An exploration of pandivisible numbers

Our system for writing integers relies on ten symbols. When we write an integer that is less than ten, the rule is easy: write the corresponding symbol; for example, “nine” is expressed as “9”. However, for integers greater than or equal to ten, the rules are more complicated.

Update: Michael Kielstra has run further computer searches and discovered that there are no pandivisible numbers in bases less than 32 other than the ones listed in the paper.