# Fourth Loneliest Number

Algebra Level 4

Consider the recurrence relation $$f_n (x) = x^{f_{n-1}(x)}$$ with $$f_0(x) = 16$$. Find the number of integer solutions of $$n$$ in between 1 and 1000 inclusive such that $$f_n(\sqrt[4]2) = 16$$.

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