m has magnitude n^2/2ln2.

Example

Thus a(7)=32 for instance implies that among 7 persons bearing the same astrological sign(extending over 30 days or so) the odds are trifle better than even for at least two of them further sharing a common birthday.

Mathematica

f[n_] := (k = 1; While[ Product[1 - i/k, {i, 1, (n - 1)}] <= 1/2, k++ ]; Return[k - 1]); Table[ f[n], {n, 2, 53}]

Crossrefs

Cf. A033810, A064619.

Sequence in context: A024519 A160664 A345140 * A169740 A360419 A282044

Adjacent sequences: A072826 A072827 A072828 * A072830 A072831 A072832

Keyword

nonn

Author

Lekraj Beedassy, Jul 22 2002

Extensions

Edited and extended by Robert G. Wilson v, Jul 23 2002

More terms from David Terr, Jan 03 2005

Status

approved