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

2000,1

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

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

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

Cf. A116386.

Sequence in context: A126767 A143723 A252713 * A327374 A327109 A327108

Adjacent sequences: A249401 A249402 A249403 * A249405 A249406 A249407

Keyword

nonn

Author

Rick L. Shepherd, Oct 27 2014

Status

approved