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%I #12 Sep 08 2022 08:46:16
%S 1,5,25,24,19,95,71,52,58,88,36,79,92,56,78,87,31,54,68,37,84,16,80,
%T 97,81,1,5,25,24,19,95,71,52,58,88,36,79,92,56,78,87,31,54,68,37,84,
%U 16,80,97,81,1,5,25,24,19,95,71,52,58,88,36,79,92,56,78
%N a(n) = 5^n mod 101.
%C Period 25: repeat [1, 5, 25, 24, 19, 95, 71, 52, 58, 88, 36, 79, 92, 56, 78, 87, 31, 54, 68, 37, 84, 16, 80, 97, 81].
%H Vincenzo Librandi, <a href="/A271379/b271379.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
%F G.f.: (1 +5*x +25*x^2 +24*x^3 +19*x^4 +95*x^5 +71*x^6 +52*x^7 +58*x^8 +88*x^9 +36*x^10 +79*x^11 +92*x^12 +56*x^13 +78*x^14 +87*x^15 +31*x^16 +54*x^17 +68*x^18 +37*x^19 +84*x^20 +16*x^21 +80*x^22 +97*x^23 +81*x^24)/(1-x^25).
%F a(n) = a(n-25).
%t PowerMod[5, Range[0, 100], 101]
%o (Magma) [Modexp(5, n, 101): n in [0..100]];
%o (PARI) a(n) = lift(Mod(5, 101)^n); \\ _Altug Alkan_, Apr 07 2016
%Y Cf. similar sequences listed in A271378.
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Apr 07 2016
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