Sorted positions of the elements of the quasicyclic group Z+(2a+1)/(2^b) [a > 0 and a < 2^(b-1), b > 0] at the ]0,1[ side of the Stern Brocot Tree (A007305/A007306).

It is easily proved that in the denominators given by A007306, the even values occur only at every third position, but can one find a simple rule for these positions of the denominators which are the powers of 2 only?