TL;DR
This paper proves that the observed similarities in nine sequences with similar parities are mathematically inevitable rather than coincidental, providing a formal proof of this phenomenon.
Contribution
It offers the first formal proof that the similarities among these sequences are not coincidental but are mathematically grounded.
Findings
The nine sequences share an inherent mathematical property.
The similarities are proven to be non-coincidental.
Provides a formal proof of the sequences' parity-related similarities.
Abstract
This paper is inspired by a seqfan post by Jeremy Gardiner. The post listed nine sequences with similar parities. In this paper I prove that the similarities are not a coincidence but a mathematical fact.
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Taxonomy
TopicsArtificial Intelligence in Games · Computability, Logic, AI Algorithms · Algorithms and Data Compression