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pentation and hexation
#7
(09/03/2017, 11:52 PM)JmsNxn Wrote: There is a result posted on here about how the "eta constants" converge to 2 and the "euler constants" converge to 4. The n'th eta constant is the sup of the  x'th n'th hyperoperator root of x. And the "euler constants" are the actual values x_n such that x_n'th n'th hyperoperator root of x_n = n'th eta constant...

How interesting!  I haven't seen this conjecture before.  This is base 1.84, for which septation almost has an upper fixed point, that would be somewhere near 3.7  So octation for base=1.84 wouldn't quite be bounded, but oct(45)~=4.05, so it would take awhile before octation escapes; I can only calculate integer values for octation, until I do a theta mapping.  Also, notice that the solution for base(e) above, behaves nicer than base 1.84.

Why would do the "euler constants" converge to 4, as n gets arbitrarily large for the "nth" hyperoperator for bases approaching 2?  
   
- Sheldon
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Messages In This Thread
pentation and hexation - by sheldonison - 08/07/2017, 07:33 PM
RE: pentation and hexation - by JmsNxn - 08/21/2017, 08:05 PM
RE: pentation and hexation - by sheldonison - 08/22/2017, 02:03 PM
RE: pentation and hexation - by JmsNxn - 08/22/2017, 10:38 PM
RE: pentation and hexation - by sheldonison - 09/03/2017, 10:11 PM
RE: pentation and hexation - by JmsNxn - 09/03/2017, 11:52 PM
RE: pentation and hexation - by sheldonison - 09/04/2017, 03:04 AM
RE: pentation and hexation - by JmsNxn - 09/04/2017, 04:07 AM
RE: pentation and hexation - by Ember Edison - 09/18/2019, 06:34 AM
RE: pentation and hexation - by sheldonison - 09/18/2019, 02:34 PM

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