Persistence: a digit problem

Abstract

We examine the persistence of a number, defined as the number of iterations of the function which multiplies the digits of a number until one reaches a single digit number. We give numerical evidence supporting Sloane's 1973 conjecture that there exists a maximum persistence for every base. In particular, we give evidence that the maximum persistence in each base 2 through 12 is 1,

A Successful Senior Seminar: Unsolved Problems in Number Theory

“…Conjecturally (see [3]) the maximal persistence in He also noted various recurring shapes, and eventually focused on…”