Leap year starting on Thursday

A leap year starting on Thursday is any year with 366 days (i.e. it includes 29 February) that begins on Thursday, 1 January, and ends on Friday, 31 December. Its dominical letters hence are DC, such as the years 1920, 1948, 1976, 2004, 2032, 2060, 2088, and 2128 in the Gregorian calendar[1] or, likewise, 1988 and 2016 in the obsolete Julian calendar. Any leap year that starts on Monday, Wednesday or Thursday has two Friday the 13ths. This leap year contains two Friday the 13ths in February and August.

Calendars

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

January
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
February
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
29  
 
March
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
April
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
252627282930
 
May
Su Mo Tu We Th Fr Sa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031  
June
Su Mo Tu We Th Fr Sa
0102030405
06070809101112
13141516171819
20212223242526
27282930  
 
July
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
August
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
293031  
 
September
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
2627282930  
 
October
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31  
November
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
282930  
 
December
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
262728293031  
 

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

January
Wk Mo Tu We Th Fr Sa Su
01 01020304
02 05060708091011
03 12131415161718
04 19202122232425
05 262728293031  
   
April
Wk Mo Tu We Th Fr Sa Su
14 01020304
15 05060708091011
16 12131415161718
17 19202122232425
18 2627282930  
   
July
Wk Mo Tu We Th Fr Sa Su
27 01020304
28 05060708091011
29 12131415161718
30 19202122232425
31 262728293031  
   
October
Wk Mo Tu We Th Fr Sa Su
40 010203
41 04050607080910
42 11121314151617
43 18192021222324
44 25262728293031
   
February
Wk Mo Tu We Th Fr Sa Su
05 01
06 02030405060708
07 09101112131415
08 16171819202122
09 23242526272829
   
May
Wk Mo Tu We Th Fr Sa Su
18 0102
19 03040506070809
20 10111213141516
21 17181920212223
22 24252627282930
23 31  
August
Wk Mo Tu We Th Fr Sa Su
31 01
32 02030405060708
33 09101112131415
34 16171819202122
35 23242526272829
36 3031  
November
Wk Mo Tu We Th Fr Sa Su
45 01020304050607
46 08091011121314
47 15161718192021
48 22232425262728
49 2930  
   
March
Wk Mo Tu We Th Fr Sa Su
10 01020304050607
11 08091011121314
12 15161718192021
13 22232425262728
14 293031  
   
June
Wk Mo Tu We Th Fr Sa Su
23 010203040506
24 07080910111213
25 14151617181920
26 21222324252627
27 282930  
   
September
Wk Mo Tu We Th Fr Sa Su
36 0102030405
37 06070809101112
38 13141516171819
39 20212223242526
40 27282930  
   
December
Wk Mo Tu We Th Fr Sa Su
49 0102030405
50 06070809101112
51 13141516171819
52 20212223242526
53 2728293031  
   

Applicable years

Gregorian Calendar

Leap years that start on Thursday occur 13 (or ≈ 13.4%) out of all 97 total leap years in a 400 cycle. Their overall occurrence is 3.25%. For this kind of year, the corresponding ISO year has 53 weeks, and the ISO week 10 (which begins March 1) and all subsequent ISO weeks occur earlier than in all other years. That means, moveable holidays may occur one calendar week later than otherwise possible, e.g. Gregorian Easter Sunday in week 17.

Gregorian leap years starting on Thursday[1]
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
17th century 1604 1632 1660 1688
18th century 1728 1756 1784
19th century 1824 1852 1880
20th century 1920 1948 1976
21st century 2004 2032 2060 2088
22nd century 2128 2156 2184
Gregorian year types per leap cycle by Dominical letter (DL)[1] and Doomsday (DD)
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 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 %

Julian Calendar

Like all leap year types, the one starting with 1 January on a Thursday occurs exactly once in a 28-year cycle in the Julian calendar, i.e. in 3.57% of years. 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).

Julian leap years starting on Thursday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1428 1456 1484
16th century 1512 1540 1568 1596
17th century 1624 1652 1680
18th century 1708 1736 1764 1792
19th century 1820 1848 1876
20th century 1904 1932 1960 1988
21st century 2016 2044 2072 2100
22nd century 2128 2156 2184

References

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