User blog comment:Dchew89/General Idea for my d(n) Function/@comment-35470197-20190306060453

It is ill-defined because the first 4 entries of a given fundamental sequence does not determine the limit. Say, \(\omega^2\) can be equipped with the following fundamental sequence: \begin{eqnarray*} 0,1,2,\omega,\omega+1,\omega+2,\omega\times 2,\omega \times 2+1,\omega \times 2 +2, \omega \times 3,\ldots \end{eqnarray*} Therefore "the fundamental sequence climbing" does not work at all.

Another serious problem is that the word "defined" is not defined in your definition. It is quite ambiguous.