Carmichael numbers composed of Piatetski-Shapiro primes in Beatty sequences
The Piatetski-Shapiro sequences are sequences of the form (⌊nc⌋)n=1∞{\left(\lfloor {n}^{c}\rfloor )}_{n=1}^{\infty } and the Beatty sequence is the sequence of integers (⌊αn+β⌋)n=1∞{(\lfloor \alpha n+\beta \rfloor )}_{n=1}^{\infty }. We prove that there are infinitely many Carmichael numbers compose...
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De Gruyter
2025-05-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2025-0157 |
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| author | Qi Jinyun Guo Victor Zhenyu |
| author_facet | Qi Jinyun Guo Victor Zhenyu |
| author_sort | Qi Jinyun |
| collection | DOAJ |
| description | The Piatetski-Shapiro sequences are sequences of the form (⌊nc⌋)n=1∞{\left(\lfloor {n}^{c}\rfloor )}_{n=1}^{\infty } and the Beatty sequence is the sequence of integers (⌊αn+β⌋)n=1∞{(\lfloor \alpha n+\beta \rfloor )}_{n=1}^{\infty }. We prove that there are infinitely many Carmichael numbers composed of entirely the primes from the intersection of a Piatetski-Shapiro sequence and a Beatty sequence for c∈1,1913718746c\in \left(\phantom{\rule[-0.75em]{}{0ex}},1,\frac{19137}{18746}\right), α>1\alpha \gt 1 irrational and of finite type by investigating the Piatetski-Shapiro primes in arithmetic progressions in a Beatty sequence. Moreover, we also discuss the intersection of a Piatetski-Shapiro sequence and multiple Beatty sequences in arithmetic progressions. |
| format | Article |
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| institution | Kabale University |
| issn | 2391-5455 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-abe33a491dcb4644beca1729eb06f9c92025-08-20T03:55:16ZengDe GruyterOpen Mathematics2391-54552025-05-0123155956610.1515/math-2025-0157Carmichael numbers composed of Piatetski-Shapiro primes in Beatty sequencesQi Jinyun0Guo Victor Zhenyu1School of Information Engineering, Xi’an University, Xi’an 710065, Shaanxi, P. R. ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, P. R. ChinaThe Piatetski-Shapiro sequences are sequences of the form (⌊nc⌋)n=1∞{\left(\lfloor {n}^{c}\rfloor )}_{n=1}^{\infty } and the Beatty sequence is the sequence of integers (⌊αn+β⌋)n=1∞{(\lfloor \alpha n+\beta \rfloor )}_{n=1}^{\infty }. We prove that there are infinitely many Carmichael numbers composed of entirely the primes from the intersection of a Piatetski-Shapiro sequence and a Beatty sequence for c∈1,1913718746c\in \left(\phantom{\rule[-0.75em]{}{0ex}},1,\frac{19137}{18746}\right), α>1\alpha \gt 1 irrational and of finite type by investigating the Piatetski-Shapiro primes in arithmetic progressions in a Beatty sequence. Moreover, we also discuss the intersection of a Piatetski-Shapiro sequence and multiple Beatty sequences in arithmetic progressions.https://doi.org/10.1515/math-2025-0157beatty sequencepiatetski-shapiro primecarmichael number11n0511l0711n8011b83 |
| spellingShingle | Qi Jinyun Guo Victor Zhenyu Carmichael numbers composed of Piatetski-Shapiro primes in Beatty sequences Open Mathematics beatty sequence piatetski-shapiro prime carmichael number 11n05 11l07 11n80 11b83 |
| title | Carmichael numbers composed of Piatetski-Shapiro primes in Beatty sequences |
| title_full | Carmichael numbers composed of Piatetski-Shapiro primes in Beatty sequences |
| title_fullStr | Carmichael numbers composed of Piatetski-Shapiro primes in Beatty sequences |
| title_full_unstemmed | Carmichael numbers composed of Piatetski-Shapiro primes in Beatty sequences |
| title_short | Carmichael numbers composed of Piatetski-Shapiro primes in Beatty sequences |
| title_sort | carmichael numbers composed of piatetski shapiro primes in beatty sequences |
| topic | beatty sequence piatetski-shapiro prime carmichael number 11n05 11l07 11n80 11b83 |
| url | https://doi.org/10.1515/math-2025-0157 |
| work_keys_str_mv | AT qijinyun carmichaelnumberscomposedofpiatetskishapiroprimesinbeattysequences AT guovictorzhenyu carmichaelnumberscomposedofpiatetskishapiroprimesinbeattysequences |