A070368 a(n) = 5^n mod 13.

1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1, 5, 12, 8, 1

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Comments

Period 4: repeat [1, 5, 12, 8].

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,-1,1).

Crossrefs

Cf. A000351.

Programs

Magma

[Modexp(5, n, 13): n in [0..100]]; // Vincenzo Librandi, Jun 29 2016

Maple

seq(op([1, 5, 12, 8]), n=0..50); # Wesley Ivan Hurt, Jul 06 2016

Mathematica

Table[Mod[5^n, 13], {n, 0, 100}] (* G. C. Greubel, Mar 05 2016 *)
PowerMod[5,Range[0,100],13] (* or *) PadRight[{},100,{1,5,12,8}] (* Harvey P. Dale, Jul 03 2019 *)

PARI

a(n)=lift(Mod(5,13)^n) \\ Charles R Greathouse IV, Mar 22 2016

Sage

[power_mod(5,n,13) for n in range(0,93)] # Zerinvary Lajos, Nov 25 2009

Formula

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

a(n) = a(n-1) - a(n-2) + a(n-3) for n>2.

G.f.: ( 1+4*x+8*x^2 ) / ( (1-x)*(1+x^2) ). (End)

a(n) = (26-(11+3*I)*(-I)^n-(11-3*I)*I^n)/4. - Bruno Berselli, Feb 07 2011

From G. C. Greubel, Mar 05 2016: (Start)

a(n) = a(n-4) for n>3.

E.g.f.: (1/2)*(13*cosh(x) + 13*sinh(x) - 11*cos(x) - 3*sin(x)). (End)