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

0,2

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).

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

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 *)

Prog

(Sage) [power_mod(3, n, 17)for n in range(0, 68)] # Zerinvary Lajos, Nov 25 2009
(PARI) a(n)=lift(Mod(3, 17)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(3, n, 17): n in [0..100]]; // Bruno Berselli, Mar 23 2016
(Python) for n in range(0, 100): print(int(pow(3, n, 17)), end=' ') # Stefano Spezia, Oct 17 2018
(GAP) List([0..55], n->PowerMod(3, n, 17)); # Muniru A Asiru, Oct 17 2018

Crossrefs

Cf. A000244 (3^n).

Sequence in context: A030354 A108865 A319497 * A211185 A229269 A363954

Adjacent sequences: A036116 A036117 A036118 * A036120 A036121 A036122

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved