User blog comment:Boboris02/MBOT/@comment-1605058-20161220212557/@comment-30118230-20161221210124

Ok,fine

The first one is very simple.It just returns the input(n) as n+7.

It is essentialy the same as \(\Phi(n) = n+7\).This goes to show that \(\neg\) and \(\Leftrightarrow\) are not usefull in computable functions,because they can be replaced with other operators.

The second one is a bit more tricky.It is the system that represents Hollom's Doodle function.

I know there was no way you would've guessed that,so I apologise.But from the existing uncomputable functions I only know how to mimic \(\Sigma(n)\) and the doodle function in Phi systems.You have already seen the one for the busy beaver function,so it would be useless showing it to you again.As for making my own uncomputable function and keeping it simple for the example at the same time - I don't know how to do that.:P