Recursive Sequences

Suppose we have a function $f$ which satisfies $f(8) = 20$, $f(20) = 5$, $f(5) = 128$, and $f(128) = 1$. Now suppose we have a sequence which satisfies $a_0 = 1$ and $a_n = f(a_{n-1})$ for $n \ge 1$. If $a_{n+4} = a_n$ for all $n\ge0$, which of these are possible values for $a_1$?