OFFSET
2000,1
COMMENTS
There are 71 ISO 8601 53-week years per 400-year Gregorian cycle. The other years have 52 ISO 8601 weeks. These terms were calculated by using the .NET Framework's Calendar.GetWeekOfYear method with both CalendarWeekRule.FirstFourDayWeek and DayOfWeek.Monday specified for 12/28 of each year (as this date is always in the last week of an ISO 8601-week year).
On the Gregorian Calendar, each 400-year cycle includes 97 leap years, giving a total of 400*365 + 97 = 146097 days, which is exactly 20871 weeks; this matches the total number of ISO 8601 weeks per 400-year cycle: 71*53 + (400-71)*52 = 20871. - Jon E. Schoenfield, Oct 30 2014
LINKS
Rick L. Shepherd, Table of n, a(n) for n = 2000..2399
Microsoft Developer Network, CalendarWeekRule Enumeration
Shawn Steele, ISO 8601 Week of Year Format in Microsoft .Net
Wikipedia, ISO week date
Wikipedia, Leap week calendar
Wikipedia, Seven-day week
FORMULA
a(n) = a(n - 400) for all n and n - 400 that are defined (proleptic) Gregorian calendar years.
EXAMPLE
a(2015) = 53 because Gregorian year 2015 has 53 associated ISO 8601 weeks (with week 1 beginning Monday, December 29, 2014).
CROSSREFS
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Oct 27 2014
STATUS
approved