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Inequalities for the arithmetic mean of the first n prime numbers
Alzer, Horst
Hassani, Mehdi
2024
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e-ISSN
2464-8728
Abstract
Abstract. Let An be the (unweighted) arithmetic mean of the first n prime numbers. We prove that for n ≥ 2,
An1+α/(n*log(n)) ≤ An+1 ≤ An1+β/(n*log(n)) with the best possible constants α ≈ 0.43525 and β ≈ 1.22596. The right-hand side improves a result given by Z.-W. Sun in 2013.
An1+α/(n*log(n)) ≤ An+1 ≤ An1+β/(n*log(n)) with the best possible constants α ≈ 0.43525 and β ≈ 1.22596. The right-hand side improves a result given by Z.-W. Sun in 2013.
Source
Horst Alzer and Mehdi Hassani, "Inequalities for the arithmetic mean of the first n prime numbers" in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.56 (2024)", EUT Edizioni Università di Trieste, Trieste, 2024, pp. 23-32
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
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