Common year starting on Thursday

A common year starting on Thursday is any non-leap year (i.e. a year with 365 days) that begins on Thursday, 1 January, and ends on Thursday, 31 December. Its dominical letter hence is D. The most recent year of such kind was 2015 and the next one will be 2026 in the Gregorian calendar[1] or, likewise, 2010 and 2021 in the obsolete Julian calendar, see below for more. This is the only common year with three occurrences of Friday the 13th; specifically, the months of February, March, and November. Leap years starting on Sunday share this characteristic and with the exception of skipped leap years, leap year beginning on a Sunday fall exactly three years either side of two consecutive common years starting on Thursday - for example 2012 between 2009 and 2015.

From February until March in this type of year is also the shortest period (one month) that runs between two instances of Friday the 13th. In 2015, for example, February 13th, March 13th and November 13th, all fell on a Friday, so there were 3 Friday the 13ths in 2015, February, March and November. In this common year, February is rectangular in calendar where week starts on Sunday, U.S. Independence Day and Halloween are on a Saturday, Thanksgiving is on November 26, and Christmas is on a Friday. This common year is also the only one where Memorial Day and Labor Day are not 14 weeks (98 days) apart: they are 15 weeks (105 days) apart in this common year. Leap years starting on Wednesday share this characteristic.

Calendars

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

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

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

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

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

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

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

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

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

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

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

Wk	Mo	Tu	We	Th	Fr	Sa	Su
	November
44							01
45	02	03	04	05	06	07	08
46	09	10	11	12	13	14	15
47	16	17	18	19	20	21	22
48	23	24	25	26	27	28	29
49	30

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

Applicable years

Gregorian Calendar

In the (currently used) Gregorian calendar, alongside Tuesday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-four common years per cycle or exactly 11% start on a Thursday. The 28-year sub-cycle does only span across century years divisible by 400, e.g. 1600, 2000, and 2400.

Gregorian common years starting on Thursday[1]
Decade	1st		2nd	3rd	4th		5th	6th		7th		8th	9th		10th
16th century	prior to first adoption (proleptic)													1587	1598
17th century	1609		1615	1626	1637		1643	1654		1665		1671	1682		1693	1699
18th century	1705		1711	1722	1733	1739	1750	—		1761	1767	1778	1789		1795
19th century	1801	1807	1818	1829	1835		1846	1857		1863		1874	1885		1891
20th century	1903		1914	1925	1931		1942	1953	1959	-		1970	1981	1987	1998
21st century	2009		2015	2026	2037		2043	2054		2065		2071	2082		2093	2099

Julian Calendar

In the now-obsolete Julian calendar, the fourteen types of year (seven common, seven leap) repeat in a 28-year cycle (1461 weeks). A leap year has two adjoining dominical letters (one for January and February and the other for March to December, as 29 February has no letter). This sequence occurs exactly once within a cycle, and every common letter thrice.

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). Years 3, 14 and 20 of the cycle are common years beginning on Thursday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Thursday.

Julian common years starting on Thursday
Decade	1st		2nd		3rd		4th		5th		6th		7th		8th		9th		10th
15th century	1405		1411		1422		1433	1439		1450		—		1461	1467		1478		1489	1495
16th century	1506		1517		1523		1534		1545		1551		1562		1573	1579		1590		—
17th century	1601	1607		1618		1629		1635	1646		1657		1683		1674		1685		1691
18th century	1702		1713	1719		1730		—		1741	1747	1758		1769		1775		1786		1797
19th century	1803		1814		1825		1831		1842		1853	1859	1870		—		1881	1887	1898
20th century	1909		1915		1926		1937		1943		1954		1965		1971		1982		1993	1999
21st century	2010		—		2021	2027	2038		2049		2055		2066		2077		2083		2094

References

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.

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