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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES Martin Gardner, "Card Shuffles," Mathematical Carnival chapter 10, pp. 123-138. 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. Tim Folger, Shuffling Into Hyperspace, Discover, 1991 (vol. 12, no. 1), pp. 66-67. EXAMPLE a(52)=8: a deck of size 52 returns to its original order in 8 perfect faro shuffles. MAPLE A002326 := proc(n) if n =0 then 1; else numtheory[order](2, 2*n+1) ; end if; end proc: A024222 := proc(n) if n <= 1 then n-1 ; else A002326(floor((n-1)/2)) ; end if; end proc: # R. J. Mathar, Nov 14 2018 MATHEMATICA A002326 [n_] := If[n == 0, 1, MultiplicativeOrder[2, 2n+1]]; A024222[n_] := If[n <= 1 , n-1, A002326[Floor[(n-1)/2]]]; Table[A024222[n], {n, 1, 76}] (* Jean-François Alcover, May 05 2023, after R. J. Mathar *) CROSSREFS A002326 is really the fundamental sequence for this problem. Cf. A024542. Sequence in context: A263856 A090277 A324662 * A196063 A205450 A215674 Adjacent sequences: A024219 A024220 A024221 * A024223 A024224 A024225 KEYWORD easy,nonn AUTHOR Enoch Haga STATUS approved

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Last modified May 22 21:38 EDT 2024. Contains 372758 sequences. (Running on oeis4.)