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A036137 a(n) = 5^n mod 97.

%I A036137 #30 Sep 08 2022 08:44:52
%S A036137 1,5,25,28,43,21,8,40,6,30,53,71,64,29,48,46,36,83,27,38,93,77,94,82,
%T A036137 22,13,65,34,73,74,79,7,35,78,2,10,50,56,86,42,16,80,12,60,9,45,31,58,
%U A036137 96,92,72,69,54,76,89,57,91,67
%N A036137 a(n) = 5^n mod 97.
%D A036137 I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
%H A036137 Vincenzo Librandi, <a href="/A036137/b036137.txt">Table of n, a(n) for n = 0..1000</a>
%H A036137 <a href="/index/Rec#order_49">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,-1,1).
%F A036137 From _G. C. Greubel_, Oct 17 2018: (Start)
%F A036137 a(n) = a(n-1) - a(n-48) + a(n-49).
%F A036137 a(n+96) = a(n). (End)
%e A036137 As 5^5 = 3125 = k * 97 + 21 for some k and 0 <= 21 < 97, a(5) = 21. - _David A. Corneth_, Oct 17 2018
%p A036137 [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];
%t A036137 PowerMod[5, Range[0, 100], 97] (* _G. C. Greubel_, Oct 17 2018 *)
%o A036137 (PARI) a(n)=lift(Mod(5,97)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o A036137 (Python) for n in range(0, 100): print(int(pow(5, n, 97)), end=' ') # _Stefano Spezia_, Oct 17 2018
%o A036137 (GAP) List([0..60],n->PowerMod(5,n,97)); # _Muniru A Asiru_, Oct 17 2018
%o A036137 (Magma) [Modexp(5, n, 97): n in [0..100]]; // _G. C. Greubel_, Oct 18 2018
%Y A036137 Cf. A000351 (5^n).
%K A036137 nonn,easy
%O A036137 0,2
%A A036137 _N. J. A. Sloane_