Global maximum of ?(x)-x

Joseph Biberstine jrbibers at indiana.edu
Sun Jun 11 01:10:08 CEST 2006


	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).  Specifically I'm curious how the c.f. expansion for 
xmax grows (based on the definition of f it should make for a very 
interesting sequence!)
	To the few places I've been able to calculate, neither c.f. nor decimal 
expansions for xmax or f(xmax) are in OEIS.  Note the c.f. expansion 
looks about as we'd expect so far (that is, when zero-indexed, odd 
entries are 1 and even entries slowly grow).

xmax =~ {0; 1, 3, 1, 4, 1, 4, ?1, ...} =~ 0.79285714...

- Joseph





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