Power of Two--Classes in k--Generalized Fibonacci Sequences
The k-generalized Fibonacci sequence \big(Fn(k)\big)n\geq 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\ge 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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Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
2014
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oai:scielo:S0034-742620140002000062015-11-20Power of Two--Classes in k--Generalized Fibonacci SequencesGÓMEZ,CARLOS ALEXISLUCA,FLORIAN k--Generalized Fibonacci numbers Lower bounds for nonzero linear forms in logarithms of algebraic numbers The k-generalized Fibonacci sequence \big(Fn(k)\big)n\geq 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\ge 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.info:eu-repo/semantics/openAccessUniversidad Nacional de Colombia y Sociedad Colombiana de MatemáticasRevista Colombiana de Matemáticas v.48 n.2 20142014-12-01info:eu-repo/semantics/articletext/htmlhttp://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262014000200006in10.15446/recolma.v48n2.54128 |
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GÓMEZ,CARLOS ALEXIS LUCA,FLORIAN |
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GÓMEZ,CARLOS ALEXIS LUCA,FLORIAN Power of Two--Classes in k--Generalized Fibonacci Sequences |
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GÓMEZ,CARLOS ALEXIS LUCA,FLORIAN |
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GÓMEZ,CARLOS ALEXIS |
| title |
Power of Two--Classes in k--Generalized Fibonacci Sequences |
| title_short |
Power of Two--Classes in k--Generalized Fibonacci Sequences |
| title_full |
Power of Two--Classes in k--Generalized Fibonacci Sequences |
| title_fullStr |
Power of Two--Classes in k--Generalized Fibonacci Sequences |
| title_full_unstemmed |
Power of Two--Classes in k--Generalized Fibonacci Sequences |
| title_sort |
power of two--classes in k--generalized fibonacci sequences |
| description |
The k-generalized Fibonacci sequence \big(Fn(k)\big)n\geq 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\ge 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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Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas |
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2014 |
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http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262014000200006 |
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AT gomezcarlosalexis poweroftwoclassesinkgeneralizedfibonaccisequences AT lucaflorian poweroftwoclassesinkgeneralizedfibonaccisequences |
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