To get my very unpredictable cycle I start at year 0 with a blue moon. I find year 3 has one as well but the calendar if you don't look at the moon phase one but the one with the days of the week showing major moon phase dates below the calendar for that month of that year it clearly shows that there is no blue moon in january of year 1.
How I get this 3,5,3,16,17,2,9,16,17,2,9 etc cycle is I look at the calendar with the days of the week(which is supposed to be accurate in their moon phases especially full moons), see which ones I see more than 1 full moon in a month on subtract the previous year with that same thing from the year that I am looking at and get this unpredictable cycle of years between blue moons.
You guys are looking at the moon phase calendar and the moon phase calendar and days of week calendar are contradicting. The moon phase calendar says it is every 2-3 years but the days of the week one says that it is this cycle of differences between years starting with year 0(which I needed to go to a different site for) and year 3: 3,5,3,16,7,2,9,16,17,2,9 etc.
Year 1 moon phase calendar:
http://www.timeanddate.com/calendar/moonphases.html?year=1&n=0
says there is a blue moon in that year.
Year 1 calendar with days of the week:
http://www.timeanddate.com/calendar/?year=1&country=1
This is what I look at and says there is no blue moon during that year.