Matches in SemOpenAlex for { <https://semopenalex.org/work/W1901474581> ?p ?o ?g. }
- W1901474581 abstract "The $3x+1$ Problem asks if whether for every natural number $n$, there exists a finite number of iterations of the piecewise function $$f(2n)=n, quad f(2n-1)=6n-2, $$ with an iterate equal to the number $1$, or in other words, every sequence contains the trivial cycle $leftlangle {4,2,1}rightrangle$. We use a set-theoretic approach to get representations of all inverse iterates of the number $1$. The representations, which are exponential Diophantine equations, help us study both the textit{mixing} property of $f$ and the asymptotic behavior of sequences containing the trivial cycle. Another one of our original results is the new insight that the textit{ones-ratio} approaches zero for such sequences, where the number of odd terms is textit{arbitrarily large}." @default.
- W1901474581 created "2016-06-24" @default.
- W1901474581 creator A5009289931 @default.
- W1901474581 date "2015-04-13" @default.
- W1901474581 modified "2023-09-27" @default.
- W1901474581 title "The 3x+1 Problem and Integer Representations" @default.
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