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

0,2

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.

Links

Table of n, a(n) for n=0..61.

Time And Date, Repeating Calendar

Time And Date, Gregorian Calendar

Example

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.

Prog

(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)))

Crossrefs

Cf. A230995-A231014.

Cf. A231000 (Julian calendar).

Sequence in context: A026309 A073936 A184811 * A362929 A064615 A300957

Adjacent sequences: A230992 A230993 A230994 * A230996 A230997 A230998

Keyword

nonn,easy

Author

Aswini Vaidyanathan, Nov 02 2013

Status

approved