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%I #22 Dec 18 2023 14:15:51
%S 1,5,25,2,10,9,4,20,18,8,40,36,16,39,31,32,37,21,23,33,1,5,25,2,10,9,
%T 4,20,18,8,40,36,16,39,31,32,37,21,23,33,1,5,25,2,10,9,4,20,18,8,40,
%U 36,16,39,31,32,37,21,23,33,1,5,25,2,10,9,4,20,18,8,40,36,16,39,31,32,37
%N a(n) = 5^n mod 41.
%H G. C. Greubel, <a href="/A070387/b070387.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1, 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-10) + a(n-11).
%F G.f.: ( -1-4*x-20*x^2+23*x^3-8*x^4+x^5+5*x^6-16*x^7+2*x^8+10*x^9-33*x^10 ) / ( (x-1)*(x^2+1)*(x^8-x^6+x^4-x^2+1) ). (End)
%F a(n) = a(n-20). - _G. C. Greubel_, Mar 16 2016
%t PowerMod[5, Range[0, 50], 41] (* _G. C. Greubel_, Mar 16 2016 *)
%o (Sage) [power_mod(5,n,41) for n in range(0,77)] # _Zerinvary Lajos_, Nov 26 2009
%o (PARI) a(n) = lift(Mod(5, 41)^n); \\ _Altug Alkan_, Mar 16 2016
%K nonn
%O 0,2
%A _N. J. A. Sloane_, May 12 2002
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