A070373 a(n) = 5^n mod 19.

1, 5, 6, 11, 17, 9, 7, 16, 4, 1, 5, 6, 11, 17, 9, 7, 16, 4, 1, 5, 6, 11, 17, 9, 7, 16, 4, 1, 5, 6, 11, 17, 9, 7, 16, 4, 1, 5, 6, 11, 17, 9, 7, 16, 4, 1, 5, 6, 11, 17, 9, 7, 16, 4, 1, 5, 6, 11, 17, 9, 7, 16, 4, 1, 5, 6, 11, 17, 9, 7, 16, 4, 1, 5, 6, 11, 17, 9, 7, 16, 4, 1, 5, 6, 11, 17, 9, 7, 16

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn

Comments

Period 9: repeat [1, 5, 6, 11, 17, 9, 7, 16, 4].

Links

• G. C. Greubel, Table of n, a(n) for n = 0..999
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1). [_R. J. Mathar_, Apr 20 2010]

Crossrefs

Cf. A000351.

Programs

Magma

[Modexp(5, n, 19): n in [0..100]]; // Vincenzo Librandi, Jun 29 2016

Mathematica

PowerMod[5,Range[0,100],19] (* Harvey P. Dale, Aug 18 2015 *)
PadRight[{},100,{1,5,6,11,17,9,7,16,4}] (* Harvey P. Dale, Aug 18 2015 *)

PARI

a(n) = lift(Mod(5, 19)^n); \\ Michel Marcus, Mar 05 2016

Sage

[power_mod(5,n,19) for n in range(0,89)] # Zerinvary Lajos, Nov 26 2009

Formula

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

a(n) = a(n-9).

G.f.: ( -1-5*x-6*x^2-11*x^3-17*x^4-9*x^5-7*x^6-16*x^7-4*x^8 ) / ( (x-1)*(1+x+x^2)*(x^6+x^3+1) ). (End)