A230995 Number of years after which a date can fall on the same day of the week, in the Gregorian calendar.

0, 5, 6, 7, 11, 12, 17, 18, 22, 23, 28, 29, 33, 34, 35, 39, 40, 45, 46, 50, 51, 56, 57, 61, 62, 63, 67, 68, 73, 74, 78, 79, 84, 85, 89, 90, 91, 95, 96, 101, 102, 106, 107, 108, 112, 113, 114, 117, 118, 119, 123, 124, 125, 129, 130, 131, 134, 135, 136, 140, 141, 142

Offset: 0

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.

Examples

			5 belongs to this sequence because January 1, 2008 falls on same day as January 1, 2013.
6 belongs to this sequence because January 1, 2009 falls on same day as January 1, 2015.
7 belongs to this sequence because January 1, 2097 falls on same day as January 1, 2104.
		

Links

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

Crossrefs

Cf. A230995-A231014.

Cf. A231000 (Julian calendar).

Programs

PARI

for(i=0,400,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),print1(i", ");break)))