

A024222


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


10



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

Martin Gardner, "Card Shuffles," Mathematical Carnival chapter 10, pp. 123138. New York: Vintage Books, 1977.
S. Brent Morris, Magic Tricks, Card Shuffling and Dynamic Computer Memories, Math. Assoc. Am., 1998, p. 107.


LINKS



EXAMPLE

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


MAPLE

if n =0 then
1;
else
numtheory[order](2, 2*n+1) ;
end if;
end proc:
if n <= 1 then
n1 ;
else
end if;


MATHEMATICA

A002326 [n_] := If[n == 0, 1, MultiplicativeOrder[2, 2n+1]];


CROSSREFS

A002326 is really the fundamental sequence for this problem. Cf. A024542.


KEYWORD

easy,nonn


AUTHOR



STATUS

approved



