|
%I #40 Dec 14 2023 05:13:17
%S 1,5,11,13,9,3,1,5,11,13,9,3,1,5,11,13,9,3,1,5,11,13,9,3,1,5,11,13,9,
%T 3,1,5,11,13,9,3,1,5,11,13,9,3,1,5,11,13,9,3,1,5,11,13,9,3,1,5,11,13,
%U 9,3,1,5,11,13,9,3,1,5,11,13,9,3,1,5,11,13,9,3,1,5,11,13,9,3,1,5,11,13,9,3
%N a(n) = 5^n mod 14.
%C Period 6: repeat [1, 5, 11, 13, 9, 3].
%H G. C. Greubel, <a href="/A070369/b070369.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 (2,-2,1).
%F a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) for n>2. _R. J. Mathar_, Apr 20 2010
%F G.f.: ( 1+3*x+3*x^2 ) / ( (1-x)*(x^2-x+1) ). _R. J. Mathar_, Apr 20 2010
%F From _G. C. Greubel_, Mar 05 2016: (Start)
%F a(n) = a(n-6) for n>5.
%F E.g.f.: 7*exp(x) + (2/sqrt(3))*exp(x/2)*sin(sqrt(3)*x/2) - 6*exp(x/2)*cos(sqrt(3)*x/2). (End)
%F a(n) = (21 - 18*cos(n*Pi/3) + 2*sqrt(3)*sin(n*Pi/3))/3. - _Wesley Ivan Hurt_, Jun 27 2016
%p A070369:=n->power(5,n) mod 14: seq(A070369(n), n=0..100); # _Wesley Ivan Hurt_, Jun 27 2016
%t Table[Mod[5^n, 14], {n, 0, 100}] (* _G. C. Greubel_, Mar 05 2016 *)
%o (Sage) [power_mod(5,n,14)for n in range(0,90)] # _Zerinvary Lajos_, Nov 26 2009
%o (PARI) a(n) = lift(Mod(5, 14)^n); \\ _Michel Marcus_, Mar 05 2016
%o (Magma) [Modexp(5, n, 14): n in [0..100]]; // _Wesley Ivan Hurt_, Jun 27 2016
%Y Cf. A000351.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, May 12 2002
|
