InfiniteSeries SMT Difficult

Problem - 4593

For a given $x > 0$, let $a_n$ be the sequence defined by $a_1=x$ for $n = 1$ and $a_n = x^{a_{n−1}}$ for $n\ge 2$. Find the largest $x$ for which the limit $\displaystyle\lim_{n\to\infty} a_n$ converges.

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