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Search: id:A161172
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| A161172 |
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a(n) is the order (or period) of the "Yummie" permutation applied to a set of n objects. |
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+0
2
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| 1, 2, 3, 3, 5, 5, 6, 7, 15, 20, 11, 24, 24, 14, 6, 28, 17, 120, 55, 180, 21, 18, 60, 42, 90, 153, 140, 429, 56, 152, 60, 70, 483, 3640, 180, 272, 72, 1260, 180, 252, 174, 1260, 36, 442, 1404, 660, 47, 496, 240, 481, 48, 98, 570, 572
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The Yummie permutation is done as follows. Start with a packet of n cards (numbered 1 to n from top to bottom), and deal them into two piles, first to a spectator (pile A), and then to yourself (pile B), saying "You, me," silently to yourself over and over. Then, pick up pile B and deal again, first to the spectator, thereby adding to the existing pile A, and then to yourself, forming a new pile B. Repeat, picking up the diminished pile B, and dealing "You, me" as before. Eventually, just one card remains in pile B; place it on top of pile A. The sequence of cards in pile A determines the Yummie permutation ("You, me" said fast sounds like "Yummie").
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LINKS
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Colm Mulcahy, The Yummie Deal and Variations , Card Colm, MAA Online, April 2009
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EXAMPLE
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a(9) = 15, because when the Yummie permutation is applied to {1,2,3,4,5,6,7,8,9} we get {6,2,4,8,9,7,5,3,1}, which corresponds to the product of a disjoint five cycle and a three cycle, and hence has order 15.
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CROSSREFS
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Cf. A161173
Sequence in context: A023816 A159237 A010761 this_sequence A093505 A146071 A167411
Adjacent sequences: A161169 A161170 A161171 this_sequence A161173 A161174 A161175
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KEYWORD
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nonn
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AUTHOR
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Colm Mulcahy (colm(AT)spelman.edu), Jun 04 2009
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