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Simple Question about e^(1/e)
#1
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.
Reply


Messages In This Thread
Simple Question about e^(1/e) - by rsgerard - 04/20/2010, 10:07 PM
RE: Simple Question about e^(1/e) - by tommy1729 - 04/22/2010, 02:09 PM
RE: Simple Question about e^(1/e) - by andydude - 04/28/2010, 08:35 PM
RE: Simple Question about e^(1/e) - by bo198214 - 05/26/2010, 04:55 PM
RE: Simple Question about e^(1/e) - by rsgerard - 05/26/2010, 05:21 PM
RE: Simple Question about e^(1/e) - by tommy1729 - 05/26/2010, 06:04 PM

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