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%I #41 Sep 08 2022 08:45:05
%S 1,5,8,6,13,14,2,10,16,12,9,11,4,3,15,7,1,5,8,6,13,14,2,10,16,12,9,11,
%T 4,3,15,7,1,5,8,6,13,14,2,10,16,12,9,11,4,3,15,7,1,5,8,6,13,14,2,10,
%U 16,12,9,11,4,3,15,7,1,5,8,6,13,14,2,10,16,12,9,11,4,3,15,7,1,5,8,6,13,14
%N a(n) = 5^n mod 17.
%C Periodic with period 16 (5 is a primitive root of 17). [_Joerg Arndt_, Mar 06 2016]
%H G. C. Greubel, <a href="/A070371/b070371.txt">Table of n, a(n) for n = 0..999</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,-1,1). [From _R. J. Mathar_, Apr 20 2010]
%F From _R. J. Mathar_, Apr 20 2010: (Start)
%F a(n) = a(n-1) - a(n-8) + a(n-9).
%F G.f.: (-1-4*x-3*x^2+2*x^3-7*x^4-x^5+12*x^6-8*x^7-7*x^8) / ((x-1)*(1+x^8)). (End)
%F a(n) = a(n-16). - _G. C. Greubel_, Mar 05 2016
%t PowerMod[5,Range[0,90],17] (* or *) LinearRecurrence[ {1,0,0,0,0,0,0,-1,1},{1,5,8,6,13,14,2,10,16},90] (* _Harvey P. Dale_, Jun 26 2013 *)
%t Table[Mod[5^n, 17], {n, 0, 100}] (* _G. C. Greubel_, Mar 05 2016 *)
%o (Sage) [power_mod(5,n,17) for n in range(0,86)] # _Zerinvary Lajos_, Nov 26 2009
%o (PARI) a(n) = lift(Mod(5, 17)^n); \\ _Michel Marcus_, Mar 05 2016
%o (PARI) x='x+O('x^100); Vec((-1-4*x-3*x^2+2*x^3-7*x^4-x^5+12*x^6-8*x^7-7*x^8)/((x-1)*(1+x^8))) \\ _Altug Alkan_, Mar 05 2016
%o (Magma) &cat[[1,5,8,6,13,14,2,10,16,12,9,11,4,3,15,7]^^5]; // _Vincenzo Librandi_, Mar 06 2016
%Y Cf. A000351.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, May 12 2002
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