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

Source abstract

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