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A271378 a(n) = 5^n mod 31.

%I A271378 #24 Sep 08 2022 08:46:16
%S A271378 1,5,25,1,5,25,1,5,25,1,5,25,1,5,25,1,5,25,1,5,25,1,5,25,1,5,25,1,5,
%T A271378 25,1,5,25,1,5,25,1,5,25,1,5,25,1,5,25,1,5,25,1,5,25,1,5,25,1,5,25,1,
%U A271378 5,25,1,5,25,1,5,25,1,5,25,1,5,25,1,5,25,1,5,25
%N A271378 a(n) = 5^n mod 31.
%C A271378 Period 3: repeat [1, 5, 25].
%H A271378 Vincenzo Librandi, <a href="/A271378/b271378.txt">Table of n, a(n) for n = 0..1000</a>
%H A271378 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F A271378 G.f.: (1+5*x+25*x^2)/(1-x^3).
%F A271378 a(n) = a(n-3) for n>2.
%F A271378 a(n) = 5^(n mod 3).
%F A271378 a(n) = (31 - 28*cos(2*n*Pi/3) - 20*sqrt(3)*sin(2*n*Pi/3))/3. - _Wesley Ivan Hurt_, Jun 30 2016
%p A271378 seq(op([1, 5, 25]), n=0..50); # _Wesley Ivan Hurt_, Jun 30 2016
%t A271378 PowerMod[5, Range[0, 100], 31]
%o A271378 (Magma) [Modexp(5, n, 31): n in [0..100]];
%o A271378 (Magma) &cat [[1,5,25]^^30]; // _Bruno Berselli_, Apr 07 2016
%o A271378 (PARI) x='x+O('x^99); Vec((1+5*x+25*x^2)/(1-x^3)) \\ _Altug Alkan_, Apr 06 2016
%Y A271378 Cf. similar sequences of the type 5^n mod p, where p is a prime: A070365 (p=7), A070367 (p=11), A070368 (p=13), A070371 (p=17), A070373 (p=19), A036121 (p=23), A070379 (p=29), this sequence (p=31), A070384 (p=37), A070387 (p=41), A070389 (p=43), A036127 (p=47), A036133 (p=73), A036137 (p=97), A271379 (p=101), A036139 (p=103), A036149 (p=157), A271380 (p=163) A036151 (p=167), A036156 (p=193).
%K A271378 nonn,easy
%O A271378 0,2
%A A271378 _Vincenzo Librandi_, Apr 06 2016
%E A271378 Edited by _Bruno Berselli_, Apr 07 2016