• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Crazy conjecture connecting the sqrt(e) and tetrations! bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 04/22/2010, 12:41 PM (04/21/2010, 07:48 PM)rsgerard Wrote: (04/21/2010, 07:19 PM)rsgerard Wrote: e^(1/e) = 1.444... Let d = 1/e Set infinity to be some arbitrarily high number, e.g. 9.99e10000000 I can further generalize this conjecture: if d= 1/c, for any constant > 1 the infinite tetration of e^(1/e) + d, will reach "infinity" after 1/sqrt© iterations. I can post the data if anyone is interested: For example, when d=1/10 we reach "infinity" after: 12, 34, 104, 325, 1024 iterations for d=(1/10,1/100,1/10^3,1/10^4) This series grows at sqrt(10) for each iteration approximately. Ryan Hm, so what you are saying is that $\lim_{y\to\infty} \frac{\operatorname{slog}_{\eta+1/c^{n+1}}(y)}{\operatorname{slog}_{\eta+1/c^n}(y)}\to \sqrt{c}$ Or at least $\lim_{n\to\infty}\lim_{y\to\infty} \frac{\operatorname{slog}_{\eta+1/c^{n+1}}(y)}{\operatorname{slog}_{\eta+1/c^n}(y)}\to \sqrt{c}$ where $\eta=e^{1/e}$ and $\operatorname{slog}_b$ is the inverse function of $f(z)=\exp_b^{\circ z}(1)$ Sounds really interesting, however I have no idea how to tackle. « 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

 Possibly Related Threads... Thread Author Replies Views Last Post Inspired by the sqrt tommy1729 0 1,632 02/13/2017, 01:11 AM Last Post: tommy1729 @Gottfried : answer to your conjecture on MSE. tommy1729 2 3,048 02/05/2017, 09:38 PM Last Post: Gottfried Are tetrations fixed points analytic? JmsNxn 2 3,345 12/14/2016, 08:50 PM Last Post: JmsNxn Polygon cyclic fixpoint conjecture tommy1729 1 2,448 05/18/2016, 12:26 PM Last Post: tommy1729 2015 Continuum sum conjecture tommy1729 3 3,735 05/26/2015, 12:24 PM Last Post: tommy1729 Conjecture on semi-exp base change [2015] tommy1729 0 1,927 03/24/2015, 03:14 PM Last Post: tommy1729 tetration base sqrt(e) tommy1729 2 3,670 02/14/2015, 12:36 AM Last Post: tommy1729 Tommy's conjecture : every positive integer is the sum of at most 8 pentatope numbers tommy1729 0 2,302 08/17/2014, 09:01 PM Last Post: tommy1729 [2014] sqrt boundary tommy1729 0 1,921 06/19/2014, 08:03 PM Last Post: tommy1729 Wild conjecture about 2 fixpoints. tommy1729 0 1,968 05/03/2014, 10:56 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)