User blog comment:Dchew89/Possible (Uncomputable) Function with Growth Rate of w 1^CK/@comment-35470197-20190213072103/@comment-35470197-20190213133655

I agree. But I guess that there would be more restrictions, because there are infinitely many recursive functions other than \(n+1\) which sends \(0\) to a natural number in \(\{0,1\}\). Those might be restrictions on a certain expression of functions.