TL;DR
This paper explores seven intriguing integer sequences, highlighting their unique properties and significance, and discusses their relevance in recreational mathematics and mathematical research.
Contribution
It introduces and analyzes seven notable integer sequences, providing insights into their behaviors and mathematical importance, expanding understanding of sequence diversity.
Findings
Identification of seven interesting integer sequences
Insights into the properties and behaviors of these sequences
Connections to broader mathematical concepts and problems
Abstract
When my "Handbook of Integer Sequences" came out in 1973, Philip Morrison gave it an enthusiastic review in the Scientific American and Martin Gardner was kind enough to say in his Mathematical Games column that "every recreational mathematician should buy a copy forthwith." That book contained 2372 sequences. Today the "On-Line Encyclopedia of Integer Sequences" contains 117000 sequences. This paper will describe seven that I find especially interesting. These are the EKG sequence, Gijswijt's sequence, a numerical analog of Aronson's sequence, approximate squaring, the integrality of n-th roots of generating functions, dissections, and the kissing number problem. (Paper for conference in honor of Martin Gardner's 91st birthday.)
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Taxonomy
TopicsAdvanced Mathematical Theories