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

0,2

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).

Formula

a(n) = (1/12)*{34*(n mod 4)+25*[(n+1) mod 4]-8*[(n+2) mod 4]+[(n+3) mod 4]}. - Paolo P. Lava, Feb 24 2010

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)

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 *)

Prog

(Sage) [power_mod(5, n, 13)for n in range(0, 93)] # Zerinvary Lajos, Nov 25 2009
(PARI) a(n)=lift(Mod(5, 13)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(5, n, 13): n in [0..100]]; // Vincenzo Librandi, Jun 29 2016

Crossrefs

Cf. A000351.

Sequence in context: A046610 A009842 A169729 * A066326 A015242 A009415

Adjacent sequences: A070365 A070366 A070367 * A070369 A070370 A070371

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved