On a sequence of rational numbers with unusual divisibility by a power of 2

Dubickas, Artūras (2024) On a sequence of rational numbers with unusual divisibility by a power of 2. Miskolc Mathematical Notes, 25 (1). pp. 203-208. ISSN 1787-2413

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Abstract

In this note we consider the sequence of rational numbers b_n = ∑_{k=1}^{n} 2^k∕k. We show that the power of 2 in the expansion of bn is unusually large, at least n + 1 − log2(n + 1), and that this bound is best possible. The sequence bn, n = 1,2,3,…, is related to the sequence A0031449 in the On-Line Encyclopedia of Integer Sequences.

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