Global maximum of ?(x)-x : local maximum between .42 and .5

[Gene Smith]

On 6/13/06, Gerald McGarvey <Gerald.McGarvey at comcast.net> wrote:
>
> The local maximum of ?(x)-x between .42 and .5 appears to occur at an
> interesting
> value of x. I believe it occurs at around .460495713337621635801842 which
> has a
> continued fraction beginning as
> [0, 2, 5, 1, 4, 1, 4, 1, 4, 1, 4, 1, 5, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1,
> 5,
> 1, 4, 1, 4, 1, 4, 1,


I think it would be of considerable interest to push this farther.  Has
anyone considered using box rather than the ? function? I continue to
suspect it would be easier.
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