A070387 a(n) = 5^n mod 41.

1, 5, 25, 2, 10, 9, 4, 20, 18, 8, 40, 36, 16, 39, 31, 32, 37, 21, 23, 33, 1, 5, 25, 2, 10, 9, 4, 20, 18, 8, 40, 36, 16, 39, 31, 32, 37, 21, 23, 33, 1, 5, 25, 2, 10, 9, 4, 20, 18, 8, 40, 36, 16, 39, 31, 32, 37, 21, 23, 33, 1, 5, 25, 2, 10, 9, 4, 20, 18, 8, 40, 36, 16, 39, 31, 32, 37

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn

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, 0, 0, 0, 0, -1, 1).

Programs

Mathematica

PowerMod[5, Range[0, 50], 41] (* G. C. Greubel, Mar 16 2016 *)

PARI

a(n) = lift(Mod(5, 41)^n); \\ Altug Alkan, Mar 16 2016

Sage

[power_mod(5,n,41) for n in range(0,77)] # Zerinvary Lajos, Nov 26 2009

Formula

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

a(n) = a(n-1) - a(n-10) + a(n-11).

G.f.: ( -1-4*x-20*x^2+23*x^3-8*x^4+x^5+5*x^6-16*x^7+2*x^8+10*x^9-33*x^10 ) / ( (x-1)*(x^2+1)*(x^8-x^6+x^4-x^2+1) ). (End)

a(n) = a(n-20). - G. C. Greubel, Mar 16 2016