A249404 Number of ISO 8601 weeks associated with the Gregorian year n.

52, 52, 52, 52, 53, 52, 52, 52, 52, 53, 52, 52, 52, 52, 52, 53, 52, 52, 52, 52, 53, 52, 52, 52, 52, 52, 53, 52, 52, 52, 52, 52, 53, 52, 52, 52, 52, 53, 52, 52, 52, 52, 52, 53, 52, 52, 52, 52, 53, 52, 52, 52, 52, 52, 53, 52, 52, 52, 52, 52, 53, 52, 52, 52, 52, 53, 52, 52, 52

Offset: 2000

Author

Rick L. Shepherd, Oct 27 2014

Keywords

• nonn

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

Examples

			a(2015) = 53 because Gregorian year 2015 has 53 associated ISO 8601 weeks (with week 1 beginning Monday, Dec 29 2014).
		

Links

• Rick L. Shepherd, Table of n, a(n) for n = 2000..2399
• ISO, ISO 8601:2004 - Data elements and interchange formats -- Information interchange -- Representation of dates and times
• 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
• Index entries for sequences related to calendars

Crossrefs

Cf. A116386.

Formula

a(n) = a(n - 400) for all n and n - 400 that are defined (proleptic) Gregorian calendar years.