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Number of months after which a date can fall on the same day of the week, and the two months can have the same number of days, in the Gregorian calendar.
3

%I #4 Nov 02 2013 23:40:00

%S 0,3,6,8,9,14,15,17,18,20,22,23,26,29,31,32,34,35,37,38,40,41,43,46,

%T 49,50,52,54,55,57,58,60,63,64,66,67,68,69,72,75,76,77,78,80,81,84,86,

%U 87,89,90,92,94,95,98,101,103,104,106,107,109,110,112,113,114,115,117,118

%N Number of months after which a date can fall on the same day of the week, and the two months can have the same number of days, in the Gregorian calendar.

%C In the Gregorian calendar, a non-century year is a leap year if and only if it is a multiple of 4 and a century year is a leap year if and only if it is a multiple of 400.

%C Assuming this fact, this sequence is periodic with a period of 4800.

%C This is a subsequence of A231005.

%H Time And Date, <a href="http://www.timeanddate.com/calendar/repeating-month.html">Repeating Months</a>

%H Time And Date, <a href="http://www.timeanddate.com/calendar/gregorian-calendar.html">Gregorian Calendar</a>

%e 3 belongs to this sequence because December 1, 2011 falls on the same day as March 1, 2012 and both December and March have 31 days each.

%e 6 belongs to this sequence because January 1, 2012 falls on the same day as July 1, 2012 and both January and July have 31 days each.

%e 8 belongs to this sequence because May 1, 2013 falls on the same day as January 1, 2014 and both May and January have 31 days each.

%e 9 belongs to this sequence because January 1, 2013 falls on the same day as October 1, 2013 and both January and October have 31 days each.

%o (PARI) m=[0,3,3,6,1,4,6,2,5,0,3,5];n=[31,28,31,30,31,30,31,31,30,31,30,31];y=vector(4800,i,(m[((i-1)%12)+1]+((5*((i-1)\48)+(((i-1)\12)%4)-((i-1)\1200)+((i-1)\4800)-!((i-1)%48)+!((i-1)%1200)-!((i-1)%4800)-!((i-2)%48)+!((i-2)%1200)-!((i-2)%4800))))%7);x=vector(4800,i,n[((i-1)%12)+1]+!((i-2)%48)-!((i-2)%1200)+!((i-2)%4800));for(p=0,4800,for(q=0,4800,if(y[(q%4800)+1]==y[((q+p)%4800)+1]&&x[(q%4800)+1]==x[((q+p)%4800)+1],print1(p", ");break)))

%Y Cf. A230995-A231014.

%Y Cf. A231011 (Julian calendar).

%K nonn,easy

%O 0,2

%A _Aswini Vaidyanathan_, Nov 02 2013