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%I #27 Sep 08 2022 08:44:52
%S 1,3,9,27,19,26,16,17,20,29,25,13,8,24,10,30,28,22,4,12,5,15,14,11,2,
%T 6,18,23,7,21,1,3,9,27,19,26,16,17,20,29,25,13,8,24,10,30,28,22,4,12,
%U 5,15,14,11,2,6,18,23,7,21,1,3
%N a(n) = 3^n mod 31.
%D I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
%H G. C. Greubel, <a href="/A036123/b036123.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).
%F a(n) = a(n+30). - _R. J. Mathar_, Jun 04 2016
%F a(n) = a(n-1) - a(n-15) + a(n-16). - _G. C. Greubel_, Oct 16 2018
%F a(n) = 31 - a(n+15) for all n in Z. - _Michael Somos_, Oct 17 2018
%p [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];
%t PowerMod[3, Range[0, 100], 31] (* _G. C. Greubel_, Oct 16 2018 *)
%o (PARI) a(n)=lift(Mod(3,31)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o (Magma) [Modexp(3, n, 31): n in [0..100]]; // _G. C. Greubel_, Oct 18 2018
%o (GAP) List([0..65],n->PowerMod(3,n,31)); # _Muniru A Asiru_, Oct 18 2018
%Y Cf. A000244 (3^n).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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