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 Friday the 13th in this leap year occurs in May. Common years starting on Saturday share this characteristic. In this leap year, the leap day, U.S. Independence Day, and Halloween are on a Monday, Thanksgiving is on November 24 and Christmas is on a Sunday.

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 that start on Sunday, 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 thus 3.75% (15 out of 400).

Gregorian leap years starting on Friday^[1]
Decade	1st	2nd	4th	5th	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

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

References

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

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

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

[1]

[2]

1 Jan	Count	Ratio	31 Dec	DL	DD	Count	Ratio	31 Dec	DL	DD	Count	Ratio
Year starts			Common years					Leap years
Sun	58	14.50 %	Sun	A	Tue	43	10.75 %	Mon	AG	Wed	15	03.75 %
Sat	56	14.00 %	Sat	B	Mon	43	10.75 %	Sun	BA	Tue	13	03.25 %
Fri	58	14.50 %	Fri	C	Sun	43	10.75 %	Sat	CB	Mon	15	03.75 %
Thu	57	14.25 %	Thu	D	Sat	44	11.00 %	Fri	DC	Sun	13	03.25 %
Wed	57	14.25 %	Wed	E	Fri	43	10.75 %	Thu	ED	Sat	14	03.50 %
Tue	58	14.50 %	Tue	F	Thu	44	11.00 %	Wed	FE	Fri	14	03.50 %
Mon	56	14.00 %	Mon	G	Wed	43	10.75 %	Tue	GF	Thu	13	03.25 %
∑	400	100.0 %				303	75.75 %				97	24.25 %