On this page there is a reference to Knuth's conjecture but it says he starts with 4
But since
3 == _sqrt(sqrt(_sqrt(sqrt(sqrt(sqrt(sqrt(4!!)))))_!))_
and
4 == _sqrt(sqrt(sqrt(sqrt(sqrt(sqrt((_sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(((sqrt(sqrt(3!!))_)!)!)))))))_)!))))))_
both "conjectures" are equivalent.
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