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A088141
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a(n) = the largest k such that, if k samples are taken from a group of n items, with replacement, a duplication is unlikely (p<1/2).
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7
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1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11
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OFFSET
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2,2
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COMMENTS
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Related to the birthday paradox. This is essentially the same as A033810.
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LINKS
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EXAMPLE
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a(365)=22 because if 22 people are sampled, it is unlikely that two have the same birthday; but if 23 are sampled, it is likely.
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MATHEMATICA
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lst = {}; s = 1; Do[Do[If[Product[(n - i)/n, {i, j}] <= 1/2, If[j > s, s = j]; AppendTo[lst, j]; Break[]], {j, s, s + 1}], {n, 2, 86}]; lst (* Arkadiusz Wesolowski, Apr 29 2012 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Artemario Tadeu Medeiros da Silva (artemario(AT)uol.com.br), Nov 06 2003
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EXTENSIONS
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STATUS
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approved
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