A055388 Number of riffle shuffles of 2n cards required to return the deck to its initial state.

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

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-François 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: 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