Complexity of natural numbers
J. Arias de Reyna
TL;DR
This paper discusses conjectures related to the complexity of natural numbers, resolves the last of these conjectures, and provides a translated version of the original Spanish paper for reference.
Contribution
It introduces several conjectures about natural number complexity and resolves the final conjecture in a subsequent joint publication.
Findings
Resolution of the last conjecture on natural number complexity
Introduction of new conjectures about natural number complexity
Clarification of the structure of natural number complexity
Abstract
This is the English version of the paper: "Complejidad de los n\'umeros naturales", Gaceta de la Real Sociedad Matem\'atica Espa\~nola 3 (2000) 230--250. In this paper, several conjectures about the complexity of natural numbers are proposed. In a recent joint paper with H. Altman "Integer Complexity, stability, and self-similarity" arXiv:2111.00671, we resolve the last of these conjectures. This is why I consider its translation useful now as a reference.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Computability, Logic, AI Algorithms · Advanced Topology and Set Theory