A070376 - OEIS

%I #38 Dec 25 2023 13:46:39

%S 1,5,25,21,1,5,25,21,1,5,25,21,1,5,25,21,1,5,25,21,1,5,25,21,1,5,25,

%T 21,1,5,25,21,1,5,25,21,1,5,25,21,1,5,25,21,1,5,25,21,1,5,25,21,1,5,

%U 25,21,1,5,25,21,1,5,25,21,1,5,25,21,1,5,25,21,1,5,25,21,1,5,25,21,1,5,25,21

%N a(n) = 5^n mod 26.

%H G. C. Greubel, <a href="/A070376/b070376.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1).

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

%F a(n) = a(n-1) - a(n-2) + a(n-3).

%F G.f.: ( -1-4*x-21*x^2 ) / ( (x-1)*(1+x^2) ). (End)

%F a(n) = 13 - 2*((3+2*i)*(-i)^n + (3-2*i)*i^n), where i = sqrt(-1). - _Bruno Berselli_, Feb 07 2011

%F From _G. C. Greubel_, Mar 13 2016: (Start)

%F a(n) = a(n-4).

%F E.g.f.: 13*exp(x) - 12*cos(x) - 8*sin(x). (End)

%p A070376:=n->5^n mod 26: seq(A070376(n), n=0..100); # _Wesley Ivan Hurt_, Mar 13 2016

%t PowerMod[5, Range[0, 50], 26] (* _G. C. Greubel_, Mar 13 2016 *)

%o (Sage) [power_mod(5,n,26) for n in range(0,84)] # _Zerinvary Lajos_, Nov 26 2009

%o (PARI) a(n)=lift(Mod(5,26)^n) \\ _Charles R Greathouse IV_, Mar 22 2016

%K nonn,easy

%O 0,2

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