

A024222


Number of shuffles (perfect faro shuffles with cut) required to return a deck of size n to original order.


5



0, 1, 2, 2, 4, 4, 3, 3, 6, 6, 10, 10, 12, 12, 4, 4, 8, 8, 18, 18, 6, 6, 11, 11, 20, 20, 18, 18, 28, 28, 5, 5, 10, 10, 12, 12, 36, 36, 12, 12, 20, 20, 14, 14, 12, 12, 23, 23, 21, 21, 8, 8, 52, 52, 20, 20, 18, 18, 58, 58, 60, 60, 6, 6, 12, 12, 66, 66, 22, 22, 35, 35, 9, 9, 20, 20
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OFFSET

1,3


REFERENCES

Tim Folger, "Shuffling Into Hyperspace," Discover, 1991 (vol 12, no 1), pages 6667.
Martin Gardner, "Card Shuffles," Mathematical Carnival chapter 10, pages 123138. New York: Vintage Books, 1977.
S. Brent Morris, Magic Tricks, Card Shuffling and Dynamic Computer Memories, Math. Assoc. Am., 1998, p. 107.


LINKS

Table of n, a(n) for n=1..76.


EXAMPLE

a(52)=8: a deck of size 52 returns to original order in 8 perfect faro shuffles.


CROSSREFS

A002326 is really the fundamental sequence for this problem. Cf. A024542.
Sequence in context: A182923 A263856 A090277 * A196063 A205450 A215674
Adjacent sequences: A024219 A024220 A024221 * A024223 A024224 A024225


KEYWORD

easy,nonn


AUTHOR

Enoch Haga


STATUS

approved



