|
| |
|
|
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
|
|
|
|
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
|
|
|
|
KEYWORD
|
nonn,nice
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
