%I #8 Jun 04 2024 10:52:00

%S 0,1,2,3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,24,25,26,27,

%T 28,29,30,31,32,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,52,

%U 53,54,55,56,57,58,59,60,62,63,64,65,66,67,68,69,70,71,72,73,74,75

%N Number of years after which it is either not possible to have a date falling on same day of the week, or the entire year can have the same calendar, in the Julian calendar.

%C In the Julian calendar, a year is a leap year if and only if it is a multiple of 4 and all century years are leap years.

%C Assuming this fact, this sequence is periodic with a period of 28.

%C This is the complement of A231002.

%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/julian-calendar.html">Julian Calendar</a>

%H <a href="/index/Rec#order_26">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-1).

%F From _Chai Wah Wu_, Jun 04 2024: (Start)

%F a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - 2*a(n-6) + 2*a(n-7) - 2*a(n-8) + 2*a(n-9) - 2*a(n-10) + 2*a(n-11) - 2*a(n-12) + 2*a(n-13) - 2*a(n-14) + 2*a(n-15) - 2*a(n-16) + 2*a(n-17) - 2*a(n-18) + 2*a(n-19) - 2*a(n-20) + 2*a(n-21) - 2*a(n-22) + 2*a(n-23) - 2*a(n-24) + 2*a(n-25) - a(n-26) for n > 26.

%F G.f.: x^2*(x^4 + 1)*(x^2 - x + 1)*(x^18 + x^17 + x^16 - x^13 + x^10 + x^9 + x^8 - x^5 + x^2 + x + 1)/((x - 1)^2*(x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1)*(x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). (End)

%o (PARI) for(i=0,420,j=0;for(y=0,420,if(((5*(y\4)+(y%4))%7)==((5*((y+i)\4)+((y+i)%4))%7),j=1;break));for(y=0,420,if(((5*(y\4)+(y%4))%7)==((5*((y+i)\4)+((y+i)%4))%7)&&((5*(y\4)+(y%4)-!(y%4))%7)==((5*((y+i)\4)+((y+i)%4)-!((y+i)%4))%7),j=2;break));if(j!=1,print1(i", ")))

%Y Cf. A230995-A231014, A231236-A231239.

%Y Cf. A231236 (Gregorian calendar).

%K nonn,easy

%O 1,3

%A _Aswini Vaidyanathan_, Nov 06 2013