Journal of Integer Sequences, Vol. 25 (2022), Article 22.2.6

Average of the Fibonacci Numbers

Amirali Fatehizadeh
Department of Mathematical Sciences
Sharif University of Technology

Daniel Yaqubi
Department of Computer Science
University of Torbat-e Jam
Torbat-e Jam


The arithmetic mean of the first n Fibonacci numbers is not an integer for all n. However, for some values of n, it is. In this paper we consider the sequence of integers n for which the average of the first n Fibonacci numbers is an integer. We prove some interesting properties and present two related conjectures.

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(Concerned with sequences A000032 A000045 A001175 A111035 A124456 A331870 A331976 A331977.)

Received July 30 2021; revised version received August 27 2021; November 2 2021; February 7 2022. Published in Journal of Integer Sequences, February 7 2022.

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