For what positive x's the number of distinct values taken by x^x^...^x with parentheses inserted in all possible ways is not represented by the sequence [A000081](http://oeis.org/A000081)? <s>Is it exactly the set of positive algebraic numbers?</s> Is it a superset of positive algebraic numbers? Is it countable? Is $2^{\sqrt 2}$ or $\log_2 3$ in the set?