04/22/2010, 12:41 PM

(04/21/2010, 07:48 PM)rsgerard Wrote:(04/21/2010, 07:19 PM)rsgerard Wrote: e^(1/e) = 1.444...

Let d = 1/e

Set infinity to be some arbitrarily high number, e.g. 9.99e10000000

I can further generalize this conjecture:

if d= 1/c, for any constant > 1

the infinite tetration of e^(1/e) + d, will reach "infinity" after 1/sqrt© iterations. I can post the data if anyone is interested:

For example, when d=1/10 we reach "infinity" after:

12, 34, 104, 325, 1024 iterations for d=(1/10,1/100,1/10^3,1/10^4)

This series grows at sqrt(10) for each iteration approximately.

Ryan

Hm, so what you are saying is that

Or at least

where and is the inverse function of

Sounds really interesting, however I have no idea how to tackle.