Common year starting on Tuesday

A common year starting on Tuesday is any non-leap year (i.e. a year with 365 days) that begins on Tuesday, 1 January, and ends on Tuesday, 31 December. Its dominical letter hence is F. The most recent year of such kind was 2019 and the next one will be 2030, or, likewise, 2014 and 2025 in the obsolete Julian calendar, see below for more. Any common year that starts on Sunday, Monday or Tuesday has two Friday the 13ths. This common year contains two Friday the 13ths in September and December. Leap years starting on Monday share this characteristic. From July of the year that precedes this year until September in this type of year is the longest period (14 months) that occurs without a Friday the 13th. Leap years starting on Saturday share this characteristic, from August of the common year that precedes it to October in that type of year. In this common year, U.S. Independence Day and Halloween are on a Thursday, Thanksgiving is on its latest possible date, November 28, and Christmas is on a Wednesday.

Calendars

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

0102030405
06070809101112
13141516171819
20212223242526
2728293031  
 
0102
03040506070809
10111213141516
17181920212223
2425262728
 
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  
 

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

010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
010203
04050607080910
11121314151617
18192021222324
25262728
 
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  
 
01020304
05060708091011
12131415161718
19202122232425
262728293031  
 
01
02030405060708
09101112131415
16171819202122
23242526272829
30  
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
010203
04050607080910
11121314151617
18192021222324
252627282930
 
01
02030405060708
09101112131415
16171819202122
23242526272829
3031  

Applicable years

Gregorian Calendar

In the (currently used) Gregorian calendar, along with Thursday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-four common years per cycle or exactly 11% start on a Tuesday. The 28-year sub-cycle does only span across century years divisible by 400, e.g. 1600, 2000, and 2400.

Gregorian common years starting on Tuesday[1]
Decade 1st2nd3rd4th5th6th7th8th9th10th
17th century 16021613161916301641164716581669167516861697
18th century 17091715172617371743175417651771178217931799
19th century 18051811182218331839185018611867187818891895
20th century 19011907191819291935194619571963197419851991
21st century 20022013201920302041204720582069207520862097
22nd century 21092115212621372143215421652171218221932199

Julian Calendar

In the now-obsolete Julian calendar, the fourteen types of year (seven common, seven leap) repeat in a 28-year cycle (1461 weeks). A leap year has two adjoining dominical letters (one for January and February and the other for March to December in the Church of England as 29 February has no letter). Each of the seven two-letter sequences occurs once within a cycle, and every common letter thrice.

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). Years 7, 18 and 24 of the cycle are common years beginning on Tuesday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Tuesday.

Julian common years starting on Tuesday
Decade 1st2nd3rd4th5th6th7th8th9th10th
15th century 14091415142614371443145414651471148214931499
16th century 1510152115271538154915551566157715831594
17th century 16051611162216331639165016611667167816891695
18th century 1706171717231734174517511762177317791790
19th century 18011807181818291835184618571863187418851891
20th century 19021913191919301941194719581969197519861997
21st century 20032014202520312042205320592070208120872098

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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