Appears to be the sequence of n such that n never divides 3^x-2^x for x>=0. - Benoit Cloitre, Aug 19 2002
Numbers divisible by 2 or 3. - Nick Hobson, Mar 13 2007
Numbers k such that average of squares of the first k positive integers is not integer. A089128(a(n)) > 1. For n >= 2, a(n) = complement of A007310. - Jaroslav Krizek, May 28 2010
Numbers k such that k*Fibonacci(k) is even. - Gary Detlefs, Oct 27 2011
Also numbers that have a divisor d with 2^1 <= d < 2^2 (see Ei definition p. 340 in Besicovitch article). - Michel Marcus, Oct 31 2013
Starting with 0, 2, a(n) is the smallest number greater than a(n-1) that is not relatively prime to a(n-2). - Franklin T. Adams-Watters, Dec 04 2014
a(n) = (6*(n-1) - (1+(-1)^n)*(-1)^(n*(1+(-1)^n)/4))/4; also a(n) = (6*(n-1) - (-i)^n - i^n)/4, where i is the imaginary unit. - Bruno Berselli, Nov 08 2010
G.f.: x^2*(2-x+2*x^2) / ( (x^2+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
a(n) = floor((6*n-5)/4) + floor((1/2)*cos((n+2)*Pi/2) + 1/2). - Gary Detlefs, Oct 28 2011 and corrected by Aleksey A. Solomein, Feb 08 2016
