A204671 - OEIS

%I #39 Sep 08 2022 08:46:01

%S 1,1,4,3,4,5,0,1,4,3,4,5,0,1,4,3,4,5,0,1,4,3,4,5,0,1,4,3,4,5,0,1,4,3,

%T 4,5,0,1,4,3,4,5,0,1,4,3,4,5,0,1,4,3,4,5,0,1,4,3,4,5,0,1,4,3,4,5,0,1,

%U 4,3,4,5,0,1,4,3,4,5,0,1,4,3,4,5,0,1,4

%N a(n) = n^n (mod 6).

%C For n>0, periodic with period 6 = A174824: repeat [1, 4, 3, 4, 5, 0].

%H Andrew Howroyd, <a href="/A204671/b204671.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).

%F G.f.: (x^6-5*x^5-4*x^4-3*x^3-4*x^2-x-1)/((x-1)*(x+1)*(x^2-x+1)*(x^2+x+1)). [_Colin Barker_, Jul 20 2012]

%F From _Wesley Ivan Hurt_, Jun 23 2016: (Start)

%F a(n) = a(n-6) for n>5.

%F a(0) = 1, a(n) = (17 - cos(n*Pi) - 8*cos(n*Pi/3) - 8*cos(2*n*Pi/3) - 4*sqrt(3)*sin(n*Pi/3) - 4*sqrt(3)*sin(2*n*Pi/3))/6 for n>0. (End)

%F a(n) = A010875(A000312(n)). - _Michel Marcus_, Jun 27 2016

%p A204671:=n->[1, 4, 3, 4, 5, 0][(n mod 6)+1]: 1, seq(A204671(n), n=0..100); # _Wesley Ivan Hurt_, Jun 23 2016

%t Table[PowerMod[n,n,6], {n,0,140}]

%t Join[{1},LinearRecurrence[{0, 0, 0, 0, 0, 1},{1, 4, 3, 4, 5, 0},86]] (* _Ray Chandler_, Aug 26 2015 *)

%o (Magma) [1] cat &cat [[1, 4, 3, 4, 5, 0]^^20]; // _Wesley Ivan Hurt_, Jun 23 2016

%o (PARI) a(n)=lift(Mod(n, 6)^n) \\ _Andrew Howroyd_, Feb 25 2018

%Y Cf. A000312, A010875, A174824, A204690.

%K nonn,easy

%O 0,3

%A _José María Grau Ribas_, Jan 18 2012