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

1,2

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

Links

Table of n, a(n) for n=1..62.

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A000364, A045326, A080148.

Sequence in context: A321623 A375045 A077063 * A197218 A080460 A080456

Adjacent sequences: A081725 A081726 A081727 * A081729 A081730 A081731

Keyword

nonn

Author

Benoit Cloitre, Apr 06 2003

Extensions

More terms from John W. Layman, Jul 29 2005

Extended by Ray Chandler, Mar 15 2007

Status

approved