On a Problem of Douglass and Ono for the Plane Partition Function

It is known that the plane partition function of n denoted \(\textrm{PL}(n)\) $\text{PL}(n)$ obeys Benford’s law in any integer base \(b\ge 2\) $b\ge 2$ . We give an upper bound for the smallest positive integer n such that \(\textrm{PL}(n)\) $\text{PL}(n)$ starts with a prescribed string f of digits in base b.