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A072829
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Greatest m such that Product_{k=1..n-1} (1 - k/m) <= 1/2.
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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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COMMENTS
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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 Terr, Jan 03 2005
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LINKS
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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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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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