Erdős Problem #422

`IsHofstadterQ f` means that \(f\) is Hofstadter's \(Q\)-sequence (OEIS A005185): \(f(1) = f(2) = 1\) and for \(n > 2\) \[ f(n) = f(n - f(n - 1)) + f(n - f(n - 2)), \] where the recurrence requires \(f(n - 1) < n\) and \(f(n - 2) < n\), so that both arguments on the right-hand side are positive integers. The sequence begins \(1, 1, 2, 3, 3, 4, \ldots\). At most one function satisfies this predicate. Some function satisfies it if and only if \(f(n)\) is well-defined for all \(n\), which is not known.