cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Rick L. Shepherd, Oct 27 2014

Keywords

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

Crossrefs

Cf. A116386.

Formula

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