
A discrete iteration related to Pierce expansions
Conjecture Let
be integers. Set
and
for
. Eventually we have
; put
.






Example: , since
,
,
,
,
,
,
,
.
Prove or disprove: .
The best upper bound is currently . For more information, see [ES].
Bibliography
[ES] P. Erd\"os and J. Shallit, ``New bounds on the length of finite Pierce and Engel series'', S\'eminaire de Th\'eorie des Nombres de Bordeaux 3 (1991), 43--53.
* indicates original appearance(s) of problem.
A different upper bound
This paper shows an upper bound of
.
Edit: But looking at the title page of the paper, I see you already knew that ;)