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 Simple Question about e^(1/e) tommy1729 Ultimate Fellow Posts: 1,372 Threads: 336 Joined: Feb 2009 04/22/2010, 02:09 PM (04/20/2010, 10:07 PM)rsgerard Wrote: 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 « Next Oldest | Next Newest »

 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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