Leap year starting on Friday

A leap year starting on Friday is any year with 366 days (i.e. it includes 29 February) that begins on Friday 1 January and ends on Saturday 31 December. Its dominical letters hence are CB. The most recent year of such kind was 2016 and the next one will be 2044 in the Gregorian calendar^[1] or, likewise, 2000 and 2028 in the obsolete Julian calendar.

Any leap year that starts on Tuesday, Friday or Saturday has only one Friday the 13th: the only one in this leap year occurs in May. Common years starting on Saturday share this characteristic.

In this type of year, all dates (except 29 February) fall on their respective weekdays 58 times in the 400 year Gregorian calendar cycle. Leap years starting on Sunday share this characteristic.

Calendars

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

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

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

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

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

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

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

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

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

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

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	September
35				01	02	03	04
36	05	06	07	08	09	10	11
37	12	13	14	15	16	17	18
38	19	20	21	22	23	24	25
39	26	27	28	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	October
39						01	02
40	03	04	05	06	07	08	09
41	10	11	12	13	14	15	16
42	17	18	19	20	21	22	23
43	24	25	26	27	28	29	30
44	31

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	November
44		01	02	03	04	05	06
45	07	08	09	10	11	12	13
46	14	15	16	17	18	19	20
47	21	22	23	24	25	26	27
48	28	29	30

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	December
48				01	02	03	04
49	05	06	07	08	09	10	11
50	12	13	14	15	16	17	18
51	19	20	21	22	23	24	25
52	26	27	28	29	30	31

Applicable years

Gregorian Calendar

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

Gregorian leap years starting on Friday^[1]
Decade	1st	2nd	4th	5th	6th	7th	8th	9th	10th
17th century		1616		1644			1672
18th century		1712	1740			1768			1796
19th century	1808		1836			1864			1892
20th century	1904		1932		1960			1988
21st century		2016		2044			2072
22nd century		2112	2140			2168			2196
23rd century	2208		2236			2264			2292
24th century	2304		2332		2360			2388
25th century		2416		2444			2472
26th century		2512	2540			2568			2596

400 year cycle

century 1: 16, 44, 72

century 2: 112, 140, 168, 196

century 3: 208, 236, 264, 292

century 4: 304, 332, 360, 388

Julian Calendar

Like all leap year types, the one starting with 1 January on a Friday 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 Friday
Decade	1st	2nd	3rd	4th	5th	6th	7th	8th	9th	10th
15th century		1412		1440			1468			1496
16th century			1524			1552		1580
17th century	1608			1636			1664			1692
18th century		1720			1748			1776
19th century	1804			1832		1860			1888
20th century		1916			1944			1972		2000
21st century			2028			2056			2084
22nd century		2112		2140			2168			2196

Holidays

International

- Valentine's Day falls on a Sunday. This is the only type of leap year when Valentine’s Day falls in ISO week 6. They fall in ISO week 7 in all other leap years.
- The leap day (February 29) falls on a Monday
- World Day for Grandparents and the Elderly falls on July 24
- Halloween falls on a Monday
- Christmas Day falls on a Sunday. This is the only type of leap year when Christmas Day falls in ISO week 51. They fall in ISO week 52 in all other leap years.

Roman Catholic Solemnities

- Epiphany falls on a Wednesday
- Candlemas falls on a Tuesday
- Saint Joseph's Day falls on a Saturday
- The Annunciation of Jesus falls on a Friday
- The Nativity of John the Baptist falls on a Friday
- The Solemnity of Saints Peter and Paul falls on a Saturday
- The Transfiguration of Jesus falls on a Saturday
- The Assumption of Mary falls on a Monday
- The Exaltation of the Holy Cross falls on a Wednesday
- All Saints' Day falls on a Tuesday
- All Souls' Day falls on a Wednesday
- The Feast of Christ the King falls on its earliest possible date, November 20 (or on October 30 in versions of the calendar between 1925 and 1962)
- The First Sunday of Advent falls on its earliest possible date, November 27. This is the only leap year when The First Sunday of Advent falls in ISO week 47. They fall in ISO week 48 in all other leap years.
- The Immaculate Conception falls on a Thursday
- Gaudete Sunday falls on its earliest possible date, December 11. This is the only leap year when Gaduete Sunday falls in ISO week 49. They fall in ISO week 50 in all other leap years.
- Rorate Sunday falls on its earliest possible date, December 18. This is the only leap year when Rorate Sunday falls in ISO week 50. They fall in ISO week 51 in all other leap years.

Australia and New Zealand

- Australia Day falls on a Tuesday
- Waitangi Day falls on a Saturday
- Daylight saving ends on April 3
- ANZAC Day falls on a Monday
- Mother's Day falls on its earliest possible date, May 8. This is the only leap year when Mother’s Day falls in ISO week 18. They fall in ISO week 19 in all other leap years.
- Father's Day falls on September 4
- Daylight saving begins on September 25 in New Zealand and October 2 in Australia

British Isles

- Saint David's Day falls on a Tuesday
- Mother's Day falls on March 6, March 13, March 20, March 27 or April 3
- Daylight saving begins on March 27
- Saint Patrick's Day falls on a Thursday
- Saint George's Day falls on a Saturday
- Father's Day falls on June 19
- Orangeman's Day falls on a Tuesday
- Daylight saving ends on October 30
- Guy Fawkes Night falls on a Saturday
- Saint Andrew's Day falls on a Wednesday

Canada

- Daylight saving begins on March 13
- Mother's Day falls on its earliest possible date, May 8. This is the only leap year when Mother’s Day falls in ISO week 18. They fall in ISO week 19 in all other leap years
- Victoria Day falls on May 23
- Father's Day falls on June 19
- Canada Day falls on a Friday
- Labour Day falls on September 5
- Thanksgiving Day falls on October 10
- Daylight saving ends on November 6

United States

- Martin Luther King Jr. Day falls on January 18
- President's Day falls on its earliest possible date, February 15. This is the only leap year when President’s Day falls in ISO week 7. They fall in ISO week 8 in all other leap years. This is also the only leap year when Labor Day that precedes this type of year to President’s Day in this type of year are only 23 weeks apart. They are 24 weeks apart in all other leap years
- Daylight saving begins on March 13
- Mother's Day falls on its earliest possible date, May 8. This is the only leap year when Mother’s Day falls in ISO week 18. They fall in ISO week 19 in all other leap years.
- Memorial Day falls on May 30
- Juneteenth and Father's Day coincide on Sunday, June 19. This is the only leap year when Juneteenth falls in ISO week 24. They fall in ISO week 25 in all other leap years.
- Independence Day falls on a Monday
- Labor Day falls on September 5
- Grandparents' Day falls on September 11
- Columbus Day falls on October 10
- Daylight saving ends on November 6
- Election Day falls on its latest possible date, November 8
- Thanksgiving Day falls on November 24

References

↑ ^1.0 ^1.1 Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.

[math-1] 1.0 ^1.1 Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.

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