Binary digit distribution over naturally defined sequences
David J. Newman, Morton L. Slater · Transactions of the American Mathematical Society · 1975
In a previous paper the first author showed that multiples of 3 prefer to have an even number of ones in their binary digit expansion. In this paper it is shown that in some general classes of naturally defined sequences, the probability that a member of a particular sequence has an even number of ones in its binary expansion is 1 / 2 1/2 .