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A036122 a(n) = 2^n mod 29.

%I A036122 #43 Sep 08 2022 08:44:52
%S A036122 1,2,4,8,16,3,6,12,24,19,9,18,7,14,28,27,25,21,13,26,23,17,5,10,20,11,
%T A036122 22,15,1,2,4,8,16,3,6,12,24,19,9,18,7,14,28,27,25,21,13,26,23,17,5,10,
%U A036122 20,11,22,15,1,2,4,8,16,3
%N A036122 a(n) = 2^n mod 29.
%C A036122 The sequence is 28-periodic.
%D A036122 I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
%H A036122 G. C. Greubel, <a href="/A036122/b036122.txt">Table of n, a(n) for n = 0..10000</a>
%H A036122 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,-1,1).
%F A036122 a(n) = a(n-1) - a(n-14) + a(n-15). - _R. J. Mathar_, Feb 06 2011
%F A036122 G.f.: (-1 - x - 2*x^2 - 4*x^3 - 8*x^4 + 13*x^5 - 3*x^6 - 6*x^7 - 12*x^8 + 5*x^9 + 10*x^10 - 9*x^11 + 11*x^12 - 7*x^13 - 15*x^14) / ((x-1)*(x^2+1)*(x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1)). - _R. J. Mathar_, Feb 06 2011
%F A036122 a(n) = a(n+28). - _R. J. Mathar_, Jun 04 2016
%F A036122 a(n) = 29 - a(n+14) for all n in Z. - _Michael Somos_, Oct 17 2018
%p A036122 i := pi(29) ; [ seq(primroot(ithprime(i))^j mod ithprime(i),j=0..100) ];
%t A036122 PowerMod[2,Range[0,70],29] (* _Harvey P. Dale_, Mar 26 2012 *)
%o A036122 (Sage) [power_mod(2,n,29) for n in range(0,62)] # _Zerinvary Lajos_, Nov 03 2009
%o A036122 (PARI) a(n)=lift(Mod(2,29)^n) \\ _Charles R Greathouse IV_, Mar 22 2016
%o A036122 (Magma) [Modexp(2, n, 29): n in [0..100]]; // _G. C. Greubel_, Oct 16 2018
%o A036122 (GAP) List([0..65],n->PowerMod(2,n,29)); # _Muniru A Asiru_, Oct 18 2018
%Y A036122 Cf. A000079 (2^n).
%K A036122 nonn,easy
%O A036122 0,2
%A A036122 _N. J. A. Sloane_