turkmath.org

Partition function p(n) and plane partition function PL(n) both follow Benford’s law in any integer base b ≥ 2. Douglass and Ono explored this in their recent paper and sought an explicit version of their results. They specifically asked for a value N(b, f) for any integer base b ≥ 2 and a string f of digits in base b, such that there exists an n ≤ N(b, f) where PL(n) starts with the string f in base b. In my talk, I will provide an explicit value for N(b, f) for both the partition function p(n) and the plane partition function PL(n).