A131921 Years between consecutive Leap Days for Gregorian calendar.

8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 4, 4

Offset: 1

Author

Rick L. Shepherd, Jul 28 2007

Keywords

• easy
• nonn

Comments

There are 97 leap years per 400 years of the Gregorian calendar. To facilitate different search patterns, this period-97 sequence starts for a year such as 1804 (+ or - k*400). Starting this way, the runs of fours have lengths 23, 48, then 23, 23, 48, 23, 23, 48, .... The Gregorian calendar was decreed in 1582, so 1584, the next leap year, corresponds to a(45)=4; 1580 was a leap year in both the Julian and (proleptic) Gregorian calendars.

Examples

			a(1) = 8 as there are eight years between Leap Day of 1796 and the next Leap Day, which is in 1804. Century years such as 1800 not divisible by 400 are not leap years in the Gregorian calendar.
		

Links

• Index entries for sequences related to calendars

Formula

a(n+97) = a(n) for n >= 1.