A070386 a(n) = 5^n mod 39.

1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1, 5, 25, 8, 1

Offset

0,2

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).

G.f.: ( -1-5*x-25*x^2-8*x^3 ) / ( (x-1)*(1+x)*(x^2+1) ). (End)

a(n) = (13*(-1)^n-3*((8+i)*(-i)^n+(8-i)*i^n)+39)/4, where i=sqrt(-1). - Bruno Berselli, Feb 07 2011

E.g.f.: (1/2)*(26*cosh(x) + 13*sinh(x) - 24*cos(x) - 3*sin(x)). - G. C. Greubel, Mar 16 2016

Mathematica

PowerMod[5, Range[0, 120], 39] (* Harvey P. Dale, Nov 19 2014 *)
(* Alternative: *)
PadRight[{}, 120, {1, 5, 25, 8}] (* Harvey P. Dale, Nov 19 2014 *)

Prog

(SageMath) [power_mod(5, n, 39) for n in range(0, 93)] # Zerinvary Lajos, Nov 26 2009
(PARI) a(n) = lift(Mod(5, 39)^n); \\ Altug Alkan, Mar 16 2016

Crossrefs

Sequence in context: A331272 A123748 A050108 * A050084 A070379 A143254

Adjacent sequences: A070383 A070384 A070385 * A070387 A070388 A070389

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, May 12 2002

Status

approved