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A070369 a(n) = 5^n mod 14. 1
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 (list; graph; refs; listen; history; text; internal format)
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) = (1/15)*{12*(n mod 6)+22*[(n+1) mod 6]+17*[(n+2) mod 6]+2*[(n+3) mod 6]-8*[(n+4) mod 6]-3*[(n+5) mod 6]}. - Paolo P. Lava, Feb 24 2010

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 xrange(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 * A104215 A287123 A227146

Adjacent sequences:  A070366 A070367 A070368 * A070370 A070371 A070372

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 12 2002

STATUS

approved

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Last modified November 21 05:01 EST 2017. Contains 294988 sequences.