A002139 Shuffling 2n cards. (Formerly M0737 N0276)

2, 3, 5, 12, 14, 11, 13, 20, 72, 19, 42, 132, 84, 114, 29, 30, 110, 156, 37, 156, 420, 210, 156, 552, 462, 72, 53, 420, 342, 59, 61, 42, 156, 67, 506, 1260, 90, 420, 930, 1560, 990, 83, 72, 812, 132, 156, 110, 1332, 2352, 930, 101, 2652, 156

Offset

1,1

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..5000

S. W. Golomb, Permutations by cutting and shuffling, SIAM Rev., 3 (1961), 293-297.

Formula

a(n) = (f(n)+1) * phi(p^(k-1)) if 2 is primitive mod 2n-1 in which case necessarily 2n-1=p^k, p prime; otherwise, a(n) = lcm(f(n), f(n)+1), where f(n) = A002326(n-1). - Sean A. Irvine, Jul 17 2013

Mathematica

f[n_] := MultiplicativeOrder[2, 2*n-1]; a[n_] := If[f[n] == EulerPhi[2*n-1], {p, k} = FactorInteger[2*n-1] // First; (f[n]+1)*EulerPhi[p^(k-1)], LCM[f[n], f[n]+1]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Mar 06 2014, after Sean A. Irvine *)

Crossrefs

Cf. A002326.

Sequence in context: A158936 A271227 A293696 * A140489 A331101 A193776

Adjacent sequences: A002136 A002137 A002138 * A002140 A002141 A002142

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Jul 17 2013

Status

approved