OFFSET
0,1
COMMENTS
For n>1: a(n) = GCD of the n-th and (n+2)-th triangular numbers = A050873(A000217(n+2), A000217(n)). - Reinhard Zumkeller, May 28 2007
From Klaus Brockhaus, May 24 2010: (Start)
Continued fraction expansion of (3+sqrt(17))/2.
Decimal expansion of 311/999. (End)
LINKS
FORMULA
a(n) = 1 + 2*[3|n] = 1 + 2(1 + 2*cos(2*n*Pi/3))/3, where [x|y] = 1 when x divides y, 0 otherwise.
a(n) = a(n-3) for n>2.
Multiplicative with a(p^e, 3) = gcd(p^e, 3). - David W. Wilson, Jun 12 2005
O.g.f.: -(3+x+x^2)/((x-1)*(x^2+x+1)). - R. J. Mathar, Nov 24 2007
Dirichlet g.f. zeta(s)*(1+2/3^s). - R. J. Mathar, Apr 08 2011
a(n) = 2*floor(((n-1) mod 3)/2) + 1. - Gary Detlefs, Dec 28 2011
a(n) = 3^(1 - sgn(n mod 3)). - Wesley Ivan Hurt, Jul 24 2016
a(n) = 3/(1 + 2*((n^2) mod 3)). - Timothy Hopper, Feb 25 2017
a(n) = (5 + 4*cos(2*n*Pi/3))/3. - Wesley Ivan Hurt, Oct 04 2018
MAPLE
MATHEMATICA
GCD[Range[0, 100], 3] (* or *) PadRight[{}, 110, {3, 1, 1}] (* Harvey P. Dale, Jun 28 2015 *)
PROG
(PARI) a(n)=gcd(n, 3) \\ Charles R Greathouse IV, Sep 24 2015
(Magma) [Gcd(n, 3) : n in [0..100]]; // Wesley Ivan Hurt, Jul 24 2016
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
STATUS
approved