Seven Staggering Sequences

Details Seven Staggering Sequences Seven Staggering Sequences

2009-12-12

arxiv.org/abs/0912.2394v1

Mathematics

Combinatorics

12 pages. A somewhat different version appeared in "Homage to a Pied Puzzler", E. Pegg Jr., A. H. Schoen and T. Rodgers (edito

Scientific paper

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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