Name
Abstract | ||
|---|---|---|
The EKG or electrocardiogram sequence is defined by a(1) = 1, a(2) = 2 and, for n greater than or equal to 3, a(n) is the smallest natural number not already in the sequence with the property that gcd{a(n - 1), a(n)} > 1. In spite of its erratic local behavior, which when plotted resembles an electrocardiogram, its global behavior appears quite regular. We conjecture that almost all a(n) satisfy the asymptotic formula a(n) = n(1 + 1/(3 log n)) + o(n/ log n) as n --> infinity; and that the exceptional values a(n) =p and a(n) = 3p, for p a prime, produce the spikes in the EKG sequence. We prove that fa(n) : n greater than or equal to 1} is is a permutation of the natural numbers and that c(1)n less than or equal to a(n) less than or equal to c(2)n for constants c(1), c(2). There remains a large gap between what is conjectured and what is proved. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1080/10586458.2002.10504486 | EXPERIMENTAL MATHEMATICS |
Keywords | Field | DocType |
electrocardiagram sequence,EKG sequence | Prime (order theory),Discrete mathematics,Binary logarithm,Asymptotic formula,Natural number,Permutation,Electrocardiogram Sequence,Conjecture,Mathematics | Journal |
Volume | Issue | ISSN |
11.0 | 3.0 | 1058-6458 |
Citations | PageRank | References |
1 | 12.33 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| J. C. Lagarias | 1 | 563 | 235.61 |
| E. M. Rains | 2 | 77 | 22.92 |
| N. J. A. Sloane | 3 | 1879 | 543.23 |