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open problems survey
#13
(10/31/2010, 07:13 PM)dantheman163 Wrote: We have the sequence of "Eulers" {2.718281828,3.0885322718...} and the sequence of "Etas" {1.44466786,1.6353244967...}.

"Eulers" and "Etas" can be defined as the x-coordinate and y-coordinate of the maximum of the nth order self root.

Conjecture:

The limit of the sequence of "Eulers" is 4.
The limit of the sequence of "Etas" is 2.

Some discussion can be found here

If you can find a better name for these sequences feel free to use it.

let the "Eulers" be eul(n) and the "Etas" be et(n).

now i conjecture :

1) et(n)^2 < eul(n-1)

2) lim n-> oo (et(n)^2 - eul(n-1)) / (et(n-1)^2 - eul(n-2)) = 1

regards

tommy1729
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Messages In This Thread
open problems survey - by bo198214 - 05/17/2008, 10:03 AM
Exponential Factorial, TPID 2 - by andydude - 05/26/2008, 03:24 PM
Existence of bounded b^z TPID 4 - by bo198214 - 10/08/2008, 04:22 PM
A conjecture on bounds. TPID 7 - by andydude - 10/23/2009, 05:27 AM
Logarithm reciprocal TPID 9 - by bo198214 - 07/20/2010, 05:50 AM
RE: open problems survey - by nuninho1980 - 10/31/2010, 09:50 PM
Tommy's conjecture about Eulers and Etas. TPID 11. - by tommy1729 - 12/01/2010, 03:56 PM
Tommy's conjecture TPID 16 - by tommy1729 - 06/07/2014, 10:44 PM
The third super-root TPID 18 - by andydude - 12/25/2015, 06:16 AM

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