Year 0 in some systems exists and in year 0 there is a blue moon. There are also blue moons in year 3, year 8 etc. This 4,5 I have seen so far and this timeanddate.com makes me think that it has that 4,5,3,16,17,2,9, and then repeats at 16 cycle. Sites including wikipedia say that a blue moon occurs every 2 to 3 years. Well they are wrong on that.