User blog comment:Wythagoras/Proof that TREE(n+1) divided by TREE(n) is strictly increasing/@comment-223.255.230.227-20141220074940/@comment-1605058-20141220081953

Because we must have TREE(2)^mTREE(n-1)^TREE(n-1)>TREE(n-1)^TREE(3)>TREE(n-1)^log_3 TREE(3). So maximal m is log_3 TREE(3).