These are the four years per cycle that are a leap year that should have been moved up to the following year. In other words, we have Pesach one month late, and should have been what is currently 14 Adar Beth, or thereabout. That is Purim, or Shushan Purim, or, in rare cases, just before or after these days, and that seems more than a mere coincidence.
Let me suggest that it is proper to include into Purim festivities, a Pesach meal, with Matzot, on the day (evening) that should have been the first day of Pesach. The first such opportunity will be 14 Adar Beth 5779, after that it will be 16 Adar Beth of 5784, 14 Adar Beth of 5787, and 13 Adar Beth of 5795.
We call this day Hemshech Purim, and it appears that Hemshech Purim can be on the days 13, 14, 15, 16 of Adar Beth. Starting from year 7001 in can also fall in the month of Adar in a regular year, if by then we have not changed the calendar.
Actually, the dates 13, 15, 16 of Adar Beth are rare for Hemshech Purim to fall on. I counted that Hemshech Purim is 14 Adar Beth in 16 out of the 22 cases that will occur in the years 5779 - 5879. It will be 13 Adar Beth in 3 cases, 15 Adar Beth in one case, and 16 Adar Beth in 2 cases.
I found a total of six kinds of calendrical differences among the 22 cases, three of them corresponding to the same date for Hemshech Purim, 14 Adar Beth.
Shavuot Sameach!
אֱֽלֹהַ֗י אֶקְרָ֣א י֭וֹמָם וְלֹ֣א תַעֲנֶ֑ה
וְ֝לַ֗יְלָה וְֽלֹא־דֻֽמִיָּ֥ה לִֽי
(Tehilim 22)
וְ֝לַ֗יְלָה וְֽלֹא־דֻֽמִיָּ֥ה לִֽי
