1. This year is a common year, but in the previous generation it would have been a leap year. If the fractional part of the date of Pesach of the previous year (m) is greater than 0:15:204, and if the previous Pesach falls on a Sunday, the exception rule did not work, as it assumed that this year would be a leap year. The result is that this year has 356 days.
2. In this year, the first Molad changes, i.e. the value of z. Half a day is subtracted from M + m. This means that if, with the previous value of z, the day was deficient, 353 or 383 days, now there is a chance that it will become a year with 352 or 382 days.
The first scenario happens about once in 400 calendar generation switches, one time in every 130,000 years. The second scenario happens slightly more often, about once in 12 Molad switches, which amounts to once in every 80,000 years. All in all, there is a chance of one in 50,000 years of something happening.
The first time that actually something happens is in the year 35334, and it is the first scenario that is happening. In the first 500,000 years, the first scenario happens four times, whereas the second scenario plays out six times. This answers the question.
The following two rules make the calendar mathematically complete:
1. If scenario 1 happens, the previous year (is a deficient year and) should have two extra days, making the previous year into an abundant year and this year into a regular year of 354 days.
2. If scenario 2 happens, the previous year (is an abundant year and) should have two days less, making the previous year into a deficient year and this year into a regular year of 354 or 384 days.
I have validated the sufficiency of these rules for the first 500000 years. And I updated the English and Hebrew versions of the paper to include a section in the spirit of this post.
כׇּל־רֹ֭אַי יַלְעִ֣גוּ לִ֑י
יַפְטִ֥ירוּ בְ֝שָׂפָ֗ה יָנִ֥יעוּ רֹֽאשׁ
(Tehilim 22)
יַפְטִ֥ירוּ בְ֝שָׂפָ֗ה יָנִ֥יעוּ רֹֽאשׁ
