Choose any real r >= 0. Starting with n = 1, on the first step add r, on subsequent steps either add r or take the reciprocal as you choose. For example, if r = 1/4, we can generate the sequence 1, 5/4, 3/2, 7/4, 2, 1/2, 3/4, 1. For which r is it possible to return to 1 as does this sequence?