A070405 a(n) = 7^n mod 13.

1, 7, 10, 5, 9, 11, 12, 6, 3, 8, 4, 2, 1, 7, 10, 5, 9, 11, 12, 6, 3, 8, 4, 2, 1, 7, 10, 5, 9, 11, 12, 6, 3, 8, 4, 2, 1, 7, 10, 5, 9, 11, 12, 6, 3, 8, 4, 2, 1, 7, 10, 5, 9, 11, 12, 6, 3, 8, 4, 2, 1, 7, 10, 5, 9, 11, 12, 6, 3, 8, 4, 2, 1, 7, 10, 5, 9, 11, 12, 6, 3, 8, 4, 2, 1, 7, 10, 5, 9, 11, 12

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,-1,1).

Programs

Magma

[Modexp(7, n, 13): n in [0..100]]; // Bruno Berselli, Mar 22 2016

Mathematica

PowerMod[7,Range[0,90],13] (* or *) LinearRecurrence[{1,0,0,0,0,-1,1},{1,7,10,5,9,11,12},100] (* Harvey P. Dale, May 20 2014 *)

PARI

a(n) = lift(Mod(7, 13)^n); \\ Altug Alkan, Mar 20 2016

Sage

[power_mod(7,n,13) for n in range(0,91)] # Zerinvary Lajos, Nov 03 2009

Formula

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

a(n) = a(n-1) - a(n-6) + a(n-7).

G.f.: ( -1-6*x-3*x^2+5*x^3-4*x^4-2*x^5-2*x^6 ) / ( (x-1)*(x^2+1)*(x^4-x^2+1) ). (End)

a(n) = a(n-12). - G. C. Greubel, Mar 20 2016