Crazy conjecture connecting the sqrt(e) and tetrations!

[rsgerard]

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