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%I #46 Feb 19 2024 10:31:14
%S 1,2,4,8,16,15,13,9,1,2,4,8,16,15,13,9,1,2,4,8,16,15,13,9,1,2,4,8,16,
%T 15,13,9,1,2,4,8,16,15,13,9,1,2,4,8,16,15,13,9,1,2,4,8,16,15,13,9,1,2,
%U 4,8,16,15,13,9,1,2,4,8,16,15,13,9,1,2,4,8,16,15,13,9,1,2,4,8,16,15,13
%N a(n) = 2^n mod 17.
%C Period 8.
%D I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
%H Harry J. Smith, <a href="/A062116/b062116.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,-1,1).
%F From _R. J. Mathar_, Apr 13 2010: (Start)
%F a(n) = a(n-1) - a(n-4) + a(n-5).
%F G.f.: (1 + x + 2*x^2 + 4*x^3 + 9*x^4)/((1-x)*(1+x^4)). (End)
%F a(n) = 17 - a(n+4) = a(n+8) for all n in Z. - _Michael Somos_, Oct 17 2018
%e a(5) = 32 mod 17 = 15.
%t Mod[#,17]&/@(2^Range[0,100]) (* _Harvey P. Dale_, Mar 06 2011 *)
%o (PARI) { for (n=0, 1000, write("b062116.txt", n, " ", 2^n%17) ) } \\ _Harry J. Smith_, Aug 01 2009
%o (Sage) [power_mod(2,n,17) for n in range(0,87)] # _Zerinvary Lajos_, Nov 03 2009
%o (Magma) [2^n mod 17: n in [0..100]]; // _G. C. Greubel_, Oct 16 2018
%o (GAP) a:=List([0..70],n->PowerMod(2,n,17));; Print(a); # _Muniru A Asiru_, Jan 29 2019
%Y Cf. A036117, A036118.
%K nonn,easy
%O 0,2
%A _Olivier Gérard_, Jun 06 2001
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