04/20/2010, 10:07 PM

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.

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.

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.