Affiliation:
1. Eregli Kemal Akman Vocational School , Necmettin Erbakan University , Konya , Turkey
Abstract
Abstract
In this study, we give two sequences {L
+
n}n≥
1 and {L−
n}n≥
1 derived by altering the Lucas numbers with {±1, ±3}, terms of which are called as altered Lucas numbers. We give relations connected with the Fibonacci Fn
and Lucas Ln
numbers, and construct recurrence relations and Binet’s like formulas of the L
+
n
and L−
n
numbers. It is seen that the altered Lucas numbers have two distinct factors from the Fibonacci and Lucas sequences. Thus, we work out the greatest common divisor (GCD) of r-consecutive altered Lucas numbers. We obtain r-consecutive GCD sequences according to the altered Lucas numbers, and show that their GCD sequences are unbounded or periodic in terms of values r.
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