Common year starting on Sunday

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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 2006 and the next one will be 2017 in the Gregorian calendar[1] or, likewise, 2007 and 2018 in the obsolete Julian calendar.

Calendars[edit]

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

01 02 03 04 05 06 07
08 09 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31  
 
01 02 03 04
05 06 07 08 09 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28  
 
01 02 03 04
05 06 07 08 09 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30 31  
 
01
02 03 04 05 06 07 08
09 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30  
01 02 03 04 05 06
07 08 09 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31  
 
01 02 03
04 05 06 07 08 09 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30
 
01
02 03 04 05 06 07 08
09 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31  
01 02 03 04 05
06 07 08 09 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30 31  
 
01 02
03 04 05 06 07 08 09
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
 
01 02 03 04 05 06 07
08 09 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31  
 
01 02 03 04
05 06 07 08 09 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30  
 
01 02
03 04 05 06 07 08 09
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
31  


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

01
02 03 04 05 06 07 08
09 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31  
01 02
03 04 05 06 07 08 09
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
 
01 02
03 04 05 06 07 08 09
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
31  
01
02 03 04 05 06 07 08
09 10 11 12 13 14 15
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31  
01 02 03 04 05
06 07 08 09 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28  
 
01 02 03 04 05 06 07
08 09 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31  
 
01 02 03 04 05 06
07 08 09 10 11 12 13
14 15 16 17 18 19 20
21 22 23 24 25 26 27
28 29 30 31  
 
01 02 03 04 05
06 07 08 09 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30  
 
01 02 03 04 05
06 07 08 09 10 11 12
13 14 15 16 17 18 19
20 21 22 23 24 25 26
27 28 29 30 31  
 
01 02 03 04
05 06 07 08 09 10 11
12 13 14 15 16 17 18
19 20 21 22 23 24 25
26 27 28 29 30  
 
01 02 03
04 05 06 07 08 09 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30
 
01 02 03
04 05 06 07 08 09 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30 31
 

Applicable years[edit]

The 15 types of years repeat in a 28-year cycle (1461 weeks) in the Julian calendar. Each leap-year dominical letter occurs exactly once and every common letter thrice.

Sequence of year types in the Julian calendar
Year 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
DL G F E DC B* A G FE D C B AG F E D CB A G F ED C B A GF E D C BA
1 Jan Mo Tu We Th Sa Su Mo Tu Th Fr Sa Su Tu We Th Fr Su Mo Tu We Fr Sa Su Mo We Th Fr Sa
31 Dec Fr We Mo Sa Th Tu Su

The final two digits of Julian years repeat after 700 years, i.e. 25 cycles. When starting to count in 2001 for instance, every 1st, 7th and 18th year (equivalent to #17, #23 and #06 in the table) of these Julian cycles is a common year that starts on a Sunday, i.e. ca. 10.71 % of all years. They are always 6 or 11 years apart.

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

The 15 types of years repeat in a 400-year cycle (20871 weeks) in the Gregorian calendar. 13 leap years per cycle or exactly 10.75 % start on a Sunday. The 28-year sub-cycle does only span across century years divisible by 4, e.g. 2000.

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

Notes[edit]

  1. ^ a b Robert van Gent (2005). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. 
  2. ^ Robert H. van Gent (2005). "Mathematics of the ISO calendar". Department of Mathematics at Utrecht University.