20 Nov
2011
20 Nov
'11
9:06 p.m.
On Sun, Nov 20, 2011 at 10:58 PM, Warren Smith <warren.wds@gmail.com> wrote:
"number of distinct values taken by i^i^...^i (with n i's and parentheses inserted in all possible ways)" where i = sqrt(-1) and ^ denotes the principal value of the power function [A198683]
--If i were replaced by some generic number, then all the parenthesizations would yield distinct values and the count would be a known Catalan number (which is an upper bound on this i-based count, therefore). Right? WRONG!!! Because (x^x)^(x^x) = (x^(x^x))^x FOR *ANY* x !!! so you can actually get a stronger "generic" upper bound than the Catalan numbers!
So the more interesting question seems to be: what is this (generic x) count?