  It's the age-old recurrence with a twist: sum the last two terms and if the
result is composite, divide by its smallest prime divisor to get the next term
(e.g., 0, 1, 1, 2, 3, 5, 4, 3, 7, ...). These sequences exhibit pseudo-random
behaviour and generally terminate in a handful of cycles, properties
reminiscent of 3x+1 and related sequences. We examine the elementary properties
of these 'subprime' Fibonacci sequences.
