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I noticed that the only times that parshat Matot and Mas'ei are read separately outside Israel is during a leap year when the first day of the previous Rosh Hashannah occurred on Thursday. This would mean that the 1st day of Pesach was on either Sunday or Tuesday.

This year and the previous 3 leap years (5765, 5768 and 5771) all had Matot and Mas'ei separate. So including this year, there were 4 consecutive leap years when this occurred.

Has this pattern ever occurred previously since the current Judaic calendar was established? Is there any forseeable repeat of this pattern?

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This is the only occurrence of that phenomenon in the 247-year cycle. Source: the table in the Tur, hilchos rosh chodesh.

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  • Thanks - This is a nice useful consolidated table for me. One area, that you may be able to help me out, perhaps. I understand everything in the small squares. But I don't understand the larger rectangles near the bottom of the page that seem to list specific years which are labeled "machzor hashanim". What do these years mean?
    – DanF
    Commented Jul 4, 2014 at 18:23
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    @DanF, the top line of each of those boxes is the number of the 19-year cycle (the 267th 19-year cycle, etc.) and the bottom line is the year number of the first year in that 19-year cycle.
    – msh210 ♦
    Commented Jul 4, 2014 at 18:57
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Recall leap years are in years 3-6-8-11-14-17-19 of a nineteen year period. A three year period with one leap year is 37 months, which will push forward the Molad a mere 15 hours and 181 parts. Three of those will push it off 1 day 21 hours and 543 parts, or just 2697 parts (=2 hours 537 parts) shy of 2 days. That's possible in years 8-11-14-17 of the leap year cycle.

There is a two day window for when the Molad must fall to have Rosh Hashana on Thursday since if it fell at a time appropriate for Wednesday it is pushed off. If the Molad falls in the first 2697 parts of that window in year 8 of the leap year cycle then you have your observed phenomenon.

We also know that the calendar repeats approximately every 247 years with an error of 905 parts. Since 2697/905 is just less than 3, these events will always come in triplets with 247 year gaps between them. After 3 times though the error will move the start time out of our short 2697 part window. Thus these triplets will happen in (2697/(1080*24*7))/19/3=0.026% of years or about once every 4000 years.

You observed this starting in the year 5765. As expected it is year 8 of the leap year cycle, and the other parts of your sequence are all 3 years apart. The Molad that year was Tuesday 1367 parts after noon, more than 905 parts after noon but less than 2*905 parts after noon, which means it must be the middle of a triplet set. By adding and subtracting 247, we find another time this happened began in 5518 and the next time will begin in 6012.

(The same exact argument applies to Rosh Hashana on Monday and Saturday, and indeed the last triplet for Monday began in 3865 and for Saturday began in 2763, with the next triplet for Monday and Saturday beginning about 4000 years later in 7722 and 6620 respectively. The next Thursday set will begin in 9375. If you allow non-leap years, the same argument holds true for years 7 and 9 in the leap year cycle, and, due to the "gatrad" rule, the sets come in more than triplets for Thursdays since our window grows from 2697 parts to 2697+9516=12213 parts; coming up in 5823 there will be four non-leap years starting on Thursday spaced 3 years apart, number 3 in a sequence of 14 such events spaced 247 years apart.)

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