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...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9937647 |
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| author | Yahui Yu Jiayuan Hu |
| author_facet | Yahui Yu Jiayuan Hu |
| author_sort | Yahui Yu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ab38a2cb09474c4e9662439c8fdb8e16 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ab38a2cb09474c4e9662439c8fdb8e162025-02-03T01:04:18ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/99376479937647On the Distribution Properties of the Smarandache Prime PartYahui Yu0Jiayuan Hu1Department of Mathematics and Physics, Luoyang Institute of Science and Technology, Luoyang 471023, Henan, ChinaDepartment of Mathematics and Computer Science, Hetao College, Bayannur 015000, ChinaFor 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.http://dx.doi.org/10.1155/2021/9937647 |
| spellingShingle | Yahui Yu Jiayuan Hu On the Distribution Properties of the Smarandache Prime Part Journal of Mathematics |
| title | On the Distribution Properties of the Smarandache Prime Part |
| title_full | On the Distribution Properties of the Smarandache Prime Part |
| title_fullStr | On the Distribution Properties of the Smarandache Prime Part |
| title_full_unstemmed | On the Distribution Properties of the Smarandache Prime Part |
| title_short | On the Distribution Properties of the Smarandache Prime Part |
| title_sort | on the distribution properties of the smarandache prime part |
| url | http://dx.doi.org/10.1155/2021/9937647 |
| work_keys_str_mv | AT yahuiyu onthedistributionpropertiesofthesmarandacheprimepart AT jiayuanhu onthedistributionpropertiesofthesmarandacheprimepart |