A070371 a(n) = 5^n mod 17.

1, 5, 8, 6, 13, 14, 2, 10, 16, 12, 9, 11, 4, 3, 15, 7, 1, 5, 8, 6, 13, 14, 2, 10, 16, 12, 9, 11, 4, 3, 15, 7, 1, 5, 8, 6, 13, 14, 2, 10, 16, 12, 9, 11, 4, 3, 15, 7, 1, 5, 8, 6, 13, 14, 2, 10, 16, 12, 9, 11, 4, 3, 15, 7, 1, 5, 8, 6, 13, 14, 2, 10, 16, 12, 9, 11, 4, 3, 15, 7, 1, 5, 8, 6, 13, 14

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Comments

Periodic with period 16 (5 is a primitive root of 17). [Joerg Arndt, Mar 06 2016]

Links

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

Crossrefs

Cf. A000351.

Programs

Magma

&cat[[1,5,8,6,13,14,2,10,16,12,9,11,4,3,15,7]^^5]; // Vincenzo Librandi, Mar 06 2016

Mathematica

PowerMod[5,Range[0,90],17] (* or *) LinearRecurrence[ {1,0,0,0,0,0,0,-1,1},{1,5,8,6,13,14,2,10,16},90] (* Harvey P. Dale, Jun 26 2013 *)
Table[Mod[5^n, 17], {n, 0, 100}] (* G. C. Greubel, Mar 05 2016 *)

PARI

a(n) = lift(Mod(5, 17)^n); \\ Michel Marcus, Mar 05 2016

PARI

x='x+O('x^100); Vec((-1-4*x-3*x^2+2*x^3-7*x^4-x^5+12*x^6-8*x^7-7*x^8)/((x-1)*(1+x^8))) \\ Altug Alkan, Mar 05 2016

Sage

[power_mod(5,n,17) for n in range(0,86)] # Zerinvary Lajos, Nov 26 2009

Formula

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

a(n) = a(n-1) - a(n-8) + a(n-9).

G.f.: (-1-4*x-3*x^2+2*x^3-7*x^4-x^5+12*x^6-8*x^7-7*x^8) / ((x-1)*(1+x^8)). (End)

a(n) = a(n-16). - G. C. Greubel, Mar 05 2016