The EKG Sequence
| dc.creator | Lagarias, J. C. | |
| dc.creator | Rains, E. M. | |
| dc.creator | Sloane, N. J. A. | |
| dc.date | 2002-03-31 | |
| dc.date.accessioned | 2026-07-07T04:47:21Z | |
| dc.date.available | 2026-07-07T04:47:21Z | |
| dc.description | The EKG or electrocardiogram sequence is defined by a(1) = 1, a(2) = 2 and, for n >= 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 goes to infty; 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 {a(n): n >= 1} is a permutation of the natural numbers and that c_1 n <= a (n) <= c_2 n for constants c_1, c_2. There remains a large gap between what is conjectured and what is proved. | |
| dc.description | 15 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/math/0204011 | |
| dc.identifier | http://arxiv.org/abs/math/0204011 | |
| dc.identifier | Experimental Math. Vol. 11, No. 3 (2002), 437-446. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63684 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.title | The EKG Sequence | |
| dc.type | text |