ALTERED NUMBERS OF LUCAS NUMBER SQUARED

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Journal of Scientific Reports-A
Issue:054
ALTERED NUMBERS OF LUCAS NUMBER SQUARED

ALTERED NUMBERS OF LUCAS NUMBER SQUARED

Authors : Fikri KÖKEN, Emre KANKAL

Pages : 62-75

Doi:10.59313/jsr-a.1251592

View : 38 | Download : 27

Publication Date : 2023-09-30

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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

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