A070370 a(n) = 5^n mod 16.

1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1, 5, 9, 13, 1

Offset

0,2

Comments

Period 4: repeat [1, 5, 9, 13].

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1). [R. J. Mathar, Apr 20 2010]

Formula

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

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

G.f.: ( 1+5*x+9*x^2+13*x^3 ) / ( (1-x)*(1+x)*(1+x^2) ). (End)

a(n) = 7-2*((1+I)*(-I)^n+(1-I)*I^n+(-1)^n). - Bruno Berselli, Feb 07 2011

E.g.f.: 5*cosh(x) + 9*sinh(x) - 4*cos(x) - 4*sin(x). - G. C. Greubel, Mar 05 2016

a(n) = A130909(A000351(n)). - Michel Marcus, Jul 06 2016

Maple

seq(op([1, 5, 9, 13]), n=0..50); # Wesley Ivan Hurt, Jul 06 2016

Mathematica

Table[Mod[5^n, 16], {n, 0, 100}] (* G. C. Greubel, Mar 05 2016 *)

Prog

(Sage) [power_mod(5, n, 16)for n in range(0, 93)] # Zerinvary Lajos, Nov 26 2009
(PARI) a(n) = lift(Mod(5, 16)^n); \\ Michel Marcus, Mar 05 2016
(Magma) &cat [[1, 5, 9, 13]^^30]; // Wesley Ivan Hurt, Jul 06 2016

Crossrefs

Cf. A000351, A130909.

Sequence in context: A314650 A220187 A073853 * A277617 A103703 A143706

Adjacent sequences: A070367 A070368 A070369 * A070371 A070372 A070373

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved