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A083529 a(n) = 5^n mod 3*n.

%I A083529 #39 Sep 08 2022 08:45:10
%S A083529 2,1,8,1,5,1,5,1,26,25,5,1,5,25,35,1,5,1,5,25,62,25,5,1,50,25,80,37,5,
%T A083529 55,5,1,26,25,80,1,5,25,8,25,5,1,5,97,80,25,5,1,68,25,125,1,5,1,155,
%U A083529 25,125,25,5,145,5,25,188,1,5,181,5,13,125,205,5,1,5,25,125,169,80,181,5
%N A083529 a(n) = 5^n mod 3*n.
%C A083529 From _Robert Israel_, Dec 25 2014: (Start)
%C A083529 a(n) == (-1)^n mod 3.
%C A083529 a(n) = 1 if and only if n is even and in A067946.
%C A083529 For n > 3, a(n) = 5 if and only if n is odd and in A123091. (End)
%H A083529 Vincenzo Librandi, <a href="/A083529/b083529.txt">Table of n, a(n) for n = 1..1000</a>
%e A083529 a(3) = 8 because 5^3 = 125 and 125 mod (3 * 3) = 8.
%e A083529 a(4) = 1 because 5^4 = 625 and 625 mod (3 * 4) = 1.
%p A083529 seq(5 &^n mod 3*n, n = 1 .. 1000); # _Robert Israel_, Dec 25 2014
%t A083529 Table[Mod[5^w, 3 * w], {w, 100}]
%t A083529 Table[PowerMod[5, n, 3n], {n, 80}] (* _Harvey P. Dale_, Jul 26 2014 *)
%o A083529 (PARI) a(n)=lift(Mod(5,3*n)^n) \\ _Charles R Greathouse IV_, Oct 03 2016
%o A083529 (Magma) [Modexp(5, n, 3*n): n in [1..80]]; // _Vincenzo Librandi_, Oct 19 2018
%Y A083529 Cf. A000079, A000244, A000351, A000420, A082511, A083528, A083530, A067946, A123091.
%K A083529 easy,nonn
%O A083529 1,1
%A A083529 _Labos Elemer_, Apr 30 2003