cp's OEIS Frontend

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

%I A036119 #49 Sep 08 2022 08:44:52
%S A036119 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,
%T A036119 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,
%U A036119 16,14,8,7,4,12,2,6,1,3,9,10
%N A036119 a(n) = 3^n mod 17.
%D A036119 I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
%H A036119 G. C. Greubel, <a href="/A036119/b036119.txt">Table of n, a(n) for n = 0..10000</a>
%H A036119 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,-1,1).
%F A036119 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
%F A036119 a(n) = a(n-1) - a(n-8) + a(n-9). - _R. J. Mathar_, Apr 13 2010
%F A036119 a(n) = a(n-16). - _Vincenzo Librandi_, Mar 26 2016
%F A036119 a(n) = 17 - a(n+8) for all n in Z. - _Michael Somos_, Oct 17 2018
%p A036119 i := pi(17) ; [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];
%t A036119 PowerMod[3, Range[0, 100], 17] (* _Vincenzo Librandi_, Mar 26 2016 *)
%o A036119 (Sage) [power_mod(3,n,17)for n in range(0, 68)] # _Zerinvary Lajos_, Nov 25 2009
%o A036119 (PARI) a(n)=lift(Mod(3,17)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o A036119 (Magma) [Modexp(3, n, 17): n in [0..100]]; // _Bruno Berselli_, Mar 23 2016
%o A036119 (Python) for n in range(0, 100): print(int(pow(3, n, 17)), end=' ') # _Stefano Spezia_, Oct 17 2018
%o A036119 (GAP) List([0..55],n->PowerMod(3,n,17)); # _Muniru A Asiru_, Oct 17 2018
%Y A036119 Cf. A000244 (3^n).
%K A036119 nonn,easy
%O A036119 0,2
%A A036119 _N. J. A. Sloane_