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Is there any method to calculate, which digit occurs most often in the number

$$4 \uparrow \uparrow \uparrow \uparrow 4\ ,$$

the fourth Ackermann-number ?

Or would it be necessary to calculate the number digit by digit ?

I only know that the last n digits can be calculated, but this does not help much.

Simply Beautiful Art
  • 76,603
Peter
  • 86,576
  • been any progress ? –  Dec 09 '19 at 14:34
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    In general, we know nothing about the digits of large powers, other than their last ones. – ViHdzP Jan 06 '20 at 03:05
  • Even if we know the answer to this question, this is a dead end, unstructural information that needs a lot of work to obtain. (Despite of the bounty, please provide context and motivation, e.g. show the own effort to solve the issue. Why this function invented by humans for other reasons, why the digits in the very peculiar base ten used by humans for other reasons, and why $4\uparrow^44$?) As a parallel, let us consider some smaller "similar" number, $2\uparrow\uparrow 4=65536$, which is the profit to know a part of the statistics of the occurence of the digits? – dan_fulea Aug 12 '20 at 11:48
  • I did not offer this bounty. And this is a very old question, I just wondered whether there is a trick that allows us to answer this question, which is apparently not the case. And I would find it very interesting, if it would be possible. – Peter Aug 12 '20 at 11:52
  • According to Wolfram Alpha, the number's too large to even represent, so that's saying something. It wouldn't be practical to calculate the 4th Ackermann number much less count its digits, so I can see why the urgency to have a simpler method is here. – questionasker Aug 12 '20 at 15:58

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