NECESSARY AND SUFFICIENT CONDITIONS FOR BENFORD SEQUENCES

摘要

What makes a sequence of real numbers a Benford sequence? It turns out that a lot of sequences growing exponentially or faster are Benford sequences. However, being exponential is not sufficient to prove that the sequence is Benford. Therefore, more general sufficient conditions for Benford sequences are needed. In this paper we will explore some sufficient and necessary conditions for Benford sequences. Specifically, for any sequence {a_n}, we will explore the limit lim log_(10)(a_n+1/a_n). n→∞ We will show how this limit assists us in determining the "Benfordness" of {a_n}.