Leap year starting on Saturday

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 letters hence are BA. The most recent year kind was 2000 and the next one will be 2028 in the Gregorian calendar or, likewise 2012 and 2040 in the obsolescent Julian calendar. In the Gregorian calendar, years divisible by 400 are always leap years starting on Saturday. The most recent such occurrence was 2000 and the next one will be 2400, see below for more.[1]

Any leap year that starts on Tuesday, Friday or Saturday has only one Friday the 13th: the only one in this leap year occurs in October. Common years starting on Sunday share this characteristic, but also have another in January. From August of the common year preceding that year until October in this type of year is also the longest period (14 months) that occurs without a Friday the 13th. Common years starting on Tuesday share this characteristic, from July of the year that precedes it to September in that type of year.

In this leap year, Martin Luther King Jr. Day is on January 17, Valentine's Day is on a Monday, Presidents Day is on its latest possible date, February 21, the leap day is on a Tuesday, Saint Patrick's Day is on a Friday, Memorial Day is on May 29, Juneteenth is on a Monday, U.S. Independence Day is on a Tuesday, Labor Day is on September 4, Thanksgiving is on November 23, and Christmas is on a Monday.

This is the only type of year in which all dates (except 29 February) fall on their respective weekdays the minimal 56 times in the 400 year Gregorian Calendar cycle. Additionally, these types of years are the only ones which contain 54 different calendar weeks (2 partial, 52 in full) in areas of the world where Sunday is considered the first day of the week, and also the only type of year to contain 53 full weekends.

CalendarsEdit

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

Applicable yearsEdit

Gregorian CalendarEdit

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

Gregorian leap years starting on Saturday[1]
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
16th century prior to first adoption (proleptic) 1600
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
23rd century 2220 2248 2276
24th century 2316 2344 2372 2400
25th century 2428 2456 2484

400 year cycle

century 1: 028, 056, 084

century 2: 124, 152, 180

century 3: 220, 248, 276

century 4: 316, 344, 372, 400

Julian CalendarEdit

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. 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 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

ReferencesEdit

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