If I understand the question properly, I don't think doomsday will ever happen. The period of the moon's phases is 29.53 days. To have a blue moon, you need one full moon near the start of the month and one near the end. If there are two such months in a year, then time interval between those months must be a bit less than a whole number of moon periods. The only month that is less than a moon period is February, so you can have two blue moons, one in January, one in March.
Suppose you wanted to have a third blue moon in December. The months are:
31 (28) 31 (30 31 30 31 31 30 31 30) 31
The interval April-November is a total of 245 days, or about 8.3 moon periods. This is not close enough to a whole number of periods for the blue moon to occur in December. Earlier in the year the situation is worse.
The problem is that all months other than February are only slightly longer than a moon period so you need too many months put together for those extra days to make up a whole extra moon period.
The following is a simple proof based on Nurnani Tati's excellent answer. I add it here only to make this accepted answer more complete.
A year is at most 366/29.53 = 12.39 moon periods long, so there are at most 13 full moons in a year. If there were 3 blue moons in a year, there would be 10 normal full moons. A year has 12 months so this means that there would need to be (at least) two months without a full moon, but only February is short enough for that. Therefore 3 blue moons is impossible.