We investigate two types of altered Fibonacci numbers obtained by adding or subtracting a specific value $\{a\}$ from the square of the $n^{th}$ Fibonacci numbers $G^{(2)}_{F(n)}(a)$ and $H^{(2)}_{F(n)}(a)$. These numbers are significant as they are related to the consecutive products of the Fibonacci numbers. As a result, we establish consecutive sum-subtraction relations of altered Fibonacci numbers and their Binet-like formulas. Moreover, we explore greatest common divisor (GCD) sequences of r-successive terms of altered Fibonacci numbers represented by $\left\{G^{(2)}_{F(n), r}(a)\right\}$ and $\left\{H^{(2)}_{F(n), r}(a)\right\}$ such that $r\in\{1,2,3\}$ and $a\in\{1,4\}$. The sequences are based on the GCD properties of consecutive terms of the Fibonacci numbers and structured as periodic or Fibonacci sequences.
Altered Fibonacci number greatest common divisor (GCD) sequence Fibonacci sequence
Birincil Dil | İngilizce |
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Konular | Cebir ve Sayı Teorisi |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Erken Görünüm Tarihi | 30 Aralık 2023 |
Yayımlanma Tarihi | 31 Aralık 2023 |
Gönderilme Tarihi | 29 Eylül 2023 |
Yayımlandığı Sayı | Yıl 2023 Sayı: 45 |
As of 2021, JNT is licensed under a Creative Commons Attribution-NonCommercial 4.0 International Licence (CC BY-NC). |