A062116 - OEIS

%I #49 Dec 19 2024 13:21:24

%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) a(n) = { lift(Mod(2,17)^n) } \\ _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