A036119 a(n) = 3^n mod 17.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,-1,1).

Crossrefs

Cf. A000244 (3^n).

Programs

GAP

List([0..55],n->PowerMod(3,n,17)); # Muniru A Asiru, Oct 17 2018

Magma

[Modexp(3, n, 17): n in [0..100]]; // Bruno Berselli, Mar 23 2016

Maple

i := pi(17) ; [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];

Mathematica

PowerMod[3, Range[0, 100], 17] (* Vincenzo Librandi, Mar 26 2016 *)

PARI

a(n)=lift(Mod(3,17)^n) \\ Charles R Greathouse IV, Mar 22 2016

Python

for n in range(0, 100): print(int(pow(3, n, 17)), end=' ') # Stefano Spezia, Oct 17 2018

Sage

[power_mod(3,n,17)for n in range(0, 68)] # Zerinvary Lajos, Nov 25 2009

Formula

G.f.: (1 + 2*x + 6*x^2 + x^3 + 3*x^4 - 8*x^5 + 10*x^6 - 4*x^7 + 6*x^8)/ ((1-x) * (1+x^8)). - R. J. Mathar, Apr 13 2010

a(n) = a(n-1) - a(n-8) + a(n-9). - R. J. Mathar, Apr 13 2010

a(n) = a(n-16). - Vincenzo Librandi, Mar 26 2016

a(n) = 17 - a(n+8) for all n in Z. - Michael Somos, Oct 17 2018