Leap year starting on Thursday

A leap year starting on Thursday is any year with 366 days (i.e. it includes 29 February) that begins on Thursday 1 January, and ends on Friday 31 December. Its dominical letters hence are DC. The most recent year of such kind was 2004 and the next one will be 2032 in the Gregorian calendar[1] or, likewise, 2016 and 2044 in the obsolete Julian calendar. Any leap year that starts on Monday, Wednesday or Thursday has two Friday the 13ths. This leap year contains two Friday the 13ths in February and August. This leap year is also the longest gap between leap day (February 29) and daylight saving time begins in US (March 14) by 14 days or 2 weeks. In this leap year, the leap day is on a Sunday, U.S. Independence Day is on a Sunday, Thanksgiving is on November 25, and Christmas is on a Saturday.

Calendars

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

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

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	January
01				01	02	03	04
02	05	06	07	08	09	10	11
03	12	13	14	15	16	17	18
04	19	20	21	22	23	24	25
05	26	27	28	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	February
05							01
06	02	03	04	05	06	07	08
07	09	10	11	12	13	14	15
08	16	17	18	19	20	21	22
09	23	24	25	26	27	28	29

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	March
10	01	02	03	04	05	06	07
11	08	09	10	11	12	13	14
12	15	16	17	18	19	20	21
13	22	23	24	25	26	27	28
14	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	April
14				01	02	03	04
15	05	06	07	08	09	10	11
16	12	13	14	15	16	17	18
17	19	20	21	22	23	24	25
18	26	27	28	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	May
18						01	02
19	03	04	05	06	07	08	09
20	10	11	12	13	14	15	16
21	17	18	19	20	21	22	23
22	24	25	26	27	28	29	30
23	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	June
23		01	02	03	04	05	06
24	07	08	09	10	11	12	13
25	14	15	16	17	18	19	20
26	21	22	23	24	25	26	27
27	28	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	July
27				01	02	03	04
28	05	06	07	08	09	10	11
29	12	13	14	15	16	17	18
30	19	20	21	22	23	24	25
31	26	27	28	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	August
31							01
32	02	03	04	05	06	07	08
33	09	10	11	12	13	14	15
34	16	17	18	19	20	21	22
35	23	24	25	26	27	28	29
36	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	September
36			01	02	03	04	05
37	06	07	08	09	10	11	12
38	13	14	15	16	17	18	19
39	20	21	22	23	24	25	26
40	27	28	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	October
40					01	02	03
41	04	05	06	07	08	09	10
42	11	12	13	14	15	16	17
43	18	19	20	21	22	23	24
44	25	26	27	28	29	30	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	November
45	01	02	03	04	05	06	07
46	08	09	10	11	12	13	14
47	15	16	17	18	19	20	21
48	22	23	24	25	26	27	28
49	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	December
49			01	02	03	04	05
50	06	07	08	09	10	11	12
51	13	14	15	16	17	18	19
52	20	21	22	23	24	25	26
53	27	28	29	30	31

Applicable years

Gregorian Calendar

Leap years that begin on Thursday, along with those that start on Monday or Saturday, occur least frequently: 13 out of 97 (≈ 13.402%) total leap years in a 400-year cycle of the Gregorian calendar. Their overall occurrence is 3.25% (13 out of 400).

For this kind of year, the corresponding ISO year has 53 weeks, and the ISO week 10 (which begins March 1) and all subsequent ISO weeks occur earlier than in all other years, and exactly one week earlier than common years starting on Friday, for example, June 20 falls on week 24 in common years starting on Friday, but on week 25 in leap years starting on Thursday, despite falling on Sunday in both types of year. That means that moveable holidays may occur one calendar week later than otherwise possible, e.g. Gregorian Easter Sunday in week 17 in years when it falls on April 25 and which are also leap years, falling on week 16 in common years.[2]

Gregorian leap years starting on Thursday[1]
Decade	1st	2nd	3rd	4th	5th	6th	8th	9th
17th century	1604			1632		1660		1688
18th century			1728			1756		1784
19th century			1824			1852	1880
20th century		1920			1948		1976
21st century	2004			2032		2060		2088
22nd century			2128			2156		2184
23rd century			2224			2252	2280
24th century		2320			2348		2376
25th century	2404			2432		2460		2488
26th century			2528			2556		2584

Julian Calendar

Like all leap year types, the one starting with 1 January on a Thursday 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 Thursday
Decade	1st	2nd	3rd	4th	5th	6th	7th	8th	9th	10th
15th century			1428			1456			1484
16th century		1512		1540			1568			1596
17th century			1624			1652		1680
18th century	1708			1736			1764			1792
19th century		1820			1848			1876
20th century	1904			1932		1960			1988
21st century		2016			2044			2072		2100
22nd century			2128			2156			2184

References

Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.
Leap years when Easter Sunday falls on April 25 are only possible years when Easter Sunday can fall on week 17.
Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.

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[math-1] Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.

[2] Leap years when Easter Sunday falls on April 25 are only possible years when Easter Sunday can fall on week 17.

[3] Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.