Leap year starting on Monday

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A leap year starting on Monday is any year with 366 days (i.e. it includes 29 February) that begins on Monday, 1 January, and ends on Tuesday, 31 December. Its dominical letter hence is GF, such as the years 1940, 1968, 1996, 2024, 2052, 2080, and 2120 in the Gregorian calendar[1] or, likewise, 2008 and 2036 in the obsolete Julian calendar. Any leap year that starts on Monday, Wednesday or Thursday have two Friday the 13ths. Like common years starting on Tuesday, this leap year of such type contains two Friday the 13ths in September and December.

Calendars[edit]

Calendar for any leap year starting on Monday,
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 29
 
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 leap year starting on Monday (dominical letter GF)

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  
 
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]

Gregorian Calendar[edit]

Leap years beginning on Monday, along with those that start on Saturday, occur least frequently - 13 out of 97 (≈ 13.4%) possible total leap years in a 400 year cycle. Their overall occurrence is thus 3.25%.

Gregorian leap years starting on Monday[1]
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
17th century 1624 1652 1680
18th century 1720 1748 1776
19th century 1816 1844 1872
20th century 1912 1940 1968 1996
21st century 2024 2052 2080
22nd century 2120 2148 2176

Julian Calendar[edit]

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

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.

Julian leap years starting on Monday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1420 1448 1476
16th century 1504 1532 1560 1588
17th century 1616 1644 1672 1700
18th century 1728 1756 1784
19th century 1812 1840 1868 1896
20th century 1924 1952 1980
21st century 2008 2036 2064 2092
22nd century 2120 2148 2176

References[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.