Slowly I doubt that this sequence converges.
Have a look again at the picture:
![[Image: attachment.php?aid=719]](http://math.eretrandre.org/tetrationforum/attachment.php?aid=719)
You see, that it oscillates around 1/log(2). Now I considered only the local maxima.
If there is maxima at m then the next maxima is roughly located at 2*m+1.
I computed the values at the maxima:
If you compare with the actual value of 1/log(2.0) (at the end of the code section), it looks as if it would never be reached, because the changing digits just wander too quickly to the right. What do you think?
If this is true, then the whole intuitive method questionable, because it does not converge in the simplest case of a linear function.
Have a look again at the picture:
You see, that it oscillates around 1/log(2). Now I considered only the local maxima.
If there is maxima at m then the next maxima is roughly located at 2*m+1.
I computed the values at the maxima:
Code:
00004 1.44761904761905
00013 1.44294012536393
00028 1.44275389908130
00057 1.44272403814808
00115 1.44271536072053
00231 1.44271205805011
00464 1.44271061914438
00929 1.44270994540048
01859 1.44270961966486
03719 1.44270945950856
07439 1.44270938009939
14879 1.44270934056096
29759 1.44270932083314
oo 1.44269504088896?If you compare with the actual value of 1/log(2.0) (at the end of the code section), it looks as if it would never be reached, because the changing digits just wander too quickly to the right. What do you think?
If this is true, then the whole intuitive method questionable, because it does not converge in the simplest case of a linear function.
