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A036140 a(n) = 2^n mod 107.

%I A036140 #26 Sep 08 2022 08:44:52
%S A036140 1,2,4,8,16,32,64,21,42,84,61,15,30,60,13,26,52,104,101,95,83,59,11,
%T A036140 22,44,88,69,31,62,17,34,68,29,58,9,18,36,72,37,74,41,82,57,7,14,28,
%U A036140 56,5,10,20,40,80,53,106,105,103
%N A036140 a(n) = 2^n mod 107.
%C A036140 Cyclical with a cycle length of 106. - _Harvey P. Dale_, May 07 2013
%D A036140 I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
%H A036140 Vincenzo Librandi, <a href="/A036140/b036140.txt">Table of n, a(n) for n = 0..1000</a>
%H A036140 <a href="/index/Rec#order_54">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, -1, 1).
%F A036140 From _G. C. Greubel_, Oct 18 2018: (Start)
%F A036140 a(n+106) = a(n).
%F A036140 a(n) = a(n-1) - a(n-53) + a(n-54). (End)
%p A036140 [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];
%t A036140 PowerMod[2,Range[0,60],107] (* _Harvey P. Dale_, May 07 2013 *)
%o A036140 (PARI) a(n)=lift(Mod(2,107)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o A036140 (Magma) [Modexp(2, n, 107): n in [0..100]]; // _G. C. Greubel_, Oct 18 2018
%o A036140 (GAP) List([0..55],n->PowerMod(2,n,107)); # _Muniru A Asiru_, Oct 18 2018
%Y A036140 Cf. A000079 (2^n).
%K A036140 nonn,easy
%O A036140 0,2
%A A036140 _N. J. A. Sloane_