Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2302.02838 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915654621200384 |
|---|---|
| author | Basistha, Amit Kumar Ionascu, Eugen J. |
| author_facet | Basistha, Amit Kumar Ionascu, Eugen J. |
| contents | In this paper, we study a class of functions defined recursively on the set of natural numbers in terms of the greatest common divisor algorithm of two numbers and requiring a minimality condition. These functions are permutations, products of infinitely many cycles that depend on certain breaks in the natural numbers involving the primes, and some special products of primes with a density of approximately $29.4\%$. We show that these functions split into only two equivalence classes (modulo the natural equivalence relation of eventually identical maps): one is the class of the identity map and the other is generated by a map whose discrete derivative is almost periodic with ``periods" the primorial numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_02838 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A special sequence and primorial numbers Basistha, Amit Kumar Ionascu, Eugen J. Number Theory 11A05 In this paper, we study a class of functions defined recursively on the set of natural numbers in terms of the greatest common divisor algorithm of two numbers and requiring a minimality condition. These functions are permutations, products of infinitely many cycles that depend on certain breaks in the natural numbers involving the primes, and some special products of primes with a density of approximately $29.4\%$. We show that these functions split into only two equivalence classes (modulo the natural equivalence relation of eventually identical maps): one is the class of the identity map and the other is generated by a map whose discrete derivative is almost periodic with ``periods" the primorial numbers. |
| title | A special sequence and primorial numbers |
| topic | Number Theory 11A05 |
| url | https://arxiv.org/abs/2302.02838 |