Power of Two–Classes in k–Generalized Fibonacci Sequences Clases de potencias de dos en sucesiones k–generalizadas de Fibonacci
نویسندگان
چکیده
The k-generalized Fibonacci sequence ( F (k) n ) n≥2−k is the linear recurrent sequence of order k, whose first k terms are 0, . . . , 0, 1 and each term afterwards is the sum of the preceding k terms. Two or more terms of a k-generalized Fibonacci sequence are said to be in the same power of two-class if the largest odd factors of the terms are identical. In this paper, we show that for each k ≥ 2, there are only two kinds of power of two-classes in a k-generalized Fibonacci sequence: one, whose terms are all the powers of two in the sequence and the other, with a single term.
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