  In a recent post on the Seqfan list the third author proposed a conjecture
concerning the summatory function of odious numbers (i.e., of numbers whose sum
of binary digits is odd), and its analog for evil numbers (i.e., of numbers
whose sum of binary digits is even). We prove these conjectures here. We will
also study the sequences of "generalized" odious and evil numbers, and their
iterations, giving in particular a characterization of the sequences of usual
odious and evil numbers in terms of functional equations satisfied by their
compositions.
