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%I #48 Dec 14 2023 05:13:12
%S 1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,
%T 12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,
%U 1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1,5,12,8,1
%N a(n) = 5^n mod 13.
%C Period 4: repeat [1, 5, 12, 8].
%H G. C. Greubel, <a href="/A070368/b070368.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1).
%F From _R. J. Mathar_, Apr 20 2010: (Start)
%F a(n) = a(n-1) - a(n-2) + a(n-3) for n>2.
%F G.f.: ( 1+4*x+8*x^2 ) / ( (1-x)*(1+x^2) ). (End)
%F a(n) = (26-(11+3*I)*(-I)^n-(11-3*I)*I^n)/4. - _Bruno Berselli_, Feb 07 2011
%F From _G. C. Greubel_, Mar 05 2016: (Start)
%F a(n) = a(n-4) for n>3.
%F E.g.f.: (1/2)*(13*cosh(x) + 13*sinh(x) - 11*cos(x) - 3*sin(x)). (End)
%p seq(op([1, 5, 12, 8]), n=0..50); # _Wesley Ivan Hurt_, Jul 06 2016
%t Table[Mod[5^n, 13], {n, 0, 100}] (* _G. C. Greubel_, Mar 05 2016 *)
%t PowerMod[5,Range[0,100],13] (* or *) PadRight[{},100,{1,5,12,8}] (* _Harvey P. Dale_, Jul 03 2019 *)
%o (Sage) [power_mod(5,n,13) for n in range(0,93)] # _Zerinvary Lajos_, Nov 25 2009
%o (PARI) a(n)=lift(Mod(5,13)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o (Magma) [Modexp(5, n, 13): n in [0..100]]; // _Vincenzo Librandi_, Jun 29 2016
%Y Cf. A000351.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, May 12 2002
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