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**
Average of the Fibonacci Numbers
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Amirali Fatehizadeh

Department of Mathematical Sciences

Sharif University of Technology

Tehran

Iran

Daniel Yaqubi

Department of Computer Science

University of Torbat-e Jam

Torbat-e Jam

Iran

**Abstract:**

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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