A070369 a(n) = 5^n mod 14.

1, 5, 11, 13, 9, 3, 1, 5, 11, 13, 9, 3, 1, 5, 11, 13, 9, 3, 1, 5, 11, 13, 9, 3, 1, 5, 11, 13, 9, 3, 1, 5, 11, 13, 9, 3, 1, 5, 11, 13, 9, 3, 1, 5, 11, 13, 9, 3, 1, 5, 11, 13, 9, 3, 1, 5, 11, 13, 9, 3, 1, 5, 11, 13, 9, 3, 1, 5, 11, 13, 9, 3, 1, 5, 11, 13, 9, 3, 1, 5, 11, 13, 9, 3, 1, 5, 11, 13, 9, 3

Offset

0,2

Comments

Period 6: repeat [1, 5, 11, 13, 9, 3].

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-2,1).

Formula

a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) for n>2. R. J. Mathar, Apr 20 2010

G.f.: ( 1+3*x+3*x^2 ) / ( (1-x)*(x^2-x+1) ). R. J. Mathar, Apr 20 2010

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

a(n) = a(n-6) for n>5.

E.g.f.: 7*exp(x) + (2/sqrt(3))*exp(x/2)*sin(sqrt(3)*x/2) - 6*exp(x/2)*cos(sqrt(3)*x/2). (End)

a(n) = (21 - 18*cos(n*Pi/3) + 2*sqrt(3)*sin(n*Pi/3))/3. - Wesley Ivan Hurt, Jun 27 2016

Maple

A070369:=n->power(5, n) mod 14: seq(A070369(n), n=0..100); # Wesley Ivan Hurt, Jun 27 2016

Mathematica

Table[Mod[5^n, 14], {n, 0, 100}] (* G. C. Greubel, Mar 05 2016 *)

Prog

(Sage) [power_mod(5, n, 14)for n in range(0, 90)] # Zerinvary Lajos, Nov 26 2009
(PARI) a(n) = lift(Mod(5, 14)^n); \\ Michel Marcus, Mar 05 2016
(Magma) [Modexp(5, n, 14): n in [0..100]]; // Wesley Ivan Hurt, Jun 27 2016

Crossrefs

Cf. A000351.

Sequence in context: A103068 A277136 A176821 * A357995 A104215 A287123

Adjacent sequences: A070366 A070367 A070368 * A070370 A070371 A070372

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved