Değiştirilmiş Pell ve Pell Lucas Dizilerinin Özellikleri

Değiştirilmiş Pell ve Pell Lucas dizileri, Pell ve Pell Lucas sayıları değiştirilerek tanımlanır, bu dizilerin, Pell ve Pell Lucas dizileriyle benzer özelliklere sahip oldukları görülmektedir. Bu nedenle, değiştirilmiş dizilerin bazı indirgeme özelliklerini incelenir. Ayrıca, değiştirilmiş dizilerin en büyük ortak bölenleri (yani, EBOB) dizileri araştırılır ve EBOB dizilerinin, Pell ve Pell Lucas dizilerinin alt dizileri olduğu görülür. Bu nedenle, GCD dizilerinin Binet formülünü, Cassini, Catalan ve Docagne’nin eşitlikleri elde edilir.

Anahtar Kelimeler:

Değiştirilmiş Pell ve Pell Lucas sayıları, EBOB Dizileri, İndirgeme bağıntıları

The Properties of the Altered Pell and Pell Lucas Sequences

The altered Pell and Pell Lucas sequences are defined by altering the Pell and Pell Lucas numbers, it is seen that they have similar properties to usual the Pell and Pell Lucas sequences. Thus, we study some recursive properties of the altered sequences. Further, the greatest common divisors (i.e. GCD) sequences of the altered sequences are investigated, and it is seen that the GCD sequences are subsequences of the Pell and Pell Lucas sequences. Therefore, we obtain Binet formula, the Cassini, Catalan and D’ocagne’s identities of the GCD sequences.

Keywords:

Altered Pell and Pell Lucas numbers, GCD Sequences, Recurrence relations,

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