Leap year starting on Tuesday

Last updated

A leap year starting on Tuesday is any year with 366 days (i.e. it includes 29 February) that begins on Tuesday, 1 January, and ends on Wednesday, 31 December. Its dominical letters hence are FE. The most recent year of such kind was 2008, and the next one will be 2036 in the Gregorian calendar [1] or, likewise 2020 and 2048 in the obsolete Julian calendar.

Contents

Any leap year that starts on Tuesday has only one Friday the 13th; the only one in this leap year occurs in June. Common years starting on Wednesday share this characteristic.

Any leap year that starts on Tuesday has only one Tuesday the 13th: the only one in this leap year occurs in May.

Any leap year that starts on Tuesday has only one Friday the 17th: the only one in this leap year occurs in October.

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 17th.

Calendars

Calendar for any leap year starting on Tuesday,
presented as common in many English-speaking areas
January
SuMoTuWeThFrSa
12345
6789101112
13141516171819
20212223242526
2728293031 
 
February
SuMoTuWeThFrSa
12
3456789
10111213141516
17181920212223
242526272829
 
March
SuMoTuWeThFrSa
1
2345678
9101112131415
16171819202122
23242526272829
3031 
April
SuMoTuWeThFrSa
12345
6789101112
13141516171819
20212223242526
27282930 
 
May
SuMoTuWeThFrSa
123
45678910
11121314151617
18192021222324
25262728293031
 
June
SuMoTuWeThFrSa
1234567
891011121314
15161718192021
22232425262728
2930 
 
July
SuMoTuWeThFrSa
12345
6789101112
13141516171819
20212223242526
2728293031 
 
August
SuMoTuWeThFrSa
12
3456789
10111213141516
17181920212223
24252627282930
31 
September
SuMoTuWeThFrSa
123456
78910111213
14151617181920
21222324252627
282930 
 
October
SuMoTuWeThFrSa
1234
567891011
12131415161718
19202122232425
262728293031 
 
November
SuMoTuWeThFrSa
1
2345678
9101112131415
16171819202122
23242526272829
30 
December
SuMoTuWeThFrSa
123456
78910111213
14151617181920
21222324252627
28293031 
 
ISO 8601-conformant calendar with week numbers for
any leap year starting on Tuesday (dominical letter FE)
January
WkMoTuWeThFrSaSu
01010203040506
0207080910111213
0314151617181920
0421222324252627
0528293031 
  
February
WkMoTuWeThFrSaSu
05010203
0604050607080910
0711121314151617
0818192021222324
092526272829
  
March
WkMoTuWeThFrSaSu
090102
1003040506070809
1110111213141516
1217181920212223
1324252627282930
1431 
April
WkMoTuWeThFrSaSu
14010203040506
1507080910111213
1614151617181920
1721222324252627
18282930 
  
May
WkMoTuWeThFrSaSu
1801020304
1905060708091011
2012131415161718
2119202122232425
22262728293031 
  
June
WkMoTuWeThFrSaSu
2201
2302030405060708
2409101112131415
2516171819202122
2623242526272829
2730 
July
WkMoTuWeThFrSaSu
27010203040506
2807080910111213
2914151617181920
3021222324252627
3128293031 
  
August
WkMoTuWeThFrSaSu
31010203
3204050607080910
3311121314151617
3418192021222324
3525262728293031
  
September
WkMoTuWeThFrSaSu
3601020304050607
3708091011121314
3815161718192021
3922232425262728
402930 
  
October
WkMoTuWeThFrSaSu
400102030405
4106070809101112
4213141516171819
4320212223242526
442728293031 
  
November
WkMoTuWeThFrSaSu
440102
4503040506070809
4610111213141516
4717181920212223
4824252627282930
  
December
WkMoTuWeThFrSaSu
4901020304050607
5008091011121314
5115161718192021
5222232425262728
01293031 
  

Applicable years

Gregorian Calendar

Leap years that begin on Tuesday, along with those starting on Wednesday, occur at a rate of approximately 14.43% (14 out of 97) of all total leap years in a 400-year cycle of the Gregorian calendar. Thus, their overall occurrence is 3.5% (14 out of 400).

Gregorian leap years starting on Tuesday [1]
Decade1st2nd3rd4th5th6th7th8th9th10th
17th century 1608 1636 1664 1692
18th century 1704 1732 1760 1788
19th century 1828 1856 1884
20th century 1924 1952 1980
21st century 2008 2036 2064 2092
22nd century 2104 2132 2160 2188
23rd century 2228 2256 2284
24th century 2324 2352 2380
25th century 2408 2436 2464 2492
26th century 2504253225602588
400-year cycle
0–998366492
100–199104132160188
200–299228256284
300–399324352380

Julian Calendar

Like all leap year types, the one starting with 1 January on a Tuesday 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 Tuesday
Decade1st2nd3rd4th5th6th7th8th9th10th
14th century 1320 1348 1376
15th century 1404 1432 1460 1488
16th century 1516 1544 1572 1600
17th century 1628 1656 1684
18th century1712174017681796
19th century182418521880
20th century1908193619641992
21st century202020482076
22nd century2104213221602188

Holidays

International

Roman Catholic Solemnities

Australia and New Zealand

British Isles

Canada

United States

References

  1. 1 2 Robert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017.