Journal article Open Access

# Two-Parameter Generalization of the Collatz Function: Characterization of Terminal Cycles and Empirical Results

Boris B. Stefanov

### Dublin Core Export

<?xml version='1.0' encoding='utf-8'?>
<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:creator>Boris B. Stefanov</dc:creator>
<dc:date>2021-03-17</dc:date>
<dc:description>This paper proposes a new two-parameter generalization T_{b,s}(x) of the Z -&gt; Z Collatz function T(x) and restates the eponymous conjecture in terms of the proposed function. The generalization obviates some of the conditions for emergence of terminal cycles for the Collatz T(x) function over the integers. The stopping behavior of the T_{b,s}(x) is qualitatively similar to that of the T(x).  The paper presents theoretical discussion of the generalization and computational results on the terminal cycles and stopping times of T_{b,s}(x). The {1,2} cycle of T(x) is shown to be a case of coincidence of three independent cycle categories of T_{b,s}(x).</dc:description>
<dc:identifier>https://zenodo.org/record/4609709</dc:identifier>
<dc:identifier>10.5281/zenodo.4609709</dc:identifier>
<dc:identifier>oai:zenodo.org:4609709</dc:identifier>
<dc:language>eng</dc:language>
<dc:relation>doi:10.5281/zenodo.4609708</dc:relation>
<dc:relation>url:https://zenodo.org/communities/omj</dc:relation>
<dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
<dc:source>Online Mathematics Journal 03(01) 19–25</dc:source>
<dc:subject>Collatz conjecture</dc:subject>
<dc:subject>3x+1 problem</dc:subject>
<dc:subject>iteration</dc:subject>
<dc:subject>convergence</dc:subject>
<dc:subject>terminal cycles</dc:subject>
<dc:title>Two-Parameter Generalization of the Collatz Function: Characterization of Terminal Cycles and Empirical Results</dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
<dc:type>publication-article</dc:type>
</oai_dc:dc>

167
113
views