Leap year starting on Tuesday

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. Any leap year that starts on Tuesday, Friday or Saturday has only one Friday the 13th; the only Friday the 13th in this leap year occurs in June. Common years starting on Wednesday share this characteristic. In this leap year, the leap day, U.S. Independence Day, and Halloween are on a Friday, Thanksgiving is on November 27, and Christmas is on a Thursday.

Calendars

Calendar for any leap year starting on Tuesday,
presented as common in many English-speaking areas

0102030405
06070809101112
13141516171819
20212223242526
2728293031  
 
0102
03040506070809
10111213141516
17181920212223
242526272829
 
01
02030405060708
09101112131415
16171819202122
23242526272829
3031  
0102030405
06070809101112
13141516171819
20212223242526
27282930  
 
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
01020304050607
08091011121314
15161718192021
22232425262728
2930  
 
0102030405
06070809101112
13141516171819
20212223242526
2728293031  
 
0102
03040506070809
10111213141516
17181920212223
24252627282930
31  
010203040506
07080910111213
14151617181920
21222324252627
282930  
 
01020304
05060708091011
12131415161718
19202122232425
262728293031  
 
01
02030405060708
09101112131415
16171819202122
23242526272829
30  
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 

ISO 8601-conformant calendar with week numbers for
any leap year starting on Tuesday (dominical letter FE)

010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
010203
04050607080910
11121314151617
18192021222324
2526272829
 
0102
03040506070809
10111213141516
17181920212223
24252627282930
31  
010203040506
07080910111213
14151617181920
21222324252627
282930  
 
01020304
05060708091011
12131415161718
19202122232425
262728293031  
 
01
02030405060708
09101112131415
16171819202122
23242526272829
30  
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
01020304050607
08091011121314
15161718192021
22232425262728
2930  
 
0102030405
06070809101112
13141516171819
20212223242526
2728293031  
 
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
01020304050607
08091011121314
15161718192021
22232425262728
293031  
 

Applicable years

Gregorian Calendar

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

Gregorian leap years starting on Tuesday[1]
Decade 1st2nd3rd4th5th6th7th8th9th10th
17th century 1608163616641692
18th century 1704173217601788
19th century 182818561884
20th century 192419521980
21st century 2008203620642092
22nd century 2104213221602188

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
Decade 1st2nd3rd4th5th6th7th8th9th10th
14th century 132013481376
15th century 1404143214601488
16th century 1516154415721600
17th century 162816561684
18th century 1712174017681796
19th century 182418521880
20th century 1908193619641992
21st century 202020482076
22nd century 2104213221602188

References

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