ALTERED NUMBERS OF LUCAS NUMBER SQUARED
Authors : Fikri Köken, Emre Kankal
Pages : 62-75
Doi:10.59313/jsr-a.1251592
View : 16 | Download : 20
Publication Date : 2023-09-30
Article Type : Research
Abstract :We investigate two types altered Lucas numbers denoted and defined by adding or subtracting a value from the square of the Lucas numbers. We achieve these numbers form as the consecutive products of the Fibonacci numbers. Therefore, consecutive sum-subtraction relations of altered Lucas numbers and their Binet-like formulas are given by using some properties of the Fibonacci numbers. Also, we explore the gcd sequences of r–successive terms of altered Lucas numbers denoted and , , according to the greatest common divisor (gcd) properties of consecutive terms of the Fibonacci numbers. We show that these sequences are periodic or Fibonacci sequences.Keywords : Altered Lucas numbers, Greatest common divisor (gcd) sequences, Fibonacci sequence, Lucas sequence