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

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

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]

Crossrefs

Cf. A000351, A130909.

Programs

Magma

&cat [[1, 5, 9, 13]^^30]; // Wesley Ivan Hurt, 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 *)

PARI

a(n) = lift(Mod(5, 16)^n); \\ Michel Marcus, Mar 05 2016

Sage

[power_mod(5,n,16)for n in range(0,93)] # Zerinvary Lajos, Nov 26 2009

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