The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
KEYWORD
easy,nonn
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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