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.

5, 7, 33, 35, 61, 63, 89, 91, 117, 131, 145, 159, 173, 187, 213, 227, 241, 255, 269, 283, 309, 311, 337, 339, 365, 367, 393, 395, 405, 407, 433, 435, 461, 463, 489, 491, 517, 531, 545, 559, 573, 587, 613, 627, 641, 655, 669, 683, 709, 711, 737, 739, 765, 767, 793, 795

Offset: 1

Author

Aswini Vaidyanathan, Nov 02 2013

Keywords

• nonn
• easy

Comments

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.

Assuming this fact, this sequence is periodic with a period of 400.

These are the terms of A230995 not in A230996.

Examples

			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.
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.
		

Links

• Time And Date, Repeating Calendar
• Time And Date, Gregorian Calendar

Crossrefs

Cf. A230995-A231014.

Cf. A231002 (Julian calendar).

Programs

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", ")))