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Search: id:A094500
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| A094500 |
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Least number k such that [ (n+1)^k / n^k ] > 2. |
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+0
33
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| 1, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 19, 20, 20, 21, 22, 22, 23, 24, 24, 25, 26, 26, 27, 28, 29, 29, 30, 31, 31, 32, 33, 33, 34, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 44, 45, 45, 46, 47, 47, 48, 49, 49, 50, 51, 51
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This sequence also describes the number of n-player games, where each player has an equal chance of winning, that need to be played for a given player to have a greater than a 50% chance of winning at least once. E.g. a(3) = 3 because in a 3-player random game, a given player will have a greater than 50% of winning at least once if 3 games are played. - Bryan Jacobs (bryanjj(AT)gmail.com), Apr 28 2006
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EXAMPLE
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a(3) = 3 because (4/3)^2 < 2 and (4/3)^3 > 2
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MATHEMATICA
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f[n_] := Block[{k = 1}, While[ Floor[((n + 1)/n)^k] != 2, k++ ]; k]; Table[ f[n], {n, 75}]
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CROSSREFS
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Cf. A002379, A094969 - A094999.
Sequence in context: A099802 A112232 A039708 this_sequence A049473 A154951 A095769
Adjacent sequences: A094497 A094498 A094499 this_sequence A094501 A094502 A094503
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KEYWORD
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easy,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), May 26 2004
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EXTENSIONS
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Definition corrected by Bryan Jacobs (bryanjj(AT)gmail.com), Apr 28 2006
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