A230996 Number of years after which an entire year can have the same calendar, in the Gregorian calendar.

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

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.

This is a subsequence of A230995.

Links

Table of n, a(n) for n=0..59.

Time And Date, Repeating Calendar

Time And Date, Gregorian Calendar

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

Cf. A230995-A231014.

Cf. A231001 (Julian calendar).

Sequence in context: A276136 A152089 A212773 * A219553 A015870 A004471

Adjacent sequences: A230993 A230994 A230995 * A230997 A230998 A230999

Keyword

nonn,easy

Author

Aswini Vaidyanathan, Nov 02 2013

Status

approved