Leap year starting on Saturday

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A leap year starting on Saturday is any year with 366 days (i.e. it includes 29 February) that begins on Saturday, 1 January, and ends on Sunday, 31 December. Its dominical letter hence is BA. The most recent year of such kind was 2000 and the next one will be 2028 in the Gregorian calendar, and in 2400[1] or, likewise, 2012 and 2040 in the obsolete Julian calendar, see below for more.

This leap year of such type has a Friday the 13th in October.

Calendars

Calendar for any leap year starting on Saturday,
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 Saturday (dominical letter BA)

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

Gregorian Calendar

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

Gregorian leap years starting on Saturday[1]
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
17th century 1628 1656 1684
18th century 1724 1752 1780
19th century 1820 1848 1876
20th century 1916 1944 1972 2000
21st century 2028 2056 2084
22nd century 2124 2152 2180

The last year of the 4th, 8th ... century is always a leap year starting on Saturday and February 29 is always on Tuesday.

Julian Calendar

Like all leap year types, the one starting with 1 January on a Saturday 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 Saturday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1424 1452 1480
16th century 1508 1536 1564 1592
17th century 1620 1648 1676
18th century 1704 1732 1760 1788
19th century 1816 1844 1872 1900
20th century 1928 1956 1984
21st century 2012 2040 2068 2096
22nd century 2124 2152 2180

References

  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. 
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