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 conjecture 666 : exp^[x](0+si) tommy1729 Ultimate Fellow Posts: 1,670 Threads: 368 Joined: Feb 2009 05/15/2021, 11:14 PM (This post was last modified: 05/15/2021, 11:17 PM by tommy1729.) Many many years ago I conjectured the following :  Consider exp iterations of a starting value $y=0+si$ for $0. It seems for all such s , after some iterations we get close to 0. So we search for positive real x > 1 , such that   $exp^{[x]}(y)=0$ or it gets very close. I believe an upper bound for x is  $bound(x)=1+exp(s^2+s+1/s)$ I gave it the funny name conjecture 666 because by the formula above : $bound(2)=666.141..$ Notice the formula does not extend correctly to values such as $s=\pi$ since that sequence will never come close to zero. A sharper bound is probably attainable. But how ?  Is there an easy way ? For 1/2

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