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: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2021-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9937647 |
| id |
doaj-ab38a2cb09474c4e9662439c8fdb8e16 |
|---|---|
| record_format |
Article |
| spelling |
doaj-ab38a2cb09474c4e9662439c8fdb8e162021-08-30T00:01:30ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/9937647On the Distribution Properties of the Smarandache Prime PartYahui Yu0Jiayuan Hu1Department of Mathematics and PhysicsDepartment of Mathematics and Computer ScienceFor 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yahui Yu Jiayuan Hu |
| spellingShingle |
Yahui Yu Jiayuan Hu On the Distribution Properties of the Smarandache Prime Part Journal of Mathematics |
| author_facet |
Yahui Yu Jiayuan Hu |
| author_sort |
Yahui Yu |
| title |
On the Distribution Properties of the Smarandache Prime Part |
| title_short |
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_sort |
on the distribution properties of the smarandache prime part |
| publisher |
Hindawi Limited |
| series |
Journal of Mathematics |
| issn |
2314-4785 |
| publishDate |
2021-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2021/9937647 |
| work_keys_str_mv |
AT yahuiyu onthedistributionpropertiesofthesmarandacheprimepart AT jiayuanhu onthedistributionpropertiesofthesmarandacheprimepart |
| _version_ |
1721186014425251840 |