A110270 - OEIS

%I #24 Sep 08 2022 08:45:19

%S 0,1,0,0,0,2,0,1,0,0,0,2,0,1,0,0,0,2,0,1,0,0,0,2,0,1,0,0,0,2,0,1,0,0,

%T 0,2,0,1,0,0,0,2,0,1,0,0,0,2,0,1,0,0,0,2,0,1,0,0,0,2,0,1,0,0,0,2,0,1,

%U 0,0,0,2,0,1,0,0,0,2,0,1,0,0,0,2,0,1,0,0,0,2,0,1,0,0,0,2,0,1,0,0,0,2,0,1,0

%N a(n) = (n mod 2)*(n mod 3).

%C Period 6: repeat [0, 1, 0, 0, 0, 2]. - _Joerg Arndt_, Aug 17 2014

%C Least positive integer k such that n^k == 1 (mod 6), or 0 if GCD(n,6) > 1. - _Bruno Berselli_, Mar 22 2016

%H Colin Barker, <a href="/A110270/b110270.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 a(n) = A000035(n) * A010872(n).

%F a(n) = n mod (2 + n mod 2). - _Wesley Ivan Hurt_, Aug 16 2014

%F a(n) = a(n-6) for n>5. G.f.: x*(1+2*x^4) / ((1-x)*(1+x)*(1-x+x^2)*(1+x+x^2)). - _Colin Barker_, Mar 22 2016

%F a(n) = ( 6*sin(n*Pi/3) - sqrt(3) )*( sin(n*Pi/3) + sin(2*n*Pi/3) )/6. - _Wesley Ivan Hurt_, Jun 23 2016

%p A110270:=n->(n mod 2)*(n mod 3): seq(A110270(n), n=0..100); # _Wesley Ivan Hurt_, Aug 16 2014

%t Table[Mod[n,2]Mod[n,3],{n,0,110}] (* or *) PadRight[{},110,{0,1,0,0,0,2}] (* _Harvey P. Dale_, Oct 01 2013 *)

%o (PARI) a(n) = (n % 2) * (n % 3); \\ _Michel Marcus_, Aug 17 2014

%o (Magma) &cat [[0,1,0,0,0,2]^^20]; // _Bruno Berselli_, Mar 22 2016

%o (PARI) concat(0, Vec(x*(1+2*x^4)/((1-x)*(1+x)*(1-x+x^2)*(1+x+x^2)) + O(x^50))) \\ _Colin Barker_, Mar 22 2016

%Y Cf. A000035, A010872, A110269.

%K nonn,easy

%O 0,6

%A _Reinhard Zumkeller_, Jul 18 2005