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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