Leap year starting on Friday

A leap year starting on Friday is any year with 366 days (i.e. it includes 29 February) that begins on Friday 1 January and ends on Saturday 31 December. Its dominical letters hence are CB. The most recent year of such kind was 2016 and the next one will be 2044 in the Gregorian calendar[1] or, likewise, 2000 and 2028 in the obsolete Julian calendar.

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 May. Common years starting on Saturday share this characteristic.

In this leap year, Martin Luther King Jr. Day is on January 18, Valentine’s Day is on a Sunday, Presidents Day is on its earliest possible date, February 15, the leap day is on a Monday, St. Patrick’s Day and Cinco De Mayo is on a Thursday, Memorial Day is on May 30, Juneteenth is on a Sunday, U.S. Independence Day is on a Monday, Labor Day is on September 5, Columbus Day is on October 10, Halloween is on a Monday, Election Day in the USA is on its latest possible date, November 8th, Thanksgiving is on November 24, and Christmas is on a Sunday. Additionally, this type of year is the only year that Presidents Day does not fall on the penultimate Monday of February.

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 Sunday share this characteristic.

CalendarsEdit

Calendar for any leap year starting on Friday,
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 Friday (dominical letter CB)
January
Wk Mo Tu We Th Fr Sa Su
53 01 02 03
01 04 05 06 07 08 09 10
02 11 12 13 14 15 16 17
03 18 19 20 21 22 23 24
04 25 26 27 28 29 30 31
   
February
Wk Mo Tu We Th Fr Sa Su
05 01 02 03 04 05 06 07
06 08 09 10 11 12 13 14
07 15 16 17 18 19 20 21
08 22 23 24 25 26 27 28
09 29  
   
March
Wk Mo Tu We Th Fr Sa Su
09 01 02 03 04 05 06
10 07 08 09 10 11 12 13
11 14 15 16 17 18 19 20
12 21 22 23 24 25 26 27
13 28 29 30 31  
   
April
Wk Mo Tu We Th Fr Sa Su
13 01 02 03
14 04 05 06 07 08 09 10
15 11 12 13 14 15 16 17
16 18 19 20 21 22 23 24
17 25 26 27 28 29 30
   
May
Wk Mo Tu We Th Fr Sa Su
17 01
18 02 03 04 05 06 07 08
19 09 10 11 12 13 14 15
20 16 17 18 19 20 21 22
21 23 24 25 26 27 28 29
22 30 31  
June
Wk Mo Tu We Th Fr Sa Su
22 01 02 03 04 05
23 06 07 08 09 10 11 12
24 13 14 15 16 17 18 19
25 20 21 22 23 24 25 26
26 27 28 29 30  
   
July
Wk Mo Tu We Th Fr Sa Su
26 01 02 03
27 04 05 06 07 08 09 10
28 11 12 13 14 15 16 17
29 18 19 20 21 22 23 24
30 25 26 27 28 29 30 31
   
August
Wk Mo Tu We Th Fr Sa Su
31 01 02 03 04 05 06 07
32 08 09 10 11 12 13 14
33 15 16 17 18 19 20 21
34 22 23 24 25 26 27 28
35 29 30 31  
   
September
Wk Mo Tu We Th Fr Sa Su
35 01 02 03 04
36 05 06 07 08 09 10 11
37 12 13 14 15 16 17 18
38 19 20 21 22 23 24 25
39 26 27 28 29 30  
   
October
Wk Mo Tu We Th Fr Sa Su
39 01 02
40 03 04 05 06 07 08 09
41 10 11 12 13 14 15 16
42 17 18 19 20 21 22 23
43 24 25 26 27 28 29 30
44 31  
November
Wk Mo Tu We Th Fr Sa Su
44 01 02 03 04 05 06
45 07 08 09 10 11 12 13
46 14 15 16 17 18 19 20
47 21 22 23 24 25 26 27
48 28 29 30  
   
December
Wk Mo Tu We Th Fr Sa Su
48 01 02 03 04
49 05 06 07 08 09 10 11
50 12 13 14 15 16 17 18
51 19 20 21 22 23 24 25
52 26 27 28 29 30 31  
   

Applicable yearsEdit

Gregorian CalendarEdit

Leap years that begin on Friday, along with those that start on Sunday, 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 Friday[1]
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
17th century 1616 1644 1672
18th century 1712 1740 1768 1796
19th century 1808 1836 1864 1892
20th century 1904 1932 1960 1988
21st century 2016 2044 2072
22nd century 2112 2140 2168 2196
23rd century 2208 2236 2264 2292
24th century 2304 2332 2360 2388
25th century 2416 2444 2472
26th century 2512 2540 2568 2596

400 year cycle

century 1: 16, 44, 72

century 2: 112, 140, 168, 196

century 3: 208, 236, 264, 292

century 4: 304, 332, 360, 388

Julian CalendarEdit

Like all leap year types, the one starting with 1 January on a Friday 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 Friday
Decade 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
15th century 1412 1440 1468 1496
16th century 1524 1552 1580
17th century 1608 1636 1664 1692
18th century 1720 1748 1776
19th century 1804 1832 1860 1888
20th century 1916 1944 1972 2000
21st century 2028 2056 2084
22nd century 2112 2140 2168 2196

ReferencesEdit

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