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a(n) = 2^n mod 43.
4

%I #25 Jan 29 2019 04:40:45

%S 1,2,4,8,16,32,21,42,41,39,35,27,11,22,1,2,4,8,16,32,21,42,41,39,35,

%T 27,11,22,1,2,4,8,16,32,21,42,41,39,35,27,11,22,1,2,4,8,16,32,21,42,

%U 41,39,35,27,11,22,1,2,4,8,16,32,21,42,41,39,35,27,11,22,1,2,4,8,16,32,21

%N a(n) = 2^n mod 43.

%H G. C. Greubel, <a href="/A070349/b070349.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,-1,1).

%F From _R. J. Mathar_, Feb 06 2011: (Start)

%F a(n) = a(n-1) - a(n-7) + a(n-8).

%F G.f.: ( -1-x-2*x^2-4*x^3-8*x^4-16*x^5+11*x^6-22*x^7 ) / ( (x-1)*(1+x)*(x^6-x^5+x^4-x^3+x^2-x+1) ). (End)

%F a(n) = a(n-14). - _G. C. Greubel_, Mar 11 2016

%t PowerMod[2, Range[0, 50], 43] (* _G. C. Greubel_, Mar 11 2016 *)

%o (PARI) a(n)=lift(Mod(2,43)^n) \\ _Charles R Greathouse IV_, Mar 22 2016

%o (GAP) a:=List([0..100],n->PowerMod(2,n,43));; Print(a); # _Muniru A Asiru_, Jan 28 2019

%K nonn,easy

%O 0,2

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