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a(n) = 3^n mod 43.
3

%I #33 Sep 08 2022 08:44:52

%S 1,3,9,27,38,28,41,37,25,32,10,30,4,12,36,22,23,26,35,19,14,42,40,34,

%T 16,5,15,2,6,18,11,33,13,39,31,7,21,20,17,8,24,29,1,3,9,27,38,28,41,

%U 37,25,32,10,30,4,12,36,22,23,26

%N a(n) = 3^n mod 43.

%D I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.

%H G. C. Greubel, <a href="/A036126/b036126.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_22">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,-1,1).

%F a(n) = a(n-1) - a(n-21) + a(n-22). - _R. J. Mathar_, Feb 08 2011

%F a(n) = a(n+42). - _R. J. Mathar_, Jun 04 2016

%F a(n) = 43 - a(n+21) for all n in Z. - _Michael Somos_, Oct 17 2018

%p i := pi(43) ; [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];

%t PowerMod[3, Range[0, 100], 43] (* _G. C. Greubel_, Oct 16 2018 *)

%t PadRight[{},120,{1,3,9,27,38,28,41,37,25,32,10,30,4,12,36,22,23,26,35,19,14,42,40,34,16,5,15,2,6,18,11,33,13,39,31,7,21,20,17,8,24,29}] (* _Harvey P. Dale_, Mar 30 2019 *)

%o (PARI) a(n)=lift(Mod(3,43)^n) \\ _Charles R Greathouse IV_, Mar 22 2016

%o (Magma) [Modexp(3, n, 43): n in [0..100]]; // _G. C. Greubel_, Oct 18 2018

%o (GAP) List([0..60],n->PowerMod(3,n,43)); # _Muniru A Asiru_, Oct 18 2018

%Y Cf. A000244 (3^n).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_