R = N ^ (N ^ (N ^ ...)). What is the maximum N>0 that will yield a finite R?

(In reply to

Solution? by Richard)

I'm still working it out, but I don't think that's right, Richard.

Taking the log of both sides gives ln(R) = Rln(N).

ln(N) = ln(R)/R.

I'm going find the x = maximum value of ln(r)/r, and then n = e^x.

Using excel, I get something like N = 1.444668 and R = 2.718, but I'm trying now for an exact solution.

R looks suspiciously like e, so I suspect that N = e^(1/e)

*Edited on ***October 30, 2004, 5:48 pm**