User blog comment:Boboris02/MBOT/@comment-1605058-20161220212557/@comment-30118230-20161221160458

Ok.I can give you many examples.And in fact I have infinitly many to choose from.

Does it need to be uncomputable though?

Anyway I will give you an example for both.

Computable example:\(\Phi(n) = n \neg n \Leftrightarrow k \Leftrightarrow m = k+7\)

Uncomputable example:

\(\Phi_n(k) = k \neg n \Leftrightarrow n = \underbrace{S \ldots S} \Leftrightarrow S \Leftrightarrow k |\mathbb{U}|\)

The computable example should be obvious,but the uncomputable one is a bit more complex to understand(sorry,couldn't find a simpler one).