

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
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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. 224227.


FORMULA

a(n) = 2*min(k) with k such that 4^k=1 mod(2n1), see page 227 of article.  Michel Marcus, Jun 22 2013


MATHEMATICA

a[n_] := LCM[MultiplicativeOrder[2, 2n1], 2]; Array[a, 100] (* JeanFrançois Alcover, Dec 10 2015, adapted from PARI *)


PROG

(PARI) a(n)=lcm(znorder(Mod(2, 2*n1)), 2) \\ Charles R Greathouse IV, Jun 24 2013


CROSSREFS

Sequence in context: A005341 A137268 A008130 * A065457 A280366 A000784
Adjacent sequences: A055385 A055386 A055387 * A055389 A055390 A055391


KEYWORD

easy,nonn


AUTHOR

Robert G. Wilson v, Jul 05 2000


STATUS

approved



