• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 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 rsgerard Junior Fellow  Posts: 11 Threads: 5 Joined: May 2008 04/21/2010, 07:48 PM (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 Posts: 1,595 Threads: 101 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 Or at least where and is the inverse function of Sounds really interesting, however I have no idea how to tackle. tommy1729 Ultimate Fellow     Posts: 1,699 Threads: 373 Joined: Feb 2009 04/22/2010, 02:43 PM (04/22/2010, 12:41 PM)bo198214 Wrote: (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 Or at least where and is the inverse function of Sounds really interesting, however I have no idea how to tackle. i noticed that too , very long ago. perhaps the count till 'oo' is the confusing part. what if we replace d with -d and count until we reach 'e' (instead of 'oo') then would the limit also give sqrt© ? if so , i think we are close to a proof. or at least arrive at showing these limits depend on earlier conjectured limits ( such as the limit by gottfried ) regards tommy1729 tommy1729 Ultimate Fellow     Posts: 1,699 Threads: 373 Joined: Feb 2009 06/24/2010, 07:56 PM i couldnt help noticing that sqrt(e) occurs here , just as it does in my " use sinh " thread. could there be a link ?? it seems sqrt(e) is the number 3 constant after e^1/e. 1) e^1/e 2) fixpoint e^x 3) sqrt(e) Gottfried Ultimate Fellow     Posts: 873 Threads: 128 Joined: Aug 2007 02/28/2011, 02:43 PM (04/22/2010, 12:41 PM)bo198214 Wrote: (...) Sounds really interesting, however I have no idea how to tackle. Hmm, I do not really see a good possibility to tackle this. Just want to note that one can rewrite this where and and then with some k Gottfried Helms, Kassel tommy1729 Ultimate Fellow     Posts: 1,699 Threads: 373 Joined: Feb 2009 03/26/2014, 12:40 AM (02/28/2011, 02:43 PM)Gottfried Wrote: (04/22/2010, 12:41 PM)bo198214 Wrote: (...) Sounds really interesting, however I have no idea how to tackle. Hmm, I do not really see a good possibility to tackle this. Just want to note that one can rewrite this where and and then with some k Hmm. This is quite an old post. I remember thinking I know how Gottfried arrived at this. But I seem to have forgotten now. Maybe I should have posted my ideas back then. Could you plz explain Gottfried ? regards tommy1729 tommy1729 Ultimate Fellow     Posts: 1,699 Threads: 373 Joined: Feb 2009 03/27/2014, 11:20 PM (04/22/2010, 12:41 PM)bo198214 Wrote: Hm, so what you are saying is that Maybe I am wrong but I seem to disagree with that. Does this not contradict the base change ? Since the base change dictates that regards tommy1729 « Next Oldest | Next Newest »

 Possibly Related Threads… Thread Author Replies Views Last Post tommy's group addition isomo conjecture tommy1729 1 67 09/16/2022, 12:25 PM Last Post: tommy1729 [NT] primitive root conjecture tommy1729 0 112 09/02/2022, 12:32 PM Last Post: tommy1729 sqrt thingy at MSE tommy1729 3 221 08/14/2022, 05:44 AM Last Post: JmsNxn tommy's new conjecture/theorem/idea (2022) ?? tommy1729 0 176 06/22/2022, 11:49 PM Last Post: tommy1729 sqrt(!) and sqrt(exp) Kouznetsov 4 9,078 06/08/2022, 05:32 AM Last Post: Catullus A compilation of graphs for the periodic real valued tetrations JmsNxn 1 986 09/09/2021, 04:37 AM Last Post: JmsNxn conjecture 666 : exp^[x](0+si) tommy1729 2 1,351 05/17/2021, 11:17 PM Last Post: tommy1729 Inspired by the sqrt tommy1729 0 3,286 02/13/2017, 01:11 AM Last Post: tommy1729 @Gottfried : answer to your conjecture on MSE. tommy1729 2 6,489 02/05/2017, 09:38 PM Last Post: Gottfried Are tetrations fixed points analytic? JmsNxn 2 7,122 12/14/2016, 08:50 PM Last Post: JmsNxn

Users browsing this thread: 1 Guest(s) 