User blog comment:Vel!/Ordinal BEAF/@comment-5150073-20130315133136/@comment-5529393-20130315150315

In that case, you don't get any natural numbers n for n >= X. A bigger problem is how exactly to convert a large number into hypernomial notation. We know that there is a standard way to express a natural number in base-b exponential notation;  this is how Goodstein sequences are defined. But what about when we add tetration to the mix? From my investigations, it's not nearly as clean as for exponentiation. Certainly it's not something that is defined automatically, as your posts suggest.