TL;DR
This paper explores eight infinite integer sequences, each linked to an unsolved problem, highlighting their mathematical significance and connections to famous conjectures and puzzles.
Contribution
It provides an in-depth discussion of eight specific sequences related to unsolved problems, expanding understanding of their properties and significance.
Findings
Each sequence is connected to a notable unsolved problem.
The sequences illustrate diverse mathematical phenomena.
Potential insights into unresolved conjectures are highlighted.
Abstract
In his July 1974 Scientific American column, Martin Gardner mentioned the Handbook of Integer Sequences, which then contained 2372 sequences. Today the On-Line Encyclopedia of Integer Sequences (the OEIS) contains 140000 sequences. This paper discusses eight of them, suggested by the theme of the Eighth Gathering For Gardner: they are all infinite, and all 'ateful in one way or another. Each one is connected with an unsolved problem. The sequences are related to: hateful numbers, Angelini's 1995 puzzle, the persistence of a number, Alekseyev's 123 sequence, the curling number conjecture, Quet's prime-generating recurrence, the traveling salesman's problem, and the Riemann Hypothesis.
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Taxonomy
TopicsBenford’s Law and Fraud Detection · Analytic Number Theory Research · Advanced Mathematical Theories