User blog comment:Tetramur/My thoughts about functions and numbers/@comment-35470197-20191229115044/@comment-39541634-20191229191105

The way Kleene's O behaves depends on the way you enumerate the Turing Machines.Some of the enumerations will be pathological and some will not.

The problem is that Kleene's O isn't computable, so we don't really have a way of deciding whether a particular enumeration would behave nicely (though we could sometimes prove that an enumeration behaves badly, because that problem might be computable in certain special cases).