  An immediate corollary is that the complexity function \(C\) is not a recursive function. If it were, for any \(n\), we could effectively compute \(C(\sigma)\) for any \(\sigma\) of length \(n\). By simply listing all such sequences, we could halt after finding the first \(\sigma\) for which \(C(\sigma) \ge n\). But then we could effectively produce a random sequence, contrary to theorem  5.