A070340 - OEIS

%I #32 Dec 07 2019 12:18:23

%S 1,2,4,8,16,32,25,11,22,5,10,20,1,2,4,8,16,32,25,11,22,5,10,20,1,2,4,

%T 8,16,32,25,11,22,5,10,20,1,2,4,8,16,32,25,11,22,5,10,20,1,2,4,8,16,

%U 32,25,11,22,5,10,20,1,2,4,8,16,32,25,11,22,5,10,20

%N a(n) = 2^n mod 39.

%H G. C. Greubel, <a href="/A070340/b070340.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,-1,1,0,0,-1,1)

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

%F a(n) = a(n-1) - a(n-4) + a(n-5) - a(n-8) + a(n-9).

%F G.f.: ( -1-x-2*x^2-4*x^3-9*x^4-17*x^5+5*x^6+10*x^7-20*x^8 ) / ( (x-1)*(1+x+x^2)*(x^2-x+1)*(x^4-x^2+1) ). (End)

%F a(n) = a(n-12). - _G. C. Greubel_, Mar 12 2016

%t PowerMod[2, Range[0, 50], 39] (* _G. C. Greubel_, Mar 12 2016 *)

%o (Sage) [power_mod(2,n,39)for n in range(0,72)] # _Zerinvary Lajos_, Nov 03 2009

%o (PARI) a(n)=lift(Mod(2,39)^n) \\ _Charles R Greathouse IV_, Mar 22 2016

%o (GAP) List([0..83],n->PowerMod(2,n,39)); # _Muniru A Asiru_, Jan 30 2019

%K nonn,easy

%O 0,2

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