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}
}
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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