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A230997 Number of years after which it is possible to have a date falling on same day of the week, but the entire year does not have the same calendar, in the Gregorian calendar.

%I A230997 #4 Nov 02 2013 23:38:21
%S A230997 5,7,33,35,61,63,89,91,117,131,145,159,173,187,213,227,241,255,269,
%T A230997 283,309,311,337,339,365,367,393,395,405,407,433,435,461,463,489,491,
%U A230997 517,531,545,559,573,587,613,627,641,655,669,683,709,711,737,739,765,767,793,795
%N A230997 Number of years after which it is possible to have a date falling on same day of the week, but the entire year does not have the same calendar, in the Gregorian calendar.
%C A230997 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 A230997 Assuming this fact, this sequence is periodic with a period of 400.
%C A230997 These are the terms of A230995 not in A230996.
%H A230997 Time And Date, <a href="http://www.timeanddate.com/calendar/repeating.html">Repeating Calendar</a>
%H A230997 Time And Date, <a href="http://www.timeanddate.com/calendar/gregorian-calendar.html">Gregorian Calendar</a>
%e A230997 5 belongs to this sequence because January 1, 2012 falls on same day as January 1, 2017 but the calendar is not completely the same for both the years. In fact, a difference of 5 years can never produce the same calendar for the entire year.
%e A230997 7 belongs to this sequence because January 1, 2097 falls on same day as January 1, 2104 but the calendar is not completely the same for both the years. In fact, a difference of 7 years can never produce the same calendar for the entire year.
%o A230997 (PARI) for(i=0,400,j=0;for(y=0,400,if(((5*(y\4)+(y%4)-(y\100)+(y\400))%7)==((5*((y+i)\4)+((y+i)%4)-((y+i)\100)+((y+i)\400))%7),j=1;break));for(y=0,400,if(((5*(y\4)+(y%4)-(y\100)+(y\400))%7)==((5*((y+i)\4)+((y+i)%4)-((y+i)\100)+((y+i)\400))%7)&&((5*(y\4)+(y%4)-(y\100)+(y\400)-!(y%4)+!(y%100)-!(y%400))%7)==((5*((y+i)\4)+((y+i)%4)-((y+i)\100)+((y+i)\400)-!((y+i)%4)+!((y+i)%100)-!((y+i)%400))%7),j=2;break));if(j==1,print1(i", ")))
%Y A230997 Cf. A230995-A231014.
%Y A230997 Cf. A231002 (Julian calendar).
%K A230997 nonn,easy
%O A230997 1,1
%A A230997 _Aswini Vaidyanathan_, Nov 02 2013