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A035490 Step at which card n appears on top of deck for first time in Guy's shuffling problem A035485. 12
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; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

REFERENCES

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.

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Perfect Shuffle.

MATHEMATICA

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} ]

PROG

(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;

CROSSREFS

Cf. A035485, A035491-A035494, A060750-A060752.

Sequence in context: A021782 A155808 A052240 * A248936 A019678 A115319

Adjacent sequences:  A035487 A035488 A035489 * A035491 A035492 A035493

KEYWORD

nonn,nice

AUTHOR

Wouter Meeussen

EXTENSIONS

Thanks to Colin Mallows, David W. Wilson, Wouter Meeussen and others for helping fill 3 lines - N. J. A. Sloane.

Additional comments from David W. Wilson, Apr 22 2001

STATUS

approved

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Last modified October 18 07:58 EDT 2018. Contains 316307 sequences. (Running on oeis4.)