Common year starting on Sunday

A common year starting on Sunday is any non-leap year (i.e. a year with 365 days) that begins on Sunday, 1 January, and ends on Sunday, 31 December. Its dominical letter hence is A. The most recent year of such kind was 2017 and the next one will be 2023 in the Gregorian calendar,^[1] or, likewise, 2018 and 2029 in the obsolete Julian calendar, see below for more. Any common year that starts on Sunday, Monday or Tuesday has two Friday the 13ths. This common year contains two Friday the 13ths in January and October.

Calendars

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Applicable years

Gregorian Calendar

In the (currently used) Gregorian calendar, alongside with Monday, Wednesday, Friday or Saturday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-three common years per cycle or exactly 10.75% start on a Sunday. 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 Sunday^[1]
Decade	1st	2nd		3rd	4th		5th		6th	7th		8th		9th	10th
16th century	prior to first adoption (proleptic)													1589	1595
17th century	1606	1617		1623	1634		1645		1651	1662		1673	1679	1690	—
18th century	1702	1713	1719	1730	—		1741	1747	1758	1769		1775		1786	1797
19th century	1809	1815		1826	1837		1843		1854	1865		1871		1882	1893	1899
20th century	1905	1911		1922	1933	1939	1950		—	1961	1967	1978		1989	1995
21st century	2006	2017		2023	2034		2045		2051	2062		2073	2079	2090	—
22nd century	2102	2113	2119	2130	—		2141	2147	2158	2169		2175		2186	2197

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 11, 22 and 28 of the cycle are common years beginning on Sunday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Sunday.

Julian common years starting on Sunday
Decade	1st		2nd		3rd		4th		5th		6th		7th		8th		9th		10th
15th century	1402		1413	1419	1430		—		1441	1447	1458		1469		1475		1486		1497
16th century	1503		1514		1525		1531		1542		1553	1559	1570		—		1581	1587	1598
17th century	1609		1615		1626		1637		1643		1654		1665		1671		1682		1693	1699
18th century	1710		—		1721	1727	1738		1749		1755		1766		1777		1783		1794
19th century	1805		1811		1822		1833	1839	1850		—		1861	1867	1878		1889		1895
20th century	1906		1917		1923		1934		1945		1951		1962		1973	1979	1990		—
21st century	2001	2007	2018		2029		2035		2046		2057		2063		2074		2085		2091

References

^ ^a ^b ^c 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.

[1]

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 %