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A036133 a(n) = 5^n mod 73.

%I A036133 #23 Sep 08 2022 08:44:52
%S A036133 1,5,25,52,41,59,3,15,2,10,50,31,9,45,6,30,4,20,27,62,18,17,12,60,8,
%T A036133 40,54,51,36,34,24,47,16,7,35,29,72,68,48,21,32,14,70,58,71,63,23,42,
%U A036133 64,28,67,43,69,53,46,11,55,56
%N A036133 a(n) = 5^n mod 73.
%D A036133 I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
%H A036133 G. C. Greubel, <a href="/A036133/b036133.txt">Table of n, a(n) for n = 0..10000</a>
%H A036133 <a href="/index/Rec#order_37">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,-1,1).
%F A036133 From _G. C. Greubel_, Oct 17 2018: (Start)
%F A036133 a(n) = a(n-1) - a(n-36) + a(n-37).
%F A036133 a(n+72) = a(n). (End)
%p A036133 [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];
%t A036133 PowerMod[5,Range[0,60],73] (* _Harvey P. Dale_, Dec 24 2011 *)
%o A036133 (PARI) a(n)=lift(Mod(5,73)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o A036133 (Magma) [Modexp(5, n, 73): n in [0..100]]; // _G. C. Greubel_, Oct 17 2018
%o A036133 (Python) for n in range(0, 100): print(int(pow(5, n, 73)), end=' ') # _Stefano Spezia_, Oct 17 2018
%o A036133 (GAP) List([0..60],n->PowerMod(5,n,73)); # _Muniru A Asiru_, Oct 17 2018
%Y A036133 Cf. A000351 (5^n).
%K A036133 nonn,easy
%O A036133 0,2
%A A036133 _N. J. A. Sloane_