Jim asked: << What is known about the parity of floor of 2^n / n, for general values of n? This is a fascinating question. Some other related questions are Given b, D in Z+ 1. What is the behavior of the residue class of b^n / n mod D? 2. What is the limiting distribution of the fractional parts { frac(b^n / n) : n in Z+ } ? In particular, is it uniform? ------------------------------------------------------------------------------------ Another such question, a bit less related, and I think unsolved, is 3. What is the limiting distribution of the fractional parts { frac( (3/2)^n ) : n in Z+ } ? (It's believed to be uniform.) And while we're at it, given D in Z+, 4. What's known about { floor( (3/2)^n ) mod D : n in Z+ } ? --Dan