Search: id:A081728
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%I A081728
%S A081728 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,
%T A081728 50,102,106,54,56,126,130,68,138,74,150,78,162,166,86,178,90,190,96,98,
%U A081728 198,210,222,226,114,116,238,120,250,128,262,134,270,138,140,282,146
%N A081728 Length of periods of Euler numbers modulo prime(n).
%C A081728 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 (noe(AT)sspectra.com), 
               Mar 16 2007
%F A081728 a(n)=prime(n)-1 if prime(n) == 2 or 3 (mod 4)
%e A081728 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.
%t A081728 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] 
               (*Chandler*)
%Y A081728 Cf. A000364, A045326, A080148.
%Y A081728 Sequence in context: A034805 A051765 A077063 this_sequence A080460 A077017 
               A127404
%Y A081728 Adjacent sequences: A081725 A081726 A081727 this_sequence A081729 A081730 
               A081731
%K A081728 nonn
%O A081728 1,2
%A A081728 Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 06 2003
%E A081728 More terms from John W. Layman (layman(AT)math.vt.edu), Jul 29 2005
%E A081728 Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Mar 15 2007

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