login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A055388 Number of riffle shuffles of 2n cards required to return the deck to initial state. 2
2, 2, 4, 6, 6, 10, 12, 4, 8, 18, 6, 22, 20, 18, 28, 10, 10, 12, 36, 12, 20, 14, 12, 46, 42, 8, 52, 20, 18, 58, 60, 6, 12, 66, 22, 70, 18, 20, 30, 78, 54, 82, 8, 28, 22, 12, 10, 36, 48, 30, 100, 102, 12, 106, 36, 36, 28, 44, 12, 24, 110, 20, 100, 14, 14, 130, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Actually called overhand shuffle in the article. - Michel Marcus, Jun 22 2013

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Steve M. Cohen and Paul R. Coe, Card shuffling in discrete mathematics, The College Mathematics Journal, Vol. 26, No. 3 (May, 1995), pp. 224-227.

FORMULA

a(n) = 2*min(k) with k such that 4^k=1 mod(2n-1), see page 227 of article. - Michel Marcus, Jun 22 2013

MATHEMATICA

a[n_] := LCM[MultiplicativeOrder[2, 2n-1], 2]; Array[a, 100] (* Jean-Fran├žois Alcover, Dec 10 2015, adapted from PARI *)

PROG

(PARI) a(n)=lcm(znorder(Mod(2, 2*n-1)), 2) \\ Charles R Greathouse IV, Jun 24 2013

CROSSREFS

Sequence in context: A137268 A008130 * A065457 A280366 A000784 A092991

Adjacent sequences:  A055385 A055386 A055387 * A055389 A055390 A055391

KEYWORD

easy,nonn

AUTHOR

Robert G. Wilson v, Jul 05 2000

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified February 20 18:31 EST 2018. Contains 299381 sequences. (Running on oeis4.)