# 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 ;)