Even perfect numbers in generalized Pell sequences
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DOI: 10.1007/s10986-020-09505-6
Abstract: In this paper, by using linear forms in logarithms and the Baker–Davenport reduction procedure we prove that there are no even perfect numbers appearing in generalized Pell sequences. We also deduce some interesting results involving… read more here.
Keywords: numbers generalized; pell sequences; generalized pell; even perfect ... See more keywords
Some identities on generalized harmonic numbers and generalized harmonic functions
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DOI: 10.1515/dema-2022-0229
Abstract: Abstract The harmonic numbers and generalized harmonic numbers appear frequently in many diverse areas such as combinatorial problems, many expressions involving special functions in analytic number theory, and analysis of algorithms. The aim of this… read more here.
Keywords: harmonic numbers; harmonic functions; generalized harmonic; identities generalized ... See more keywords
Fibonacci numbers in generalized Pell sequences
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DOI: 10.1515/ms-2017-0413
Abstract: Abstract In this paper, by using lower bounds for linear forms in logarithms of algebraic numbers and the theory of continued fractions, we find all Fibonacci numbers that appear in generalized Pell sequences. Some interesting… read more here.
Keywords: numbers generalized; pell sequences; fibonacci numbers; generalized pell ... See more keywords
Combinatorial Interpretation of Numbers in the Generalized Padovan Sequence and Some of Its Extensions
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DOI: 10.3390/axioms11110598
Abstract: There is ongoing research into combinatorial methods and approaches for linear and recurrent sequences. Using the notion of a board defined for the Fibonacci sequence, this work introduces the Padovan sequence combinatorial approach. Thus, mathematical… read more here.
Keywords: combinatorial interpretation; sequence; padovan sequence; numbers generalized ... See more keywords