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A036139 a(n) = 5^n mod 103.

%I A036139 #21 Sep 08 2022 08:44:52
%S A036139 1,5,25,22,7,35,72,51,49,39,92,48,34,67,26,27,32,57,79,86,18,90,38,87,
%T A036139 23,12,60,94,58,84,8,40,97,73,56,74,61,99,83,3,15,75,66,21,2,10,50,44,
%U A036139 14,70,41,102,98,78,81,96,68
%N A036139 a(n) = 5^n mod 103.
%D A036139 I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
%H A036139 Vincenzo Librandi, <a href="/A036139/b036139.txt">Table of n, a(n) for n = 0..1000</a>
%H A036139 <a href="/index/Rec#order_52">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1).
%F A036139 From _G. C. Greubel_, Oct 17 2018: (Start)
%F A036139 a(n) = a(n-1) - a(n-51) + a(n-52).
%F A036139 a(n+102) = a(n). (End)
%p A036139 [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];
%t A036139 PowerMod[5, Range[0, 100], 103] (* _G. C. Greubel_, Oct 17 2018 *)
%o A036139 (Magma) [Modexp(5, n, 103): n in [0..100]]; // _Vincenzo Librandi_, Sep 13 2011
%o A036139 (PARI) a(n)=lift(Mod(5,103)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o A036139 (GAP) List([0..60],n->PowerMod(5,n,103)); # _Muniru A Asiru_, Oct 17 2018
%Y A036139 Cf. A000351 (5^n).
%K A036139 nonn,easy
%O A036139 0,2
%A A036139 _N. J. A. Sloane_