I found a question about the first digits of Graham's number and would like to generalize it :
We want the first n digits of the number $a\uparrow^b c$.
- Which method is the most effective to do that ?
- For which magnitude of a,b,c is the calculation feasible ?
- Is there a hope to calculate at least the first digit of Graham's number ?
If the only way to find the first digits is to simply calculate the number, then already $3\uparrow \uparrow \uparrow 3$ would be out of reach.
I tried to find out some patterns of the leading digits of powers, but there seems to be no structure.
I know, that this question is somewhat broad, nevertheless I hope for some useful hints.