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 number not already used that shares
a factor with the preceding term. 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. have computed the first
10 million terms of the sequence (Lagarias et al. 2002, Peterson 2002).

Every term 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
term . For the first terms, whenever a prime occurs, it is immediately preceded by and followed by . This results in a three lines of points when the sequence
is plotted without connecting the dots.