User blog comment:Simplicityaboveall/Extremely Large Numbers 4/@comment-28606698-20160801212403/@comment-5529393-20160801213406

I prefer

$$f_{\alpha+1}(a) = f_{\alpha}^a(1)$$

which would also give $$f_m(n) = 10\uparrow^m n$$.

But, is it really an advantage to be able to express a FGH in terms of Knuth arrows? If you want a number to be expressible in such a fashion, then just use Knuth arrows.