Global maximum of ?(x)-x

[Antti Karttunen]

Gene Smith wrote:

>
>
> On 6/12/06, *Gerald McGarvey* <Gerald.McGarvey at comcast.net 
> <mailto:Gerald.McGarvey at comcast.net>> wrote:
>
>     Another question is: Where does []x - x have a global maximum?,
>     where []x is the Conway box function (the inverse of Minkowski's
>     question mark function). 
>
>
> It has global maximums corresponding to minimums of
> ?(x)-x. Box is easier to deal with in this connection, I imagine.
>  
>
Note that by this information it can be deduced that the other
name of the Maple-functions "MinkowskisQMarkVarInv" and "ConwaysXinBoxInv"
I use on http://www.research.att.com/~njas/sequences/A065936
and http://www.research.att.com/~njas/sequences/A065937
is incorrect, or more properly put, "highly misleading".
(Although the sequences themselves are correct).
Probably the latter. I recall that it is my own
variant of the Conway's Box-function.
I didn't have ONAG at the time I submitted
the sequences, but instead relied solely on
the news-article by Robert Hill, so I got
the names wrongly.

I will edit the sequences later.
Meanwhile the variant presented in A065937
might offer yet other opportunities
for finding interesting fixed points.
SternBrocotTreeNum refers to A007305
and SternBrocotTreeDen to A047679,
althought the exact offsets might
have changed since then...


Cheers,

Antti