[math-fun] 9 * 99 * 999 * ...

One side-alley that I glanced down when I was preparing my current Mathematical Enchantments essay, but then resolutely marched myself past, involves the behavior of the decimal expansion of the product (10^1-1)(10^2-1)...(10^n-1); the initial and final digits are quite orderly, while the digits in the middle look random. Has anyone looked into this? It'd be especially interesting if one could establish some sort of phase transition. I realize I'm using vocabulary loosely; there's no randomness involved, so we're not really doing stat mech. Still, some of the concepts of stat mech might apply. Jim Propp