%I #16 Sep 08 2022 08:44:52
%S 1,6,36,107,97,37,4,24,35,101,61,39,16,96,31,77,26,47,64,57,15,90,104,
%T 79,38,10,60,33,89,98,43,40,22,23,29,65,63,51,88,92,7,42,34,95,25,41,
%U 28,59,27,53,100,55,3,18,108
%N a(n) = 6^n mod 109.
%D I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
%H G. C. Greubel, <a href="/A036141/b036141.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_55">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, 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 From _G. C. Greubel_, Oct 18 2018: (Start)
%F a(n + 108) = a(n).
%F a(n) = a(n-1) - a(n-54) + a(n-55). (End)
%p [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];
%t PowerMod[6,Range[0,60],109] (* _Harvey P. Dale_, Apr 27 2018 *)
%o (PARI) a(n)=lift(Mod(6,109)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o (Magma) [Modexp(6, n, 109): n in [0..100]]; // _G. C. Greubel_, Oct 18 2018
%o (GAP) List([0..55],n->PowerMod(6,n,109)); # _Muniru A Asiru_, Oct 18 2018
%Y Cf. A000400 (6^n).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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