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A070368 a(n) = 5^n mod 13. 3
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 (list; graph; refs; listen; history; text; internal format)
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 *)

PROG

(Sage) [power_mod(5, n, 13)for n in xrange(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

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Last modified September 26 04:27 EDT 2017. Contains 292502 sequences.