Name
Abstract | ||
|---|---|---|
We study the ``approximate squaring'' map f(x) := x ceiling(x) and its
behavior when iterated. We conjecture that if f is repeatedly applied to a
rational number r = l/d > 1 then eventually an integer will be reached. We
prove this when d=2, and provide evidence that it is true in general by giving
an upper bound on the density of the ``exceptional set'' of numbers which fail
to reach an integer. We give similar results for a p-adic analogue of f, when
the exceptional set is nonempty, and for iterating the ``approximate
multiplication'' map f_r(x) := r ceiling(x) where r is a fixed rational number. |
Year | Venue | Keywords |
|---|---|---|
2004 | Experimental Mathematics | 3x + 1 problem,iterated maps,mahler z-numbers,integer sequences,approximate multiplication,approximate squaring |
DocType | Volume | Issue |
Journal | 13 | 1 |
ISSN | Citations | PageRank |
Experimental Math. 13 (2004), 113--128. | 1 | 0.48 |
References | Authors | |
1 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| J. C. Lagarias | 1 | 563 | 235.61 |
| N. J. A. Sloane | 2 | 1879 | 543.23 |