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The Properties of the Altered Pell and Pell Lucas Sequences
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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.
Title: The Properties of the Altered Pell and Pell Lucas Sequences
Description:
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.
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