Type of year D on a solar calendar according to its starting and ending days in the week
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 , 2021 and 2027 in the obsolete Julian calendar , see below for more .
This is the only common year with three occurrences of Friday the 13th : those three in this common year occur in February , March , and November . Leap years starting on Sunday share this characteristic, for the months January, April and July. 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 this common year, February is a unique rectangle calendar when weeks start on Sundays, Martin Luther King Jr. Day is on January 19 , Valentine’s Day is on a Saturday , President's Day is on February 16 , Saint Patrick’s Day is on a Tuesday , Memorial Day is on its earliest possible date, May 25 , U.S. Independence Day and Halloween are on a Saturday, Labor Day is on its latest possible date, September 7 , 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. Also, both types of years also have the shortest gap between Halloween (October 31) and the end of Daylight Saving Time in the US (November 1) by one day as of 2007.
Calendars [ edit ]
Calendar for any common year starting on Thursday, presented as common in many English-speaking areas
January
Su
Mo
Tu
We
Th
Fr
Sa
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
February
Su
Mo
Tu
We
Th
Fr
Sa
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
March
Su
Mo
Tu
We
Th
Fr
Sa
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
April
Su
Mo
Tu
We
Th
Fr
Sa
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
May
Su
Mo
Tu
We
Th
Fr
Sa
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
June
Su
Mo
Tu
We
Th
Fr
Sa
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
July
Su
Mo
Tu
We
Th
Fr
Sa
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
August
Su
Mo
Tu
We
Th
Fr
Sa
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
September
Su
Mo
Tu
We
Th
Fr
Sa
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
October
Su
Mo
Tu
We
Th
Fr
Sa
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
November
Su
Mo
Tu
We
Th
Fr
Sa
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
December
Su
Mo
Tu
We
Th
Fr
Sa
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
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 Thursday (dominical letter D)
January
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
February
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
March
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
April
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
May
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
June
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
July
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
August
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
September
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
October
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
November
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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
December
Wk
Mo
Tu
We
Th
Fr
Sa
Su
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 [ edit ]
Gregorian Calendar [ edit ]
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 only spans across century years divisible by 400, e.g. 1600, 2000, and 2400.
Julian Calendar [ edit ]
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 [ edit ]
Year starts
Common years
Leap years
1 Jan
Count
Ratio
31 Dec
DL
DD
Count
Ratio
31 Dec
DL
DD
Count
Ratio
Sun
58
14.50 %
Sun
A
Tue
43
10.75 %
Mon
AG
Wed
15
0 3.75 %
Sat
56
14.00 %
Sat
B
Mon
43
10.75 %
Sun
BA
Tue
13
0 3.25 %
Fri
58
14.50 %
Fri
C
Sun
43
10.75 %
Sat
CB
Mon
15
0 3.75 %
Thu
57
14.25 %
Thu
D
Sat
44
11.00 %
Fri
DC
Sun
13
0 3.25 %
Wed
57
14.25 %
Wed
E
Fri
43
10.75 %
Thu
ED
Sat
14
0 3.50 %
Tue
58
14.50 %
Tue
F
Thu
44
11.00 %
Wed
FE
Fri
14
0 3.50 %
Mon
56
14.00 %
Mon
G
Wed
43
10.75 %
Tue
GF
Thu
13
0 3.25 %
∑
400
100.0 %
303
75.75 %
97
24.25 %