A110270 a(n) = (n mod 2)*(n mod 3).

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, 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, 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

Offset: 0

Author

Reinhard Zumkeller, Jul 18 2005

Keywords

• nonn
• easy

Comments

Period 6: repeat [0, 1, 0, 0, 0, 2]. - Joerg Arndt, Aug 17 2014

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

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Crossrefs

Cf. A000035, A010872, A110269.

Programs

Magma

&cat [[0,1,0,0,0,2]^^20]; // Bruno Berselli, Mar 22 2016

Maple

A110270:=n->(n mod 2)*(n mod 3): seq(A110270(n), n=0..100); # Wesley Ivan Hurt, Aug 16 2014

Mathematica

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 *)

PARI

a(n) = (n % 2) * (n % 3); \\ Michel Marcus, Aug 17 2014

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

Formula

a(n) = A000035(n) * A010872(n).

a(n) = n mod (2 + n mod 2). - Wesley Ivan Hurt, Aug 16 2014

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

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