An Effective Benford’s Law for Strictly Increasing and Log-Concave Sequences

We establish an effective form of Benford’s law for a class of strictly increasing and log-concave sequences ( f n ) n ≥ 0 (fₙ)n≥ 0 left parenthesis f Subscript n Baseline right parenthesis Subscript n greater than or equals 0 . We apply our result to the partition and plane partition functions, obtaining improvements on bounds due to Iyer for the first occurrence of prescribed leading digit strings.