A Game for a Mensa Dinner

Sitting round the Dinner Table, one person starts and is Zero.  The next person in One, going clockwise. The numbers increment in integers, but after Two and Three comes Two Squared, because only the Prime Numbers are 'real' and Composite Numbers must be express in terms of their factors.  So Five, Two Threes or Three Twos, Seven, Two Cubed and so forth.  It gets interesting with higher powers and patterns can emerge.  It is an interesting exercise to do alone, for mental training or recreation, but I am lazy and have not gone very far.  It is a nice way to think about numbers.  It may also be able to be done with diminishing fractions, but that is too much for my brain.