I'm trying to find $R_n$, where $R_n$ is the parameter for the discrete logistic map $x_{n+1} = rx_n(1-x_n)$ such that it has a superstable cycle of period $2^n$. I know that I can do this by composing the function with itself, but my textbook describes an "implicit but exact" formula for $R_n$ in terms of $x=\frac{1}{2}$ and the logistic map, so it might be possible to do better.
I haven't been able to think of a way to do this, so any help would be greatly appreciated