Simple Sequences with Puzzling Properties

Many mathematicians feel that the main impact of computers on mathematics has been not in solving problems, as one might expect, but rather in posing them. The prime illustration is probably the recent activity in discrete dynamical systems stimulated by the celebrated computer experiments of Mitchell Feigenbaum. Perhaps “explorations” is a better description of this work, for the appropriate analogy is not with physics or biology but with astronomy. The computer is the mathematician’s telescope, which when used intelligently makes it possible to find out what is “out there” in the mathematical universe. (This whole development should be a source of satisfaction to the Platonists, who have been saying all along that, like stars and galaxies, mathematical phenomena are discovered, not invented.)