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A036120 a(n) = 2^n mod 19.

%I A036120 #36 Sep 08 2022 08:44:52
%S A036120 1,2,4,8,16,13,7,14,9,18,17,15,11,3,6,12,5,10,1,2,4,8,16,13,7,14,9,18,
%T A036120 17,15,11,3,6,12,5,10,1,2,4,8,16,13,7,14,9,18,17,15,11,3,6,12,5,10,1,
%U A036120 2,4,8,16,13,7,14,9,18,17,15
%N A036120 a(n) = 2^n mod 19.
%C A036120 The sequence can be generated via a(n) = A061762(a(n-1)). Apparently any other choice of the first element leads also to periodic sequences, with fixed points of A061762 as special cases. - _Zak Seidov_, Aug 22 2007
%D A036120 I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
%H A036120 Vincenzo Librandi, <a href="/A036120/b036120.txt">Table of n, a(n) for n = 0..1000</a>
%H A036120 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, -1, 1).
%F A036120 a(n)= +a(n-1) -a(n-9) +a(n-10). - _R. J. Mathar_, Apr 13 2010
%F A036120 G.f.: (1+x+2*x^2+4*x^3+8*x^4-3*x^5-6*x^6+7*x^7-5*x^8+10*x^9)/ ((1-x) * (1+x) * (x^2- x+1) * (x^6-x^3+1)). - _R. J. Mathar_, Apr 13 2010
%F A036120 a(n) = a(n+18). - _Vincenzo Librandi_, Sep 09 2011
%p A036120 with(numtheory) ; i := pi(19) ; [ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];
%t A036120 PowerMod[2, Range[0, 100], 19] (* _G. C. Greubel_, Oct 17 2018 *)
%o A036120 (Sage) [power_mod(2,n,19) for n in range(0,66)] # _Zerinvary Lajos_, Nov 03 2009
%o A036120 (PARI) a(n)=lift(Mod(2,19)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o A036120 (Magma) [Modexp(2, n, 19): n in [0..100]]; // _G. C. Greubel_, Oct 17 2018
%o A036120 (Python) for n in range(0, 100): print(int(pow(2, n, 19)), end=' ') # _Stefano Spezia_, Oct 17 2018
%o A036120 (GAP) List([0..60],n->PowerMod(2,n,19)); # _Muniru A Asiru_, Oct 17 2018
%Y A036120 CF. A000079 (2^n).
%K A036120 nonn,easy
%O A036120 0,2
%A A036120 _N. J. A. Sloane_