Simple Question about e^(1/e)

[tommy1729]

My question is related to the infinite tetration regarding e^(1/e). Perhaps it would not be called a true tetration since each term is slightly different.

Code:

#This is arbitrary but should be high to represent infinity.
#j=0
iterations=1000
for i in range(1,iterations):
    p=e^(1/e)+1/i^(X)
    j = (p)^j

What is the smallest value of X???

In plain English:
e^(1/e) = 1.444 roughly

If X were 1:
......^(1.4444 + 1/4) ^ (1.4444 + 1/3) ^ (1.4444 + 1/2) ^ (1.4444 + 1/1)

If X were 3:
......^(1.4444 + 1/64) ^ (1.4444 + 1/27) ^ (1.4444 + 1/8.0) ^ (1.4444 + 1/1)

Based on my program 1 < X < 3
In fact, X seems to be close to 2.374 which is a constant that I haven't seen before. When X is extremely large, the sequence never seems to get past e (although I could be wrong).

Any advise from the genius' here would be greatly appreciated.

Ryan

Forgive the lack of formatting.

im not sure i got it correct.

but it seems to remind me of my ' tommy-zeta function '.

see http://www.research.att.com/~njas/sequences/A102575

regards

tommy1729