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

0,2

Comments

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

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

Links

Table of n, a(n) for n=0..89.

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

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

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 *)

Prog

(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
(PARI) a(n)=lift(Mod(7, 19)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(7, n, 19): n in [0..100]]; // Bruno Berselli, Mar 22 2016

Crossrefs

Sequence in context: A133346 A091920 A036934 * A213671 A050081 A144076

Adjacent sequences: A070418 A070419 A070420 * A070422 A070423 A070424

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved