DOI: 10.1017/s000497272610210x ISSN: 0004-9727

AN EFFECTIVE BENFORD’S LAW FOR STRICTLY INCREASING AND LOG-CONCAVE SEQUENCES

TUYUN LAN, NIAN HONG ZHOU
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Abstract

We establish an effective form of Benford’s law for a class of strictly increasing and log-concave sequences

( f n ) n ≥ 0 $(f_n)_{n\geq 0}$ 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.

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