Explicit inequalities for the nth lucky number
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910113084735488 |
|---|---|
| author | Sanna, Carlo |
| author_facet | Sanna, Carlo |
| contents | Gardiner, Lazarus, Metropolis, and Ulam introduced a variation of the sieve of Eratosthenes that (instead of producing the sequence of prime numbers) produces the sequence of "lucky numbers". The distribution of lucky numbers has a striking similarity to that of prime numbers. In particular, Hawkins and Briggs proved that if $\ell_n$ denotes the $n$th lucky number then $\ell_n \sim n \log n$, which is analogous to the prime number theorem. This work provides explicit upper and lower bounds on $\ell_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07142 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Explicit inequalities for the nth lucky number Sanna, Carlo Number Theory 11B99 (Primary) 11A99, 11N35 (Secondary) Gardiner, Lazarus, Metropolis, and Ulam introduced a variation of the sieve of Eratosthenes that (instead of producing the sequence of prime numbers) produces the sequence of "lucky numbers". The distribution of lucky numbers has a striking similarity to that of prime numbers. In particular, Hawkins and Briggs proved that if $\ell_n$ denotes the $n$th lucky number then $\ell_n \sim n \log n$, which is analogous to the prime number theorem. This work provides explicit upper and lower bounds on $\ell_n$. |
| title | Explicit inequalities for the nth lucky number |
| topic | Number Theory 11B99 (Primary) 11A99, 11N35 (Secondary) |
| url | https://arxiv.org/abs/2604.07142 |