  Define a sequence of positive integers by the rule that a(n) = n for 1 <= n
<= 3, and for n >= 4, a(n) is the smallest number not already in the sequence
which has a common factor with a(n-2) and is relatively prime to a(n-1). We
show that this is a permutation of the positive integers. The remarkable graph
of this sequence consists of runs of alternating even and odd numbers,
interrupted by small downward spikes followed by large upward spikes,
suggesting the eruption of geysers in Yellowstone National Park. On a larger
scale the points appear to lie on infinitely many distinct curves. There are
several unanswered questions concerning the locations of these spikes and the
equations for these curves.
