On Integer Numbers with Locally Smallest Order of Appearance in the Fibonacci Sequence
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 p...
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| Language: | English |
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Hindawi Limited
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/407643 |
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doaj-f7e65906d0664cc08a37f5ed2bb469e62020-11-25T02:29:37ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/407643407643On Integer Numbers with Locally Smallest Order of Appearance in the Fibonacci SequenceDiego Marques0Departament of Mathematics, University of Brasilia, Brasilia-DF 70910-900, BrazilLet 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.http://dx.doi.org/10.1155/2011/407643 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Diego Marques |
| spellingShingle |
Diego Marques On Integer Numbers with Locally Smallest Order of Appearance in the Fibonacci Sequence International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Diego Marques |
| author_sort |
Diego Marques |
| title |
On Integer Numbers with Locally Smallest Order of Appearance in the Fibonacci Sequence |
| title_short |
On Integer Numbers with Locally Smallest Order of Appearance in the Fibonacci Sequence |
| title_full |
On Integer Numbers with Locally Smallest Order of Appearance in the Fibonacci Sequence |
| title_fullStr |
On Integer Numbers with Locally Smallest Order of Appearance in the Fibonacci Sequence |
| title_full_unstemmed |
On Integer Numbers with Locally Smallest Order of Appearance in the Fibonacci Sequence |
| title_sort |
on integer numbers with locally smallest order of appearance in the fibonacci sequence |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2011-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2011/407643 |
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