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Search: id:A109630
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| A109630 |
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The winning position when playing the "eenie meenie mini moe" game with n players. |
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1
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| 1, 1, 3, 3, 1, 3, 4, 4, 3, 1, 9, 5, 13, 7, 15, 7, 15, 5, 13, 1, 9, 17, 2, 10, 18, 26, 7, 15, 23, 1, 9, 17, 25, 33, 6, 14, 22, 30, 38, 6, 14, 22, 30, 38, 1, 9, 17, 25, 33, 41, 49, 5, 13, 21, 29, 37, 45, 53, 2, 10, 18, 26, 34, 42, 50, 58, 66, 6, 14, 22, 30, 38, 46, 54, 62, 70, 1, 9, 17, 25
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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A version of the Josephus sieve - see for example A000960. - N. J. A. Sloane (njas(AT)research.att.com), May 26 2007
In this game, all the children start standing in front of a chair and the teacher will chant "eenie-meenie-mini-moe..." and eliminate every eighth player, who then has to sit. The game continues until only one child remains standing. He or she is declared the winner.
The multiples of 8 never appear in this sequence because they are always wiped out in the first round.
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FORMULA
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For n > 5: If P(n-1) + 8 > n, P(n) = P(n-1) + 8 - n, else P(n) = P(n-1) + 8.
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EXAMPLE
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For n = 4 the winner is the third kid because:
1, 2, 3, 4, 1, 2, 3, X (The fourth is eliminated)
1, 2, 3, 1, 2, 3, 1, X (The second is eliminated)
3, 1, 3, 1, 3, 1, 3, X (The first is eliminated, therefore #3 wins)"
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CROSSREFS
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Sequence in context: A161200 A110766 A166314 this_sequence A080094 A002332 A002102
Adjacent sequences: A109627 A109628 A109629 this_sequence A109631 A109632 A109633
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KEYWORD
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nonn,easy,new
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AUTHOR
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Sergio Pimentel (ferdiego(AT)cox-internet.com), Aug 02 2005
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EXTENSIONS
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Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Nov 11 2009
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