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

%I A249404 #13 Jun 28 2025 16:15:38
%S A249404 52,52,52,52,53,52,52,52,52,53,52,52,52,52,52,53,52,52,52,52,53,52,52,
%T A249404 52,52,52,53,52,52,52,52,52,53,52,52,52,52,53,52,52,52,52,52,53,52,52,
%U A249404 52,52,53,52,52,52,52,52,53,52,52,52,52,52,53,52,52,52,52,53,52,52,52
%N A249404 Number of ISO 8601 weeks associated with the Gregorian year n.
%C A249404 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).
%C A249404 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
%H A249404 Rick L. Shepherd, <a href="/A249404/b249404.txt">Table of n, a(n) for n = 2000..2399</a>
%H A249404 ISO, <a href="http://www.iso.org/iso/catalogue_detail?csnumber=40874">ISO 8601:2004 - Data elements and interchange formats -- Information interchange -- Representation of dates and times</a>
%H A249404 Microsoft Developer Network, <a href="http://msdn.microsoft.com/en-us/library/system.globalization.calendarweekrule%28v=vs.110%29.aspx">CalendarWeekRule Enumeration</a>
%H A249404 Shawn Steele, <a href="http://blogs.msdn.com/b/shawnste/archive/2006/01/24/iso-8601-week-of-year-format-in-microsoft-net.aspx">ISO 8601 Week of Year Format in Microsoft .Net</a>
%H A249404 Wikipedia, <a href="http://en.wikipedia.org/wiki/ISO_week_date">ISO week date</a>
%H A249404 Wikipedia, <a href="http://en.wikipedia.org/wiki/Leap_week_calendar">Leap week calendar</a>
%H A249404 Wikipedia, <a href="http://en.wikipedia.org/wiki/Seven-day_week">Seven-day week</a>
%H A249404 <a href="/index/Ca#calendar">Index entries for sequences related to calendars</a>
%F A249404 a(n) = a(n - 400) for all n and n - 400 that are defined (proleptic) Gregorian calendar years.
%e A249404 a(2015) = 53 because Gregorian year 2015 has 53 associated ISO 8601 weeks (with week 1 beginning Monday, Dec 29 2014).
%Y A249404 Cf. A116386.
%K A249404 nonn
%O A249404 2000,1
%A A249404 _Rick L. Shepherd_, Oct 27 2014