Let K be a field of characteristic zero and let G be a finitely generated subgroup of K∗. Given a P-recursive sequence f(n) taking values in K, we study the problem of when f(n) takes values in G. We show that this problem can be interpreted purely dynamically and, when one does so, one can prove a much more general result about algebraic dynamical systems. Using this framework, we can then show that the set of n for which f(n)∈G is a finite union of infinite arithmetic progressions along with a set of zero Banach density, which simultaneously generalizes a result of Methfessel and a separate result due to Bezivin.