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

0,2

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]

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

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 *)

Prog

(Sage) [power_mod(5, n, 17) for n in range(0, 86)] # Zerinvary Lajos, Nov 26 2009
(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
(Magma) &cat[[1, 5, 8, 6, 13, 14, 2, 10, 16, 12, 9, 11, 4, 3, 15, 7]^^5]; // Vincenzo Librandi, Mar 06 2016

Crossrefs

Cf. A000351.

Sequence in context: A145432 A335565 A365793 * A199444 A005120 A362975

Adjacent sequences: A070368 A070369 A070370 * A070372 A070373 A070374

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved