Leap year starting on Sunday

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

A leap year starting on Sunday is any year with 366 days (i.e. it includes 29 February) that begins on Sunday, 1 January, and ends on Monday, 31 December. Its dominical letters hence are AG. The most recent year of such kind was 2012 and the next one will be 2040 in the Gregorian calendar[1] or, likewise, 1996 and 2024 in the obsolete Julian calendar.

This is the only leap year with three occurrences of Friday the 13th: those three in this leap year occur three months (13 weeks) apart: in January, April, and July. Common years starting on Thursday share this characteristic, in the months of February, March, and November.

In this leap year, Martin Luther King Jr. Day is on January 16; Valentine's Day is on a Tuesday; Presidents' Day is on February 20; the leap day is on a Wednesday; Saint Patrick's Day is on a Saturday; Memorial Day is on May 28; Juneteenth is on a Tuesday; U.S. Independence Day is on a Wednesday; Labor Day is on September 3; Columbus Day is on its earliest possible date, October 8; Election Day in the USA is on November 6th; Halloween is on a Wednesday; Veterans Day is on a Sunday; Thanksgiving is on its earliest possible date, November 22; and Christmas is on a Tuesday.

In this type of year, all dates (except 29 February) fall on their respective weekdays 58 times in the 400 year Gregorian calendar cycle. Leap years starting on Friday share this characteristic.

Calendars[edit]

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

Applicable years[edit]

Gregorian Calendar[edit]

Leap years that begin on Sunday, along with those that start on Friday, occur most frequently: 15 out of the 97 (≈ 15.46%) total leap years in a 400-year cycle of the Gregorian calendar. Thus, the overall occurrence is 3.75% (15 out of 400).

Gregorian leap years starting on Sunday[1]
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
17th century 1612 1640 1668 1696
18th century 1708 1736 1764 1792
19th century 1804 1832 1860 1888
20th century 1928 1956 1984
21st century 2012 2040 2068 2096
22nd century 2108 2136 2164 2192
23rd century 2204 2232 2260 2288
24th century 2328 2356 2384
25th century 2412 2440 2468 2496
26th century 2508 2536 2564 2592
27th century 2604 2632 2660 2688

400 year cycle

century 1: 12, 40, 68, 96

century 2: 108, 136, 164, 192

century 3: 204, 232, 260, 288

century 4: 328, 356, 384

Julian Calendar[edit]

Like all leap year types, the one starting with 1 January on a Sunday 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, it will also repeat after 700 years, i.e., 25 cycles. The formula gives the year's position in the cycle ((year + 8) mod 28) + 1).

Julian leap years starting on Sunday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1408 1436 1464 1492
16th century 1520 1548 1576
17th century 1604 1632 1660 1688
18th century 1716 1744 1772 1800
19th century 1828 1856 1884
20th century 1912 1940 1968 1996
21st century 2024 2052 2080
22nd century 2108 2136 2164 2192

References[edit]

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