@article{Article_36,

title = {Some Conjectures on Average of Fibonacci and Lucas Sequences},

journal = {Communications in Combinatorics, Cryptography & Computer Science},

volume = {2022},

issue = {1},

issn = { 2783-5456 },

year = {2022},

url = {http://cccs.sgh.ac.ir/Articles/2022/issue 1/1-12-SomeConjecturesonAverageofFibonacciandLucasSequences.pdf},

author = {Daniel Yaqubi and Amirali Fatehizadeh},

keywords = {Fibonacci number, Lucas number, Pisano period, rank of appearance, restricted period.},

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

};