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, $\pi(x)$ 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 $\theta>1$ and a real $\lambda>0$, the the cardinality of total distinct prime divisors is less than or equals to the prime counting function of the last term. That is $\left|A\right|\le\pi(\lfloor N\theta+\lambda\rfloor)$ where $A$ is the set of total distinct prime divisors of a non-homogeneous Beatty sequence $(\lfloor n\theta+\lambda\rfloor)$ up to $N^{\text{th}}$ term. Also, when parameters are sufficiently large, the following estimation is sharper, $\left|A\right|\le\left(\sqrt{\theta^2+\lambda}\right)\left(\log\ N\right).$
| Mualliflar | Low, C.W., Sapar, S.H., Deraman, F., Johari, M.A.M., Yunos, F. |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2026-03-25 |
| Jild | 70 |
| Son | 1 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2026-1-13 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2026-1-13 · Maqolaning asl sahifasi
Beatty sequence, prime divisor, prime counting function
| APA | Low, C.W., Sapar, S.H., Deraman, F., Johari, M.A.M., & Yunos, F. (2026). Distribution of prime divisors of non-homogeneous Beatty sequences. O‘zbekiston matematika jurnali, 70(1). https://doi.org/10.29229/uzmj.2026-1-13 |
|---|---|
| GOST (OAK) | Low, C.W. va b. Distribution of prime divisors of non-homogeneous Beatty sequences // O‘zbekiston matematika jurnali. – 2026. – T. 70, № 1. – DOI: 10.29229/uzmj.2026-1-13. |
| MLA | Low, C.W., Sapar, S.H., Deraman, F., Johari, M.A.M., and Yunos, F. “Distribution of prime divisors of non-homogeneous Beatty sequences.” O‘zbekiston matematika jurnali, 70(1), 2026. https://doi.org/10.29229/uzmj.2026-1-13 |
| Chicago | Low, C.W., Sapar, S.H., Deraman, F., Johari, M.A.M., and Yunos, F. “Distribution of prime divisors of non-homogeneous Beatty sequences.” O‘zbekiston matematika jurnali, 70(1) (2026). https://doi.org/10.29229/uzmj.2026-1-13 |
| Harvard | Low, C.W., Sapar, S.H., Deraman, F., Johari, M.A.M., and Yunos, F (2026) ‘Distribution of prime divisors of non-homogeneous Beatty sequences’, O‘zbekiston matematika jurnali, 70(1). https://doi.org/10.29229/uzmj.2026-1-13 |
| BibTeX | @article{lowcw2026,
title = {Distribution of prime divisors of non-homogeneous Beatty sequences},
author = {Low, C.W. and Sapar, S.H. and Deraman, F. and Johari, M.A.M. and Yunos, F.},
journal = {O‘zbekiston matematika jurnali},
year = {2026},
volume = {70},
number = {1},
doi = {10.29229/uzmj.2026-1-13},
url = {https://doi.org/10.29229/uzmj.2026-1-13}
} |
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