A070421 a(n) = 7^n mod 38.

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, 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, 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

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Comments

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

Equivalently 7^n mod 19. - Zerinvary Lajos, Nov 27 2009

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Programs

Magma

[Modexp(7, n, 19): n in [0..100]]; // Bruno Berselli, Mar 22 2016

Maple

seq(op([1, 7, 11]), n=0..50); # Wesley Ivan Hurt, Jun 29 2016

Mathematica

PowerMod[7, Range[0, 50], 38] (* G. C. Greubel, Mar 21 2016 *)

PARI

a(n)=lift(Mod(7,19)^n) \\ Charles R Greathouse IV, Mar 22 2016

Sage

[power_mod(7,n,19) for n in range(0,90)] # or:
[power_mod(7,n,38) for n in range(0,90)] # Zerinvary Lajos, Nov 27 2009

Formula

From R. J. Mathar, Apr 20 2010: (Start)

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

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

a(n) = (19 - 16*cos(2*n*Pi/3) - 4*sqrt(3)*sin(2*n*Pi/3))/3. - Wesley Ivan Hurt, Jun 29 2016