A New Primes-Generating Sequence
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911151154003968 |
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| author | Bouras, Mohammed |
| author_facet | Bouras, Mohammed |
| contents | For the sequence defined by \[ a(n) = \frac{n^2 - n - 1}{\gcd\big(n^2 - n - 1,\, b(n-3) + n\,b(n-4)\big)} \] Where $b(n) = (n+2)\big(b(n-1) - b(n-2)\big),$ with initial conditions $b(-1) = 0$ and $b(0) = 1$, we find that $a(n)$ contains only $1$'s and primes, and can be represented as a finite continued fraction. It is more efficient for generating prime numbers than the Rowland sequence. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_09745 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A New Primes-Generating Sequence Bouras, Mohammed General Mathematics For the sequence defined by \[ a(n) = \frac{n^2 - n - 1}{\gcd\big(n^2 - n - 1,\, b(n-3) + n\,b(n-4)\big)} \] Where $b(n) = (n+2)\big(b(n-1) - b(n-2)\big),$ with initial conditions $b(-1) = 0$ and $b(0) = 1$, we find that $a(n)$ contains only $1$'s and primes, and can be represented as a finite continued fraction. It is more efficient for generating prime numbers than the Rowland sequence. |
| title | A New Primes-Generating Sequence |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2509.09745 |