Common year starting on Sunday

A common year starting on Sunday is any non-leap year (i.e. a year with 365 days) that begins on Sunday, 1 January, and ends on Sunday, 31 December. Its dominical letter hence is A. The most recent year of such kind was 2017 and the next one will be 2023 in the Gregorian calendar,[1] or, likewise, 2018 and 2029 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 January and October. In this common year, U.S. Independence Day and Halloween are on a Tuesday, Thanksgiving is on November 23, and Christmas is on a Monday.

Calendars

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

01020304050607
08091011121314
15161718192021
22232425262728
293031  
 
01020304
05060708091011
12131415161718
19202122232425
262728  
 
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  
0102030405
06070809101112
13141516171819
20212223242526
2728293031  
 
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
01020304050607
08091011121314
15161718192021
22232425262728
293031  
 
01020304
05060708091011
12131415161718
19202122232425
2627282930  
 
0102
03040506070809
10111213141516
17181920212223
24252627282930
31  

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

01
02030405060708
09101112131415
16171819202122
23242526272829
3031  
0102030405
06070809101112
13141516171819
20212223242526
2728  
 
0102030405
06070809101112
13141516171819
20212223242526
2728293031  
 
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
01020304050607
08091011121314
15161718192021
22232425262728
293031  
 
01020304
05060708091011
12131415161718
19202122232425
2627282930  
 
0102
03040506070809
10111213141516
17181920212223
24252627282930
31  
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
010203
04050607080910
11121314151617
18192021222324
252627282930
 
01
02030405060708
09101112131415
16171819202122
23242526272829
3031  
0102030405
06070809101112
13141516171819
20212223242526
27282930  
 
010203
04050607080910
11121314151617
18192021222324
25262728293031
 

Applicable years

Gregorian Calendar

In the (currently used) Gregorian calendar, alongside Monday, Wednesday, Friday or Saturday, the fourteen types of year (seven common, seven leap) repeat in a 400-year cycle (20871 weeks). Forty-three common years per cycle or exactly 10.75% start on a Sunday. 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 Sunday[1]
Decade 1st2nd3rd4th5th6th7th8th9th10th
16th century prior to first adoption (proleptic)15891595
17th century 1606161716231634164516511662167316791690
18th century 17021713171917301741174717581769177517861797
19th century 18091815182618371843185418651871188218931899
20th century 19051911192219331939195019611967197819891995
21st century 2006201720232034204520512062207320792090
22nd century 21022113211921302141214721582169217521862197
23rd century 22092215222622372243225422652271228222932299

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, as 29 February has no letter). This sequence occurs exactly 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 11, 22 and 28 of the cycle are common years beginning on Sunday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Sunday.

Julian common years starting on Sunday
Decade 1st2nd3rd4th5th6th7th8th9th10th
15th century 14021413141914301441144714581469147514861497
16th century 15031514152515131542155315591570158115871598
17th century 16091615162616371643165416651671168216931699
18th century 1710172117271738174917551766177717831794
19th century 18051811182218331839185018611867187818891895
20th century 1906191719231934194519511962197319791990
21st century 20012007201820292035204620572063207420852091

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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