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On Integer Numbers with Locally Smallest Order of Appearance in the Fibonacci Sequence

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  • Diego Marques

Abstract

Let be the th Fibonacci number. The order of appearance of a natural number is defined as the smallest natural number such that divides . For instance, for all , we have . In this paper, we will construct infinitely many natural numbers satisfying the previous inequalities and which do not belong to the Fibonacci sequence.

Suggested Citation

  • Diego Marques, 2011. "On Integer Numbers with Locally Smallest Order of Appearance in the Fibonacci Sequence," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-4, April.
    • Handle: RePEc:hin:jijmms:407643
    DOI: 10.1155/2011/407643
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    Cited by:

    1. Florian Luca & Thato Mosima, 2015. "On the Local Minima of the Order of Appearance Function," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-3, October.
    2. Eva Trojovská, 2020. "On the Diophantine Equation z ( n ) = (2 − 1/ k ) n Involving the Order of Appearance in the Fibonacci Sequence," Mathematics, MDPI, vol. 8(1), pages 1-8, January.
    3. Pavel Trojovský, 2019. "On Diophantine Equations Related to Order of Appearance in Fibonacci Sequence," Mathematics, MDPI, vol. 7(11), pages 1-10, November.

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