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A081728 Length of periods of Euler numbers modulo prime(n). 0
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 (list; graph; refs; listen; history; text; internal format)
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: A207975 A321623 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

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Last modified January 20 08:18 EST 2020. Contains 331081 sequences. (Running on oeis4.)