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%I #27 Dec 18 2023 14:14:57
%S 1,5,25,39,23,29,16,37,13,22,24,34,41,33,36,8,40,28,11,12,17,42,38,18,
%T 4,20,14,27,6,30,21,19,9,2,10,7,35,3,15,32,31,26,1,5,25,39,23,29,16,
%U 37,13,22,24,34,41,33,36,8,40,28,11,12,17,42,38,18,4,20,14,27,6,30,21,19
%N a(n) = 5^n mod 43.
%H G. C. Greubel, <a href="/A070389/b070389.txt">Table of n, a(n) for n = 0..1000</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 From _R. J. Mathar_, Apr 20 2010: (Start)
%F a(n) = a(n-1) - a(n-21) + a(n-22).
%F G.f.: ( -1-4*x -20*x^2 -14*x^3 +16*x^4 -6*x^5 +13*x^6-21*x^7 +24*x^8 -9*x^9 -2*x^10 -10*x^11 -7*x^12 +8*x^13 -3*x^14 +28*x^15 -32*x^16 +12*x^17 +17*x^18 -x^19 -5*x^20 -26*x^21 ) / ( (x-1)*(1+x)*(x^2-x+1)*(x^6-x^5+x^4-x^3+x^2-x+1)*(x^12+x^11-x^9-x^8+x^6-x^4-x^3+x+1) ). (End)
%F a(n) = a(n-42). - _G. C. Greubel_, Mar 16 2016
%t PowerMod[5, Range[0, 50], 43] (* _G. C. Greubel_, Mar 16 2016 *)
%o (Sage) [power_mod(5,n,43) for n in range(0,74)] # _Zerinvary Lajos_, Nov 26 2009
%o (PARI) a(n)=lift(Mod(5,43)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o (Magma) [Modexp(5, n, 43): n in [0..80]]; // _Bruno Berselli_, Mar 22 2016
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, May 12 2002
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