Another Hanukkah Miracle: The Gaps Between Consecutive Christmas-in-Hanukkah Years is ALWAYS a Fibonacci Number! (2nd ed.)

By
Lisa Budd and Shalosh B. Ekhad
.pdf   .ps   .tex  

(Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger and arxiv.org)

First edition only by SBE(.pdf  ) written: Jan. 2, 2012.

This 2nd edition written: Nov. 15, 2019.

In fond memory of Marvin Isadore KNOPP (1933-2011) one of the nicest, kindest, and wisest people whom we ever knew.
Abstract of first edition: Jane Deborah LEGRANGE, asked her husband, who asked SBE, how often does it happen that Christmas happens to fall in Hanukkah. This article answers this profound question.

Added Feb. 23, 2012: Read Stephen S. Miller's insightful message

Added Nov. 15, 2019: Lisa Budd realized that the "Fibonacci miracle" is a red herring. and wrote an insightful and beautiful draft. We decided to combine the efforts, and the result is this new edition.

Added Oct. 24, 2022: Here are some fascinating data from Lisa Budd:

Someone asked me how often we fast on Xmas day while our neighbours are feasting because it coincides with the Fast of 10th Tevet. I knocked up a list of years from 400-90,000CE, extrapolating the Gregorian calendar back before 1582. It was certainly happening by 400; the first few instances were 418, 532, 570 and 589. The last time it happens is 4996, resuming again in 82,319. The shortest possible gap is eight years; this first occurred in 706/714 and last occurs in 4559/4567. Possible gaps between 1800 and 2100 (which is the peak time) are 8, 11, 19, 30, 38 and 46. Gaps of 22 years can occur but they are rare, only three in the whole analysis.

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