How can I calculate the last digits of numbers generated by functions in the fast-growing hierarchy? From what I know, this is similar to finding the last digits of numbers defined using Steinhaus-Moser notation. Finding the last digits of $f_\alpha(n)$ is easy for $\alpha\le4$, but how can the last digits be calculated for $\alpha \ge 5$, let alone when $\alpha$ is a transfinite ordinal, as in $f_{\omega+2}(2)$?

I obtained $...1248$ as the last 4 digits of the number I gave above, but I'm not sure if that's correct. Is it possible to obtain, say, the last 10 digits?



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