Abstract
Let Sn denote the nth partial sum of the harmonic series. For a given positive integer k>1, there exists a unique integer nk such that Snk-1<Snk. It has been conjectured that nki is equal to the integer nearest ek-γ, where γ is Euler's constant. We provide an estimate on nk which suggests that this conjecture may have to be modified. We also propose a conjecture concerning the amount by which Snk- and Snk differ from k.
Original language | English (US) |
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Pages (from-to) | 83-86 |
Number of pages | 4 |
Journal | Proceedings of the American Mathematical Society |
Volume | 95 |
Issue number | 1 |
DOIs | |
State | Published - Sep 1985 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics