(adsbygoogle = window.adsbygoogle || []).push({}); An extremely long "power tower"

Hey, this isn't really a homework or classwork question. My professor always puts questions that he finds interesting on our notes. This really got my attention, ive been trying to see if it's possible to write a computer program to solve it.

However, i've come to the conclusion that this number is simply too large to be calculable in decimal notation. I was just wondering if you could tell me if i've done the right things.

First of all here is the information for the problem:

http://img62.imageshack.us/img62/4931/problemy.th.png [Broken]

And the problem itself

[PLAIN]http://img687.imageshack.us/img687/1779/49195211.png [Broken]

(Sorry for using so many pictures instead of typing this out, my browser is having some issues with using the toolbar items above).

Anyways, after working this out, the conclusion that I come to is that I need to keep a power of 2's, in the following fashion:

[PLAIN]http://img687.imageshack.us/img687/5981/part2s.png [Broken]

I have to have a height of more than 65,000 on the tower! As far as im aware, this would produce a number FAR too massive to compute. Am I on the right track and is there any possible way to even obtain a decimal notation of the above problem? Thanks.

EDIT: Just a side thought, is there any relation to this and the Ackermann function at all?`

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# An extremely long power tower

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