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Search: id:A072829
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| A072829 |
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Greatest m such that product{(1 - k/m); k=1,n-1} <= 1/2. |
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+0
2
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| 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
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OFFSET
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2,1
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COMMENT
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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 C. Terr (David_C_Terr(AT)raytheon.com), Jan 03 2005
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FORMULA
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Corresponds to the ultimate occurrence of n in A033810. For large n, m has magnitude n^2/2ln2.
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EXAMPLE
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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.
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A033810, A064619.
Sequence in context: A054253 A045649 A024519 this_sequence A138226 A007979 A097701
Adjacent sequences: A072826 A072827 A072828 this_sequence A072830 A072831 A072832
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 22 2002
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 23 2002
More terms from David C. Terr (David_C_Terr(AT)raytheon.com), Jan 03 2005
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