Favorite numeral system?

[muon2]

As k goes to infinity so does the cost so that doesn't converge. The cost normalized to the log is what I gave above, but that is only correct for a generalized cost that truly goes as ln k. The actual cost goes as floor(log_nk) which is why I drew up my table. The easiest proof is probably to find an integer j such that for all integers k>j, C(k,2) >= C(k,3).

[angus]

The actual cost goes as floor(log_nk)

That's what the Wikipedia article I mentioned does, except that it defines Economy as k*floor(log_nk + 1).  In this case, the limit as k approaches infinity is infinity times zero, which is indeterminate.  Can we say whether a quantity does not converge if in the large limit it is indeterminate?