User blog:JHeroJr/Can Someone Tell Me How To Create An Uncomputable Function That Is Not Naive?

I really wanna make an uncomputable function to play around with. I know all about Turing machines and about what makes an uncomputable function uncomputable, but all the ideas are taken by Rayo's function, the Xi function, and the busy beaver function. And if a function were defined "f(n) = the smallest number not computable to a level-N turing machine", wouldn't all the values be undefined?

Pleeeeeaaaaase tell me how to make an uncomptable function!!!!!