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Search: id:A035490
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| A035490 |
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Step at which card n appears on top of deck for first time in Guy's shuffling problem A035485. |
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+0
12
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| 0, 1, 2, 8, 5, 4, 78, 37, 6, 11, 28, 12, 349, 13, 383, 10, 18, 16, 29, 17, 33, 210, 14, 133, 32, 60, 19, 106, 57, 20, 48, 26, 21, 35, 97, 217, 25, 22, 13932, 863, 205, 54, 30452, 306, 2591, 40, 44, 39, 49, 38, 51, 47, 30, 252992198, 2253, 101, 112, 246, 402, 119, 53, 139
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Card #1 is initially at the top of the deck, and next appears at the top of the deck after 3 shuffles. Here we accept 0 as a valid number of shuffles, and so we say that card #1 first shows up on top after 0 shuffles (i.e. initially). A057983 and A057984 also adopt this convention. Alternatively, we can say that card #1 first shows up on top after 3 shuffles; this leads to sequences A060750, A060751, A060752.
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REFERENCES
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D. Gale, Mathematical Entertainments: "Careful Card-Shuffling and Cutting Can Create Chaos," The Mathematical Intelligencer, vol. 14, no. 1, 1992, pages 54-56.
D. Gale, Tracking the Automatic Ant and Other Mathematical Explorations, A Collection of Mathematical Entertainments Columns from The Mathematical Intelligencer, Springer, 1998.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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MATHEMATICA
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riguy[ deck_List ] := Module[ {le=Length[ deck ]}, Flatten[ Transpose[ Reverse@ Partition[ Flatten[ {deck, le+1, le+2 } ], le/2+1 ] ] ] ]
Table[ Length[ FixedPoint[ riguy, {}, SameTest->(#2[ [ 1 ] ]=== i &) ] ]/2, {i, 2, 38} ]
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PROGRAM
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(UBASIC) 10 input N; 20 clr time; 30 I=(N-1)\2; 40 while N>1; 50 inc I; 60 if N>I then N=2*(N-I)-1 else N+=N; 70 wend; 80 print I; time; 90 goto 10;
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CROSSREFS
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Cf. A035485, A035491-A035494, A060750-A060752.
Adjacent sequences: A035487 A035488 A035489 this_sequence A035491 A035492 A035493
Sequence in context: A011058 A021782 A052240 this_sequence A019678 A115319 A122387
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KEYWORD
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nonn,nice
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be)
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EXTENSIONS
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Thanks to Colin Mallows, David W. Wilson (davidwwilson(AT)comcast.net), Wouter Meeussen and others for helping fill 3 lines - njas.
Additional comments from David W. Wilson, Apr 22, 2001.
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