A083537 a(0) = a(1) = 0, a(2n) = a(n)+1, a(2n+1) = a(n-1).

0, 0, 1, 0, 2, 0, 1, 1, 3, 0, 1, 2, 2, 0, 2, 1, 4, 1, 1, 3, 2, 0, 3, 1, 3, 2, 1, 2, 3, 0, 2, 2, 5, 1, 2, 4, 2, 1, 4, 1, 3, 3, 1, 2, 4, 0, 2, 3, 4, 1, 3, 3, 2, 2, 3, 1, 4, 2, 1, 3, 3, 0, 3, 2, 6, 2, 2, 5, 3, 1, 5, 2, 3, 4, 2, 2, 5, 1, 2, 4, 4, 1, 4, 3, 2, 3, 3, 1, 5, 2, 1, 4, 3