A081728 Length of periods of Euler numbers modulo prime(n).

1, 2, 2, 6, 10, 6, 8, 18, 22, 14, 30, 18, 20, 42, 46, 26, 58, 30, 66, 70, 36, 78, 82, 44, 48, 50, 102, 106, 54, 56, 126, 130, 68, 138, 74, 150, 78, 162, 166, 86, 178, 90, 190, 96, 98, 198, 210, 222, 226, 114, 116, 238, 120, 250, 128, 262, 134, 270, 138, 140, 282, 146

Offset: 1

Author

Benoit Cloitre, Apr 06 2003

Keywords

• nonn

Comments

As proved by Kummer, if the actual signed Euler numbers (A122045) are used, then the period is prime(n)-1 for n>1. - T. D. Noe, Mar 16 2007

Examples

			A000364 modulo 5=prime(3) gives : 1,1,0,1,0,1,0,1,0,1,0,... with period (1,0) of length 2, hence a(3)=2.
		

Crossrefs

Cf. A000364, A045326, A080148.

Programs

Mathematica

f[n_] := Block[{p = Prime[n], t, d = Divisors[p - 1], dk, k = 1},t = Mod[Table[Abs@EulerE[2i], {i, 2, p}], p];While[dk = d[[k]];Nand @@ Equal @@@ Partition[Partition[t, dk], 2, 1], k++ ];dk];Array[f, 63] (* Ray Chandler, Mar 15 2007 *)

Formula

a(n)=prime(n)-1 if prime(n) == 2 or 3 (mod 4)

Extensions

More terms from John W. Layman, Jul 29 2005

Extended by Ray Chandler, Mar 15 2007