Citation
Abstract
Non-homogeneous Beatty sequence is a sequence of positive integer that taking the floor value of irrational numbers. This paper using the prime counting function, π(x) to estimate the cardinality of total distinct prime divisors of a non-homogeneous Beatty sequence. When the parameters in the non-homogeneous Beatty sequence are sufficiently large, a better estimation can be obtained. From this study, we found that for a fixed irrational θ > 1 and a real λ > 0, the the cardinality of total distinct prime divisors is less than or equals to the prime counting function of the last term. That is |A| ≤ π(⌊Nθ + λ⌋) where A is the set of total distinct prime divisors of a non-homogeneous Beatty sequence (⌊nθ +λ⌋) up( to Nth term. Also, when parameters are sufficiently large, the following √ ) estimation is sharper, |A| ≤θ2 + λ (log N) .
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Additional Metadata
| Item Type: | Article |
|---|---|
| Subject: | Analysis |
| Subject: | Algebra and Number Theory |
| Subject: | Statistics and Probability |
| Divisions: | Faculty of Science Institute for Mathematical Research |
| DOI Number: | https://doi.org/10.29229/uzmj.2026-1-13 |
| Publisher: | Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan |
| Keywords: | Beatty sequence; Prime counting function; Prime divisor |
| Sustainable Development Goals (SDGs): | SDG 9: Industry, Innovation and Infrastructure, SDG 17: Partnerships for the Goals, SDG 4: Quality Education |
| Depositing User: | MS. HADIZAH NORDIN |
| Date Deposited: | 30 Apr 2026 15:28 |
| Last Modified: | 30 Apr 2026 15:28 |
| Altmetrics: | http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.29229/uzmj.2026-1-13 |
| URI: | http://psasir.upm.edu.my/id/eprint/125100 |
| Statistic Details: | View Download Statistic |
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