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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 letters hence are GF, such as the years 1720, 1748, 1776, 1816, 1844, 1872, 1912, 1940, 1968, 1996, 2024, 2052, 2080, and 2120 in the Gregorian calendar[1] or, likewise, 2008, 2036, and 2064 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 September and December. Any common year starting on Tuesday shares this characteristic.

Calendars

Calendar for any leap year starting on Monday,
presented as common in many English-speaking areas
January
Su Mo Tu We Th Fr Sa
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  
 
February
Su Mo Tu We Th Fr Sa
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
 
March
Su Mo Tu We Th Fr Sa
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  
April
Su Mo Tu We Th Fr Sa
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  
 
May
Su Mo Tu We Th Fr Sa
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  
 
June
Su Mo Tu We Th Fr Sa
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  
July
Su Mo Tu We Th Fr Sa
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  
 
August
Su Mo Tu We Th Fr Sa
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
 
September
Su Mo Tu We Th Fr Sa
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  
 
October
Su Mo Tu We Th Fr Sa
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  
 
November
Su Mo Tu We Th Fr Sa
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
 
December
Su Mo Tu We Th Fr Sa
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)
January
Wk Mo Tu We Th Fr Sa Su
01 01 02 03 04 05 06 07
02 08 09 10 11 12 13 14
03 15 16 17 18 19 20 21
04 22 23 24 25 26 27 28
05 29 30 31  
   
February
Wk Mo Tu We Th Fr Sa Su
05 01 02 03 04
06 05 06 07 08 09 10 11
07 12 13 14 15 16 17 18
08 19 20 21 22 23 24 25
09 26 27 28 29  
   
March
Wk Mo Tu We Th Fr Sa Su
09 01 02 03
10 04 05 06 07 08 09 10
11 11 12 13 14 15 16 17
12 18 19 20 21 22 23 24
13 25 26 27 28 29 30 31
   
April
Wk Mo Tu We Th Fr Sa Su
14 01 02 03 04 05 06 07
15 08 09 10 11 12 13 14
16 15 16 17 18 19 20 21
17 22 23 24 25 26 27 28
18 29 30  
   
May
Wk Mo Tu We Th Fr Sa Su
18 01 02 03 04 05
19 06 07 08 09 10 11 12
20 13 14 15 16 17 18 19
21 20 21 22 23 24 25 26
22 27 28 29 30 31  
   
June
Wk Mo Tu We Th Fr Sa Su
22 01 02
23 03 04 05 06 07 08 09
24 10 11 12 13 14 15 16
25 17 18 19 20 21 22 23
26 24 25 26 27 28 29 30
   
July
Wk Mo Tu We Th Fr Sa Su
27 01 02 03 04 05 06 07
28 08 09 10 11 12 13 14
29 15 16 17 18 19 20 21
30 22 23 24 25 26 27 28
31 29 30 31  
   
August
Wk Mo Tu We Th Fr Sa Su
31 01 02 03 04
32 05 06 07 08 09 10 11
33 12 13 14 15 16 17 18
34 19 20 21 22 23 24 25
35 26 27 28 29 30 31  
   
September
Wk Mo Tu We Th Fr Sa Su
35 01
36 02 03 04 05 06 07 08
37 09 10 11 12 13 14 15
38 16 17 18 19 20 21 22
39 23 24 25 26 27 28 29
40 30  
October
Wk Mo Tu We Th Fr Sa Su
40 01 02 03 04 05 06
41 07 08 09 10 11 12 13
42 14 15 16 17 18 19 20
43 21 22 23 24 25 26 27
44 28 29 30 31  
   
November
Wk Mo Tu We Th Fr Sa Su
44 01 02 03
45 04 05 06 07 08 09 10
46 11 12 13 14 15 16 17
47 18 19 20 21 22 23 24
48 25 26 27 28 29 30
   
December
Wk Mo Tu We Th Fr Sa Su
48 01
49 02 03 04 05 06 07 08
50 09 10 11 12 13 14 15
51 16 17 18 19 20 21 22
52 23 24 25 26 27 28 29
01 30 31  

Applicable years

Gregorian Calendar

Leap years that begin on Monday, along with those that start on Saturday or Thursday, occur least frequently: 13 out of 97 (≈ 13.402%) total leap years of the Gregorian calendar. Their overall occurrence is thus 3.25% (13 out of 400).

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
23rd century 2216 2244 2272
24th century 2312 2340 2368 2396
25th century 2424 2452 2480
26th century 2520 2548 2576

Julian Calendar

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. 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 Monday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
14th century 1308 1336 1364 1392
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

Wikimedia Commons has media related to Leap years starting on Monday and ending on Tuesday.
  1. ^ a b Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.
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