Common year starting on Saturday

A common year starting on Saturday is any non-leap year (i.e. a year with 365 days) that begins on Saturday, 1 January, and ends on Saturday, 31 December. Its dominical letter hence is B. The most recent year of such kind was 2011 and the next one will be 2022 in the Gregorian calendar^[1] or, likewise, 2017 and 2023 in the obsolete Julian calendar, see below for more. Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th. This common year has a Friday the 13th in May. Leap years starting on Friday share this characteristic.

Calendars

Calendar for any common year starting on Saturday

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

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

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
	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
	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
	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
	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
	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
	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

If the preceding year is a common year starting on Friday, then the year begins in ISO week 52; if the preceding year is a leap year starting on Thursday, then the year begins in ISO week 53.

Applicable years

Gregorian Calendar

In the (currently used) Gregorian calendar, 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 Saturday. The 28-year sub-cycle will break at a century year which is not divisible by 400 (e.g. it broke at the year 1900 but not at the year 2000).

Gregorian common years starting on Saturday^[1]
	1st		2nd	3rd		4th		5th	6th		7th		8th	9th		10th
16th century	prior to first adoption (proleptic)													1583		1594
17th century	1605		1611	1622		1633	1639	1650	—		1661	1667	1678	1689		1695
18th century	1701	1707	1718	1729		1735		1746	1757		1763		1774	1785		1791
19th century	1803		1814	1825		1831		1842	1853	1859	1870		—	1881	1887	1898
20th century	1910		—	1921	1927	1938		1949	1955		1966		1977	1983		1994
21st century	2005		2011	2022		2033	2039	2050	—		2061	2067	2078	2089		2095

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 in the Church of England, as 29 February has no letter). Each of the seven two-letter sequences occurs 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 10, 16 and 27 of the cycle are common years beginning on Saturday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Saturday.

Julian common years starting on Saturday
Decade	1st		2nd		3rd		4th		5th		6th		7th		8th		9th		10th
15th century	1401	1407	1418		1429		1435		1446		1457		1463		1474		1485		1491
16th century	1502		1513	1519	1530		—		1541	1547	1558		1569		1575		1586		1597
17th century	1603		1614		1625		1631		1642		1653	1659	1670		—		1681	1687	1698
18th century	1709		1715		1726		1737		1743		1754		1765		1771		1782		1793	1799
19th century	1810		—		1821	1827	1838		1849		1855		1866		1877		1883		1894
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		—

References

1 2 3 Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

[math-1] 1 2 3 Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.

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 %