The EKG sequence is the integer sequence having 1 as its first term, 2 as its second, and with each succeeding term being the smallest positive integer not already used whose greatest common divisor with the preceding term exceeds 1. This results in the sequence 1, 2, 4, 6, 3, 9, 12, 8, 10, 5, 15, ... (OEIS A064413). When plotted as a connect-the-dots plot (left figure), the sequence looks somewhat like an electrocardiogram (abbreviated "EKG" in medical circles), so this sequence became known as the EKG sequence (Lagarias et al. 2002). Lagarias et al. (2002) computed the first 10 million terms of the sequence (Peterson 2002).
Every positive integer appears exactly once in this sequence, and the primes occur in increasing order (Lagarias et al. 2002). The inverse permutation of the integers giving the sequence is 1, 2, 5, 3, 10, 4, 14, 8, 6, 9, 20, 7, 28, ... (OEIS A064664).
Lagarias et al. (2002) established the bounds
 |
for the 
th
term 
, where 
. For the first 
terms, whenever an odd prime 
occurs, it is immediately preceded by
and followed by 
. This results in three lines of points when the sequence
is plotted without connecting the dots.
