A230998 Number of years after which it is not possible to have a date falling on the same day of the week, in the Gregorian calendar.

1, 2, 3, 4, 8, 9, 10, 13, 14, 15, 16, 19, 20, 21, 24, 25, 26, 27, 30, 31, 32, 36, 37, 38, 41, 42, 43, 44, 47, 48, 49, 52, 53, 54, 55, 58, 59, 60, 64, 65, 66, 69, 70, 71, 72, 75, 76, 77, 80, 81, 82, 83, 86, 87, 88, 92, 93, 94, 97, 98, 99, 100, 103, 104, 105, 109, 110, 111

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.

This is the complement of A230995.

Links

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

Crossrefs

Cf. A230995-A231014.

Cf. A231003 (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));if(j==0,print1(i", ")))