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I've been working on a project for a wiki that I'm a member of. It is the Sequence of the Day for September 2. You can see my progress at https://oeis.org/wiki/Template:Sequence_of_the_Day_for_September_2 .

In short I ask, when you consider tetrations with rational heights, and compare them to exponentials with rational powers, what is the equivalent form of tetration to the exponential $n^{1/n}$?

I was wondering if anyone here knew the answer and would share it with me. If so, I would like to rephrase my project.

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Powers have the property that $(a^b)^c = a^{bc}$, so a rational power like $1/b$ has to have the effect of an inverse. Unfortunately I don't think tetrations have a similar property, so you might not be able to draw a meaningful parallel. –  trutheality Jun 25 '11 at 3:16

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