Leap Years Starting On Sunday
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Leap Years Starting On Sunday

A leap year starting on Sunday is any year with 366 days (i.e. it includes 29 February) that begins on Sunday, 1 January, and ends on Monday, 31 December. Its dominical letters hence are AG, such as the years 1888, 1928, 1956, 1984, 2012, 2040, 2068, 2096, 2108, 2136, 2164, and 2192 in the Gregorian calendar[1] or, likewise, 1996 and 2024 in the obsolete Julian calendar.

This leap year uniquely has the most occurrences of Friday the 13th. Common years starting on Thursday share this characteristic. Each instance of Friday the 13th is three months (13 weeks) apart in January, April, and July.

Calendars

Calendar for any leap year starting on Sunday,
presented as common in many English-speaking areas


ISO 8601-conformant calendar with week numbers for
any leap year starting on Sunday (dominical letter AG)

Applicable years

Gregorian Calendar

Leap years that begin on Sunday, along with those that start on Friday, occur most frequently: 15 out of the 97 (? 15.46%) total leap years in a 400-year cycle of the Gregorian calendar. Thus, the overall occurrence is 3.75% (15 out of 400).

Gregorian leap years starting on Sunday[1]
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
17th century 1612 1640 1668 1696
18th century 1708 1736 1764 1792
19th century 1804 1832 1860 1888
20th century 1928 1956 1984
21st century 2012 2040 2068 2096
22nd century 2108 2136 2164 2192

Julian Calendar

Like all leap year types, the one starting with 1 January on a Sunday occurs exactly once in a 28-year cycle in the Julian calendar, i.e. in 3.57% of years. As the Julian calendar repeats after 28 years that means it will also repeat after 700 years, i.e. 25 cycles. The year's position in the cycle is given by the formula ((year + 8) mod 28) + 1).

Julian leap years starting on Sunday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1408 1436 1464 1492
16th century 1520 1548 1576
17th century 1604 1632 1660 1688
18th century 1716 1744 1772 1800
19th century 1828 1856 1884
20th century 1912 1940 1968 1996
21st century 2024 2052 2080
22nd century 2108 2136 2164 2192

References

  1. ^ a b c Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 2017.

  This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

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