There is an offer of 500 POINTS out there for anybody who can prove that the sequence from last week's Internet Special always gets caught up in 1 - 2 - 1 - 2 - 1 - 2 ..., no matter what the starting value (a natural number, i.e., a positive integer) is. The deadline for this problem is Friday, December 14, 2001, 5:30 pm.