A230999 Number of years after which it is not possible to have the same calendar for the entire year, in the Gregorian calendar.

1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 14, 15, 16, 19, 20, 21, 24, 25, 26, 27, 30, 31, 32, 33, 35, 36, 37, 38, 41, 42, 43, 44, 47, 48, 49, 52, 53, 54, 55, 58, 59, 60, 61, 63, 64, 65, 66, 69, 70, 71, 72, 75, 76, 77, 80, 81, 82, 83, 86, 87, 88, 89, 91, 92, 93, 94, 97, 98, 99, 100

Offset

1,2

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.

This is the complement of A230996.

Links

Table of n, a(n) for n=1..70.

Time And Date, Repeating Calendar

Time And Date, Gregorian Calendar

Prog

(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)&&((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=1)); if(j==0, print1(i", ")))

Crossrefs

Cf. A230995-A231014.

Cf. A231004 (Julian calendar).

Sequence in context: A165256 A175020 A050728 * A180590 A289342 A286302

Adjacent sequences: A230996 A230997 A230998 * A231000 A231001 A231002

Keyword

nonn,easy

Author

Aswini Vaidyanathan, Nov 02 2013

Status

approved