Join us as we explore OEIS A000195, the floor of the natural logarithm. We unpack how floor(ln n) climbs in a staircase at n = e^k, connect it to base-e “digits” and related sequences like A004233 and A000193–A000196, and discuss why it defies Benford’s law. We’ll peek at practical code in Maple, Mathematica, and PARI/GP to generate terms and probe a 2024 conjecture by Joseph Shemia, plus the role of Sloan as curator and the offset. It’s a concise tour of an apparently simple sequence that reveals rich structure and cross-links across number theory.
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