A230999 - OEIS

%I #4 Nov 02 2013 23:38:51

%S 1,2,3,4,5,7,8,9,10,13,14,15,16,19,20,21,24,25,26,27,30,31,32,33,35,

%T 36,37,38,41,42,43,44,47,48,49,52,53,54,55,58,59,60,61,63,64,65,66,69,

%U 70,71,72,75,76,77,80,81,82,83,86,87,88,89,91,92,93,94,97,98,99,100

%N Number of years after which it is not possible to have the same calendar for the entire year, 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 400.

%C This is the complement of A230996.

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

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

%o (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)&&((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=1));if(j==0,print1(i", ")))

%Y Cf. A230995-A231014.

%Y Cf. A231004 (Julian calendar).

%K nonn,easy

%O 1,2

%A _Aswini Vaidyanathan_, Nov 02 2013