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Crazy conjecture connecting the sqrt(e) and tetrations!
#4
(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
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RE: Crazy conjecture connecting the sqrt(e) and tetrations! - by tommy1729 - 04/22/2010, 02:43 PM

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