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
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.
Programs
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Mathematica
a[n_] := LCM[MultiplicativeOrder[2, 2n-1], 2]; Array[a, 100] (* Jean-François Alcover, Dec 10 2015, adapted from PARI *)
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PARI
a(n)=lcm(znorder(Mod(2,2*n-1)),2) \\ Charles R Greathouse IV, Jun 24 2013
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
Comments