From Enmity to Amity
نویسنده
چکیده
Sloane’s influential On-Line Encyclopedia of Integer Sequences is an indispensable research tool in the service of the mathematical community. The sequence A001611 listing the “Fibonacci numbers + 1” contains a very large number of references and links. The sequence A000071 for the “Fibonacci numbers −1” contains an even larger number. Strangely, resentment seems to prevail between the two sequences; they do not acknowledge each other’s existence, though both stem from the Fibonacci numbers. Using an elegant result of Kimberling, we prove a theorem that links the two sequences amicably. We relate the theorem to a result about iterations of the floor function, which introduces a new game. doi:10.4169/000298910X496787 646 c © THE MATHEMATICAL ASSOCIATION OF AMERICA [Monthly 117
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ورودعنوان ژورنال:
- The American Mathematical Monthly
دوره 117 شماره
صفحات -
تاریخ انتشار 2010