On the Parity of the Order of Appearance in the Fibonacci Sequence

Pavel Trojovský
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Pavel Trojovský: Department of Mathematics, Faculty of Science, University of Hradec Králové, 500 03 Hradec Králové, Czech Republic

Mathematics, 2021, vol. 9, issue 16, 1-8

Abstract: Let ( F n ) n ? 0 be the Fibonacci sequence. The order of appearance function (in the Fibonacci sequence) z : Z ? 1 ? Z ? 1 is defined as z ( n ) : = min { k ? 1 : F k ? 0 ( mod n ) } . In this paper, among other things, we prove that z ( n ) is an even number for almost all positive integers n (i.e., the set of such n has natural density equal to 1).

Keywords: order of appearance; Fibonacci numbers; parity; natural density; prime numbers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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