

A230996


Number of years after which an entire year can have the same calendar, in the Gregorian calendar.


3



0, 6, 11, 12, 17, 18, 22, 23, 28, 29, 34, 39, 40, 45, 46, 50, 51, 56, 57, 62, 67, 68, 73, 74, 78, 79, 84, 85, 90, 95, 96, 101, 102, 106, 107, 108, 112, 113, 114, 118, 119, 123, 124, 125, 129, 130, 134, 135, 136, 140, 141, 142, 146, 147, 151, 152, 153, 157, 158, 162
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OFFSET

0,2


COMMENTS

In the Gregorian calendar, a noncentury 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



EXAMPLE

6 belongs to this sequence because year 2013 has the same calendar as year 2019.
11 belongs to this sequence because year 2002 has the same calendar as year 2013.
12 belongs to this sequence because year 2096 has the same calendar as year 2108.


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)&&((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), print1(i", "); break)))


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



