Global maximum of ?(x)-x

[Antti Karttunen]

Gene Smith wrote:

>
>
> On 6/10/06, *Joseph Biberstine* <jrbibers at indiana.edu 
> <mailto:jrbibers at indiana.edu>> wrote:
>
>             Not clever enough to figure this out a reliable
>     computation of this
>     myself.  Please help find enough accurate terms for OEIS and I will of
>     course credit you.
>
>             Consider f(x) := ?(x)-x where ?(x) is Minkowski's question
>     mark function.
>             Recently I've wondered at what value xmax f will obtain
>     its global
>     maximum (mod 1).  
>
>
>
> Another question is where does ?(x)=x, aside from the obvious places 
> at integers and half integers.

http://www.research.att.com/~njas/sequences/?q=fixed+Minkowski&sort=0&fmt=0&language=english&go=Search
(Of course there is a second non-trivial fixed point at 1- 0.42037... if 
I recall right.)

and further two sequences relating to this:
http://www.research.att.com/~njas/sequences/A065936
http://www.research.att.com/~njas/sequences/A065937


Yours,

Antti Karttunen