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a(n) = 5^n mod 18.
1

%I #40 Dec 25 2023 11:24:29

%S 1,5,7,17,13,11,1,5,7,17,13,11,1,5,7,17,13,11,1,5,7,17,13,11,1,5,7,17,

%T 13,11,1,5,7,17,13,11,1,5,7,17,13,11,1,5,7,17,13,11,1,5,7,17,13,11,1,

%U 5,7,17,13,11,1,5,7,17,13,11,1,5,7,17,13,11,1,5,7,17,13,11,1,5,7,17,13

%N a(n) = 5^n mod 18.

%H G. C. Greubel, <a href="/A070372/b070372.txt">Table of n, a(n) for n = 0..999</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,-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-3) + a(n-4).

%F G.f.: ( -1-4*x-2*x^2-11*x^3 ) / ( (x-1)*(1+x)*(x^2-x+1) ). (End)

%F a(n) = a(n-6). - _G. C. Greubel_, Mar 05 2016

%t PowerMod[5,Range[0,150],18] (* _Harvey P. Dale_, Mar 24 2011 *)

%t Table[Mod[5^n, 18], {n, 0, 100}] (* _G. C. Greubel_, Mar 05 2016 *)

%o (Sage) [power_mod(5,n,18) for n in range(0,83)] # _Zerinvary Lajos_, Nov 26 2009

%o (PARI) a(n) = lift(Mod(5, 18)^n); \\ _Michel Marcus_, Mar 05 2016

%Y Cf. A000351.

%K nonn,easy

%O 0,2

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