# The EKG Sequence

```@article{Lagarias2002TheES,
title={The EKG Sequence},
author={Jeffrey C. Lagarias and Eric M. Rains and N. J. A. Sloane},
journal={Experimental Mathematics},
year={2002},
volume={11},
pages={437 - 446}
}```
• Published 1 January 2002
• Mathematics
• Experimental Mathematics
The EKC 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/(3logn)) + o(n/log n) as n → ∞ and that the exceptional values a(n) = p and a(n) = 3p…

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• Florham Park, NJ 07932-0971 Current address: Institute for Defense Analysis