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 Crazy conjecture connecting the sqrt(e) and tetrations! rsgerard Junior Fellow Posts: 11 Threads: 5 Joined: May 2008 04/21/2010, 07:19 PM I don't have a powerful enough computer to determine this, but I would like someone to tell me that I'm wrong. I will let the data speak for itself: e^(1/e) = 1.444... Let d = 1/e Set infinity to be some arbitrarily high number, e.g. 9.99e10000000 Take the following sequences: ...^ (1.4444 + d) ^ (1.4444 + d) ^ (1.4444 + d) ^ (1.4444 + d) ^ (1.4444 + d) ...^ (1.4444 + d^2) ^ (1.4444 + d^2) ^ (1.4444 + d^2) ^ (1.4444 + d^2) ^ (1.4444 + d^2) ...^ (1.4444 + d^3) ^ (1.4444 + d^3) ^ (1.4444 + d^3) ^ (1.4444 + d^3) ^ (1.4444 + d^3) Continue to increase n toward infinity... ...^ (1.4444 + d^n) ^ (1.4444 + d^n) ^ (1.4444 + d^n) ^ (1.4444 + d^n) ^ (1.4444 + d^n) Each of these sequences reaches "infinity" after the following iterations: 8, 12, 16, 25, 41, 66, 108, 178, 293, 482, 794 when using (d,d^2,d^3,d^4,d^5,d^6,d^7,d^8,d^9,d^10) respectively. This looks like a geometric series based close to sqrt(e) = (1.645...). Perhaps the number of iterations to get to "infinity" approaches sqrt(e)??? Bo, I'm awaiting your superior mathematical intellect. Ryan « Next Oldest | Next Newest »

 Messages In This Thread Crazy conjecture connecting the sqrt(e) and tetrations! - by rsgerard - 04/21/2010, 07:19 PM RE: Crazy conjecture connecting the sqrt(e) and tetrations! - by rsgerard - 04/21/2010, 07:48 PM RE: Crazy conjecture connecting the sqrt(e) and tetrations! - by bo198214 - 04/22/2010, 12:41 PM RE: Crazy conjecture connecting the sqrt(e) and tetrations! - by tommy1729 - 04/22/2010, 02:43 PM RE: Crazy conjecture connecting the sqrt(e) and tetrations! - by Gottfried - 02/28/2011, 02:43 PM RE: Crazy conjecture connecting the sqrt(e) and tetrations! - by tommy1729 - 03/26/2014, 12:40 AM RE: Crazy conjecture connecting the sqrt(e) and tetrations! - by tommy1729 - 03/27/2014, 11:20 PM RE: Crazy conjecture connecting the sqrt(e) and tetrations! - by tommy1729 - 06/24/2010, 07:56 PM

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