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%I #43 Feb 26 2024 14:02:35
%S 1,2,4,1,2,10,4,4,8,6,2,11,20,6,28,5,10,4,12,4,20,14,4,23,7,8,52,20,6,
%T 58,20,2,4,22,22,35,3,20,10,13,18,82,8,28,11,4,10,12,16,10,100,17,4,
%U 106,12,12,28,44,4,8,110,20,100,7,14,130,6,12,68,46,46,20,28,14,148,5
%N Multiplicative order of 8 mod 2n+1.
%C In the case n=2 and any other case where a(n)=A000010(2n+1), the multiplicative group of units modulo 2n+1 is cyclic and thus 8 (and any other unit) is a generator. These moduli are A167796, so this occurs whenever 2n+1 (caution: not n) is a member of A167796. - _Kellen Myers_, Feb 06 2015
%H Vincenzo Librandi, <a href="/A053451/b053451.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativeOrder.html">Multiplicative Order</a>
%e The third term a(2) is 4 because 4 is the smallest integer such that 8^4 is congruent to 1 modulo 2*2+1=5. The orbit of 8 modulo 5 is {3, 4, 2, 1}. - _Kellen Myers_, Feb 06 2015
%t Table[MultiplicativeOrder[8, n], {n, 1, 150, 2}] (* _Robert G. Wilson v_, Apr 05 2011 *)
%o (Magma) [1] cat [Modorder(8, 2*n+1): n in [1..100]]; // _Vincenzo Librandi_, Apr 01 2014
%o (PARI) vector(80, n, n--; znorder(Mod(8, 2*n+1))) \\ _Michel Marcus_, Feb 05 2015
%o (GAP) List([0..80],n->OrderMod(8,2*n+1)); # _Muniru A Asiru_, Feb 26 2019
%Y Cf. A050980, A070667-A070675, A002326, A070676, A053447, A070677, A070681, A070678, A070679, A070682, A070680, A070683.
%K nonn
%O 0,2
%A _David W. Wilson_
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