On integer numbers with locally smallest order of appearance in the Fibonacci sequence (Q539364)
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scientific article; zbMATH DE number 5900721
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On integer numbers with locally smallest order of appearance in the Fibonacci sequence |
scientific article; zbMATH DE number 5900721 |
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On integer numbers with locally smallest order of appearance in the Fibonacci sequence (English)
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27 May 2011
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Summary: Let \(F_n\) be the be the \(n\)th 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 \(F_n\). For instance, for all \(n=F_m \geq 5\), 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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Fibonacci sequence
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Fibonacci entry point
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Binet's formula
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0.91643596
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0.9142606
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0.87996984
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0.8723388
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0.8653461
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0.8652995
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0.86473167
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