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.