Some tetration you got there

Calculus Level 4

\[ \LARGE f(x;n) = \underbrace{ x^{x^{.^{.^x}}} }_{\text{number of } x \text{'s } =\ n } \]

\(\)
A positive integer \(n\) is randomly chosen between 1 and 10000 inclusive for the function described above.

If \(p\) denotes the probability that \( \displaystyle \lim_{x \to 0} f(x;n) = 1, \) what is the value of \( \left \lfloor 1000p \right \rfloor \)?

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