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A036135 a(n) = 2^n mod 83.

%I A036135 #32 Sep 08 2022 08:44:52
%S A036135 1,2,4,8,16,32,64,45,7,14,28,56,29,58,33,66,49,15,30,60,37,74,65,47,
%T A036135 11,22,44,5,10,20,40,80,77,71,59,35,70,57,31,62,41,82,81,79,75,67,51,
%U A036135 19,38,76,69,55,27,54,25,50,17
%N A036135 a(n) = 2^n mod 83.
%D A036135 I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
%H A036135 G. C. Greubel, <a href="/A036135/b036135.txt">Table of n, a(n) for n = 0..10000</a>
%H A036135 <a href="/index/Rec#order_42">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,-1,1).
%F A036135 From _G. C. Greubel_, Oct 17 2018: (Start)
%F A036135 a(n) = a(n-1) - a(n-41) + a(n-42).
%F A036135 a(n+82) = a(n). (End)
%p A036135 [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];
%t A036135 PowerMod[2, Range[0, 100], 83] (* _G. C. Greubel_, Oct 17 2018 *)
%o A036135 (PARI) a(n)=lift(Mod(2,83)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o A036135 (Python) for n in range(0, 100): print(int(pow(2, n, 83)), end=' ') # _Stefano Spezia_, Oct 17 2018
%o A036135 (GAP) List([0..60],n->PowerMod(2,n,83)); # _Muniru A Asiru_, Oct 17 2018
%o A036135 (Magma) [Modexp(2, n, 83): n in [0..100]]; // _G. C. Greubel_, Oct 18 2018
%Y A036135 CF. A000079 (2^n).
%K A036135 nonn,easy
%O A036135 0,2
%A A036135 _N. J. A. Sloane_