Some More Homework

In the computer science class at the school in Byteland, the teacher handed out the following assignment as homework: "For an integer n, let bn denote the bit parity of the binary representation of n, i.e. bn=0 if n has an even number of ones when written down in the binary system, and bn=1 otherwise. The numbers bn, for n >=0, form an infinite sequence of bits (zeros and ones). Given a sequence