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I am compiling a short shiur for my shul on Rosh Hashanna. I plan on discussing some items related to the Judaic calendar, with a focus on some statistics that I can eventually put into Excel and / or chart.

Here are some stats that I'm seeking:

  • Frequency of the day of week that Pesach begins (I can determine the weekday for Rosh Hashanna from that)

  • Weekday pairs - I.e., if Rosh Hashanna is on Mon. this year, what possible weekdays could it be the following year? List or table should be for both regular & leap years

  • Frequency of 1st day Chanukah being on Friday

  • Frequency of 10 Tevet being on Friday

  • Frequency of each kevi'ah - If a table or chart for all of them (I think there are about 10 in total?) then something stating which is most and which is least common

  • Notable recent or upcoming (25 - 30 years before or after now) Judaic / Gregorian rare U.S. holiday coincidences. E.g. 1st day Hanuka 5774 coincided with Thanksgiving 2013. (I'm looking for "rare", here. Don't include Chanukah / XMas, Succot / Columbus Day or Shavu'ot / Memorial Day. These occur every few years. I realize that this list may not be easily available, so this is not a primary concern for me, but would be nice to have.)

If you can find one or more websites having this info, I appreciate it, greatly.

  • There's a cycle, I think 19 years. – user613 Aug 12 '15 at 2:43
  • @user613 Try 689472 years. – Double AA Aug 12 '15 at 2:48
  • @user613 The 19 year cycle affects the placement of leap years; not the days of the week for holidays or the kevi'ah. In many cases, this means that the Gregorian and Judaic date repeat, e.g. - your Hebrew and Gregorian date SHOULD coincide each 19 years. However, they are frequently a day or 2 off. (In 2016, I happen to have a multiple of 19 b'day, and, this time the dates coincide. Yahoo!!) – DanF Aug 12 '15 at 2:49
  • @DanF right. Often a day off if someone's born at night. But you're right, could be 2 days off. A year or 2 ago, we had secular days coinciding with Jewish days that will never coincide again, the Hebrew year was the earliest in the secular year that it would ever be, and the previous time was like a hundred years before – user613 Aug 12 '15 at 4:52
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    @user613: The three fundamental cycles on which the calendar is based are (a) the 7-day week (b) the synodic month of 765433/25920 days, (c) the equinoctial year (as approximated by the Metonic cycle) of 235/19 months. The lowest common multiple of all these works out to a complete cycle of 251 827 457 days = 35 975 351 weeks = 8 527 680 months = 689 472 years. – Daniel ben Noach Aug 14 '15 at 1:51
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The data you want (except the secular calendar stuff) is all here: http://hebrewcalendar.tripod.com/#24.4

For instance, you can note that in years where Marcheshvan has 30 days, the first day of Chanukka falls on the same day of the week as Rosh Hashana, and in years where Marcheshvan has 29 days, the first day of Chanukka falls on the one day of the week earlier than Rosh Hashana. (A leap year doesn't matter here.)

Since RH can't fall on Friday, the phenomenon you seek happens only in Kisidran or Chaser years with RH on Shabbat. In the site's "chart" terms, that's 353, 354, 383, 384 years in the last row, totaling 29853+0+40000+0=69853 years out of 689472 = 10.2% of years.

  • Perfect! I had seen this site a while ago when I was compiling a different lecture about 2 years ago. I forgot about this. Thanks so much, This seems to do it! – DanF Aug 12 '15 at 2:35
  • ... and thanks for the additional edits and the math calculations. It has been a while since we've had a Fri. Chanukah. I don't recall the last one, but I believe one is upcoming in about 5 years or so. – DanF Aug 13 '15 at 2:16

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