There was a discussion here recently about a non-integral sequence where the 43d term was falsely claimed to be "too big to compute exactly" Here is a different question. Sequence https://oeis.org/A198683 is defined to be the "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 exponential function." The first 11 terms are 1, 1, 2, 3, 7, 15, 34, 77, 187, 462, 1152 and there seem to be two different opinions about the 12th term, which may be either 2919 or 2926. The number of ways to insert the parens is of course a Catalan number, but the tricky part is testing for equality when the numbers get large (or small). Jon Schoenfield has been trying to settle the 12th term, and his comments (see also the "History" tab in that sequence) are very interesting. He points out that one of the values for n=11 is about 4.1007...*10^41232950809707420597749203381002924. Maybe one of experts on this list could help?