Years when Ramadan and Rosh Hashana coincide

[Hans Havermann]

Brendan McKay:

> I see errors in your list.  For example Rosh Hashana in 1974 was on  
> the 17th, not the 18th.

Indeed. That would make A118661, which appears to have used  
Mathematica for its generation wrong...

%S A118661  
25,14,3,22,11,29,20,9,26,16,4,24,12,1,21,9,28,17,7,25,13,3,22,12,29,19,
%T A118661  
8,28,16,4,24,12,1,20,9,29,16,7,25,15,2,23,12,29,19,7,27,15,5,24,12,2,
%U A118661  
19,10,28,17,6,24,15,3,22,10,1,20,7,27,15,5,22,12,2,20,9,27,18,6,24,14
%N A118661 Day of the month in which the Jewish New Year occurs in  
the Gregorian year n.
%e A118661 In 1997 the Jewish New Year occured on October 2nd, so a 
(997)=2
%t A118661 << Miscellaneous`Calendar` JewishNewYear[n][[2]]

%O A118661 1900,1
%A A118661 Yoav Kallus, (colonelmustard(AT)gmail.com), May 18 2006

The fourth-last term given corresponds to 1974. By the way, the  
coding is JewishNewYear[n][[3]] (not [[2]]), but given that this  
coding will not (necessarily) give the correct date, the entire  
sequence needs revisiting. In fact, because the associated month- 
sequence...

%S A118662  
9,9,10,9,9,9,9,9,9,9,10,9,9,10,9,9,9,9,9,9,9,10,9,9,9,9,9,9,9,10,9,9,
%T A118662  
10,9,9,9,9,9,9,9,10,9,9,9,9,9,9,9,10,9,9,10,9,9,9,9,9,9,9,10,9,9,10,9,
%U A118662  
9,9,9,10,9,9,10,9,9,9,9,9,9,9,10,9,9,9,9,9,9,9,10,9,9,9,9,9,9,9,9,9,9
%N A118662 Month in which the Jewish New Year occurs in the Gregorian  
year n.

... is dependent on the same Mathematica code, it will likely have a  
couple of errors as well.
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