A070421 - OEIS

%I #46 Sep 22 2025 16:00:38

%S 1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,

%T 11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,

%U 7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11,1,7,11

%N a(n) = 7^n mod 38.

%C Period 3: repeat [1, 7, 11].

%C Equivalently 7^n mod 19. - _Zerinvary Lajos_, Nov 27 2009

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).

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

%F a(n) = a(n-3) for n>2.

%F G.f.: ( 1+7*x+11*x^2 ) / ( (1-x)*(1+x+x^2) ). (End)

%F a(n) = (19 - 16*cos(2*n*Pi/3) - 4*sqrt(3)*sin(2*n*Pi/3))/3. - _Wesley Ivan Hurt_, Jun 29 2016

%p seq(op([1, 7, 11]), n=0..50); # _Wesley Ivan Hurt_, Jun 29 2016

%t PowerMod[7, Range[0, 50], 38] (* _G. C. Greubel_, Mar 21 2016 *)

%o (SageMath) [power_mod(7,n,19) for n in range(0,90)] # or:

%o [power_mod(7,n,38) for n in range(0,90)] # _Zerinvary Lajos_, Nov 27 2009

%o (PARI) a(n)=lift(Mod(7,19)^n) \\ _Charles R Greathouse IV_, Mar 22 2016

%o (Magma) [Modexp(7, n, 19): n in [0..100]]; // _Bruno Berselli_, Mar 22 2016

%K nonn,easy

%O 0,2

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