On integer numbers with locally smallest order of appearance in the Fibonacci sequence
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| Publication Date: | 2011 |
| Format: | Article |
| Language: | eng |
| Source: | Repositório Institucional da UnB |
| Download full: | http://repositorio.unb.br/handle/10482/12760 https://dx.doi.org/10.1155/2011/407643 |
Summary: | Let Fn be the nth Fibonacci number. The order of appearance z n of a natural number n is defined as the smallest natural number k such that n divides Fk. For instance, for all n Fm ≥ 5, we have z n − 1 >z n <z n 1 . In this paper, we will construct infinitely many natural numbers satisfying the previous inequalities and which do not belong to the Fibonacci sequence. |
| Summary: | Let Fn be the nth Fibonacci number. The order of appearance z n of a natural number n is defined as the smallest natural number k such that n divides Fk. For instance, for all n Fm ≥ 5, we have z n − 1 >z n <z n 1 . In this paper, we will construct infinitely many natural numbers satisfying the previous inequalities and which do not belong to the Fibonacci sequence. |
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