The EKG Sequence

Details The EKG Sequence The EKG Sequence

2002-03-31

arxiv.org/abs/math/0204011v1

Experimental Math. Vol. 11, No. 3 (2002), 437-446.

Mathematics

Number Theory

15 pages, 7 figures

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The EKG Sequence does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The EKG Sequence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The EKG Sequence will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-412950