A036129 - OEIS

%I #25 Sep 08 2022 08:44:52

%S 1,2,4,8,16,32,5,10,20,40,21,42,25,50,41,23,46,33,7,14,28,56,53,47,35,

%T 11,22,44,29,58,57,55,51,43,27,54,49,39,19,38,17,34,9,18,36,13,26,52,

%U 45,31,3,6,12,24,48,37,15

%N a(n) = 2^n mod 59.

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

%H G. C. Greubel, <a href="/A036129/b036129.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1).

%F a(n) = a(n+58). - _R. J. Mathar_, Jun 04 2016

%F a(n) = a(n-1) - a(n-29) + a(n-30). - _G. C. Greubel_, Oct 17 2018

%p i := pi(59) ; [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];

%t PowerMod[2, Range[0, 100], 59] (* _G. C. Greubel_, Oct 17 2018 *)

%o (PARI) a(n)=lift(Mod(2,59)^n) \\ _Charles R Greathouse IV_, Mar 22 2016

%o (Magma) [Modexp(2, n, 59): n in [0..100]]; // _G. C. Greubel_, Oct 17 2018

%o (GAP) List([0..70],n->PowerMod(2,n,59)); # _Muniru A Asiru_, Jan 30 2019

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_