On the Distribution Properties of the Smarandache Prime Part
For each integer n, denote by ppn the largest prime ≤n and by Ppn the smallest prime ≥n, called as the Smarandache inferior prime part and superior prime part of n, respectively. Define In≔1/n∑m≤nppm and Sn≔1/n∑m≤nPpm. In this short note, we proved some estimates on In−Sn and In/Sn, answering a ques...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9937647 |
| Summary: | For each integer n, denote by ppn the largest prime ≤n and by Ppn the smallest prime ≥n, called as the Smarandache inferior prime part and superior prime part of n, respectively. Define In≔1/n∑m≤nppm and Sn≔1/n∑m≤nPpm. In this short note, we proved some estimates on In−Sn and In/Sn, answering a question proposed by Kashihara and improving a result of Yan. |
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| ISSN: | 2314-4785 |