A139355 Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k's that are even, o(n) the number that are odd; sequence gives max{e(n), o(n)}.

0, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 3, 2, 3, 1, 2, 2, 2, 2, 3, 2, 3, 1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 3, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 3, 3, 2, 3, 3, 3, 1, 2, 1, 2, 2, 3, 2, 3, 1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 4, 3, 4, 2, 3, 2, 3, 3, 4, 3, 4, 1, 2, 2