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a(n) = 7^n mod 17.
2

%I #34 Sep 08 2022 08:45:05

%S 1,7,15,3,4,11,9,12,16,10,2,14,13,6,8,5,1,7,15,3,4,11,9,12,16,10,2,14,

%T 13,6,8,5,1,7,15,3,4,11,9,12,16,10,2,14,13,6,8,5,1,7,15,3,4,11,9,12,

%U 16,10,2,14,13,6,8,5,1,7,15,3,4,11,9,12,16,10,2,14,13,6,8,5,1,7,15,3,4,11

%N a(n) = 7^n mod 17.

%H G. C. Greubel, <a href="/A070407/b070407.txt">Table of n, a(n) for n = 0..1000</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).

%F From _R. J. Mathar_, Apr 20 2010: (Start)

%F a(n) = a(n-1) - a(n-8) + a(n-9).

%F G.f.: ( -1-6*x-8*x^2+12*x^3-x^4-7*x^5+2*x^6-3*x^7-5*x^8 ) / ( (x-1)*(1+x^8) ). (End)

%F a(n) = a(n-16). - _G. C. Greubel_, Mar 20 2016

%t PowerMod[7,Range[0,100],17] (* _Harvey P. Dale_, Mar 20 2011 *)

%o (Sage) [power_mod(7,n,17) for n in range(0,86)] # _Zerinvary Lajos_, Nov 27 2009

%o (PARI) a(n) = lift(Mod(7, 17)^n); \\ _Altug Alkan_, Mar 20 2016

%o (Magma) [Modexp(7, n, 17): n in [0..100]]; // _Bruno Berselli_, Mar 22 2016

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, May 12 2002