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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We show that these sequences are periodic or Fibonacci sequences.
📌 3 Key Takeaways
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Objective & Hypothesis:We investigate two types altered Lucas numbers denoted and defined by adding or subtracting a value from the square of the Lucas numbers.
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Key Findings & Data:We achieve these numbers form as the consecutive products of the Fibonacci numbers.
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Conclusion & Impact:We show that these sequences are periodic or Fibonacci sequences.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Altered Lucas numbers · Greatest common divisor (gcd) sequences · Fibonacci sequence
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.
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Cite This Article
KÖKEN, F., KANKAL, E. (2023). ALTERED NUMBERS OF LUCAS NUMBER SQUARED. Journal of Scientific Reports-A, Sayı: 054, 62–75. https://ajindex.com/articles/964516