OFFSET
1,2
COMMENTS
It appears that the four sequences include every positive integer except 6, 8, 12, 21, and 33.
It appears that the sequence is asymptotic to c*n, where c = 2.8038... is the positive root of x^4+2x^3-7x^2-16x-6. (This polynomial is obtained by solving 1/x+1/(x+1)+1/(x+2)+1/(x+3) = 1.)
PROG
(PARI) al(n) = {local(u, r); u=vector(6*n); r=vector(n);
for(i=1, n, for(k=1, 4*i,
if(!u[k]&&!u[k+i]&&!u[k+2*i]&&!u[k+3*i], r[i]=k;
u[k]=u[k+i]=u[k+2*i]=u[k+3*i]=1; break)));
r}
CROSSREFS
KEYWORD
nonn
AUTHOR
Franklin T. Adams-Watters, Sep 21 2009
STATUS
approved