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.