User blog comment:MilkyWay90/My ordinal function/@comment-35470197-20180630144403/@comment-35470197-20180630222521

> Wow, my ordinal function is slow.

Nope. FGH is VERY fast, and your is faster :D Be proud of it.

> also, i improved it.

For the improved one, one has \begin{eqnarray*} F(x_1,\ldots,x_k,a) & = & F(x_1 + \cdots + x_k,a) \\ F(n,\lodts,n,a) & = & F(n^2,a) \end{eqnarray*} and hence \begin{eqnarray*} f_{\alpha + \omega} < F(n,\ldots,n,f(n)) < f_{\alpha + \omega + 1} \end{eqnarray*} again. It implies \begin{eqnarray*} f_{\omega + \omega * \beta} < a_{\beta} < f_{\omega + (\omega + 1) * \beta + 1} \end{eqnarray*} again.