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A036138 a(n) = 2^n mod 101.

%I A036138 #33 Sep 08 2022 08:44:52
%S A036138 1,2,4,8,16,32,64,27,54,7,14,28,56,11,22,44,88,75,49,98,95,89,77,53,5,
%T A036138 10,20,40,80,59,17,34,68,35,70,39,78,55,9,18,36,72,43,86,71,41,82,63,
%U A036138 25,50,100,99,97,93,85,69,37
%N A036138 a(n) = 2^n mod 101.
%D A036138 I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
%H A036138 G. C. Greubel, <a href="/A036138/b036138.txt">Table of n, a(n) for n = 0..10000</a>
%H A036138 <a href="/index/Rec#order_51">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,-1,1).
%F A036138 From _G. C. Greubel_, Oct 17 2018: (Start)
%F A036138 a(n) = a(n-1) - a(n-50) + a(n-51).
%F A036138 a(n+100) = a(n). (End)
%p A036138 [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];
%t A036138 PowerMod[2,Range[0,60],101] (* _Harvey P. Dale_, Mar 19 2013 *)
%o A036138 (PARI) a(n)=lift(Mod(2,101)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o A036138 (Magma) [Modexp(2, n, 101): n in [0..100]]; // _G. C. Greubel_, Oct 18 2018
%o A036138 (GAP) a:=List([0..60],n->PowerMod(2,n,101));; Print(a); # _Muniru A Asiru_, Jan 26 2019
%Y A036138 Cf. A000079 (2^n).
%K A036138 nonn,easy
%O A036138 0,2
%A A036138 _N. J. A. Sloane_