A100480 a(1)=1 and, for n>1, a(n) is the smallest positive integer such that the subset S(c) of {1,2,3,...,n} defined by S(c)={k|1<=k<=n; a(k)=c} does not contain a 3-term arithmetic progression for any integer c.

1, 1, 2, 1, 1, 2, 2, 3, 3, 1, 1, 2, 1, 1, 2, 2, 3, 3, 2, 3, 3, 4, 4, 5, 4, 4, 5, 1, 1, 2, 1, 1, 2, 2, 3, 3, 1, 1, 2, 1, 1, 2, 2, 3, 3, 2, 3, 3, 4, 4, 5, 4, 4, 5, 2, 3, 3, 4, 4, 5, 4, 4, 5, 5, 6, 6, 5, 6, 6, 7, 7, 8, 5, 6, 6, 5, 6, 6, 7, 7, 8, 1, 1, 2, 1, 1, 2, 2, 3, 3, 1, 1, 2, 1, 1, 2, 2, 3, 3, 2, 3, 3, 4, 4, 5