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Common year starting on Saturday

From Wikipedia, the free encyclopedia

Acommon year starting on Saturday is any non-leap year (i.e. a year with 365 days) that begins onSaturday, 1 January, and ends on Saturday, 31 December. Itsdominical letter hence isB. The most recent year of such kind was2022, and the next one will be2033 in the Gregorian calendar[1] or, likewise,2023 and2034 in the obsoleteJulian calendar. Seebelow for more.

Any common year that starts onSaturday has only oneFriday the 13th: the only one in this common yearoccurs in May.Leap years starting on Friday share this characteristic.

FromJuly of the year that precedes this year untilSeptember in this type of year is the longest period (14 months) that occurs without aTuesday the 13th.

This year has three months (January, May and October) which begin on a weekend-day.

Calendars

[edit]
Calendar for anycommon year starting on Saturday,
presented as common in many English-speaking areas
January
SuMoTuWeThFrSa
1
2345678
9101112131415
16171819202122
23242526272829
3031 
February
SuMoTuWeThFrSa
12345
6789101112
13141516171819
20212223242526
2728 
 
March
SuMoTuWeThFrSa
12345
6789101112
13141516171819
20212223242526
2728293031 
 
April
SuMoTuWeThFrSa
12
3456789
10111213141516
17181920212223
24252627282930
 
May
SuMoTuWeThFrSa
1234567
891011121314
15161718192021
22232425262728
293031 
 
June
SuMoTuWeThFrSa
1234
567891011
12131415161718
19202122232425
2627282930 
 
July
SuMoTuWeThFrSa
12
3456789
10111213141516
17181920212223
24252627282930
31 
August
SuMoTuWeThFrSa
123456
78910111213
14151617181920
21222324252627
28293031 
 
September
SuMoTuWeThFrSa
123
45678910
11121314151617
18192021222324
252627282930
 
October
SuMoTuWeThFrSa
1
2345678
9101112131415
16171819202122
23242526272829
3031 
November
SuMoTuWeThFrSa
12345
6789101112
13141516171819
20212223242526
27282930 
 
December
SuMoTuWeThFrSa
123
45678910
11121314151617
18192021222324
25262728293031
 
ISO 8601-conformant calendar withweek numbers for
any common year starting on Saturday (dominical letter B) preceded by acommon year starting on Friday (dominical letter C)
January
WkMoTuWeThFrSaSu
520102
0103040506070809
0210111213141516
0317181920212223
0424252627282930
0531 
February
WkMoTuWeThFrSaSu
05010203040506
0607080910111213
0714151617181920
0821222324252627
0928 
  
March
WkMoTuWeThFrSaSu
09010203040506
1007080910111213
1114151617181920
1221222324252627
1328293031 
  
April
WkMoTuWeThFrSaSu
13010203
1404050607080910
1511121314151617
1618192021222324
17252627282930
  
May
WkMoTuWeThFrSaSu
1701
1802030405060708
1909101112131415
2016171819202122
2123242526272829
223031 
June
WkMoTuWeThFrSaSu
220102030405
2306070809101112
2413141516171819
2520212223242526
2627282930 
  
July
WkMoTuWeThFrSaSu
26010203
2704050607080910
2811121314151617
2918192021222324
3025262728293031
  
August
WkMoTuWeThFrSaSu
3101020304050607
3208091011121314
3315161718192021
3422232425262728
35293031 
  
September
WkMoTuWeThFrSaSu
3501020304
3605060708091011
3712131415161718
3819202122232425
392627282930 
  
October
WkMoTuWeThFrSaSu
390102
4003040506070809
4110111213141516
4217181920212223
4324252627282930
4431 
November
WkMoTuWeThFrSaSu
44010203040506
4507080910111213
4614151617181920
4721222324252627
48282930 
  
December
WkMoTuWeThFrSaSu
4801020304
4905060708091011
5012131415161718
5119202122232425
52262728293031 
  
ISO 8601-conformant calendar withweek numbers for
any common year starting on Saturday (dominical letter B) preceded by aleap year starting on Thursday (dominical letter DC)
January
WkMoTuWeThFrSaSu
530102
0103040506070809
0210111213141516
0317181920212223
0424252627282930
0531 
February
WkMoTuWeThFrSaSu
05010203040506
0607080910111213
0714151617181920
0821222324252627
0928 
  
March
WkMoTuWeThFrSaSu
09010203040506
1007080910111213
1114151617181920
1221222324252627
1328293031 
  
April
WkMoTuWeThFrSaSu
13010203
1404050607080910
1511121314151617
1618192021222324
17252627282930
  
May
WkMoTuWeThFrSaSu
1701
1802030405060708
1909101112131415
2016171819202122
2123242526272829
223031 
June
WkMoTuWeThFrSaSu
220102030405
2306070809101112
2413141516171819
2520212223242526
2627282930 
  
July
WkMoTuWeThFrSaSu
26010203
2704050607080910
2811121314151617
2918192021222324
3025262728293031
  
August
WkMoTuWeThFrSaSu
3101020304050607
3208091011121314
3315161718192021
3422232425262728
35293031 
  
September
WkMoTuWeThFrSaSu
3501020304
3605060708091011
3712131415161718
3819202122232425
392627282930 
  
October
WkMoTuWeThFrSaSu
390102
4003040506070809
4110111213141516
4217181920212223
4324252627282930
4431 
November
WkMoTuWeThFrSaSu
44010203040506
4507080910111213
4614151617181920
4721222324252627
48282930 
  
December
WkMoTuWeThFrSaSu
4801020304
4905060708091011
5012131415161718
5119202122232425
52262728293031 
  

Applicable years

[edit]

Gregorian Calendar

[edit]

In the (currently used) Gregorian calendar, alongsideSunday,Monday,Wednesday orFriday, 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 Saturday. The 28-year sub-cycle will break at a century year which is not divisible by 400 (e.g. it broke at the year 1900 but not at the year 2000).

Gregorian common years starting on Saturday
1st2nd3rd4th5th6th7th8th9th10th
16th centuryprior to first adoption (proleptic)15831594
17th century16051611162216331639165016611667167816891695
18th century17011707171817291735174617571763177417851791
19th century1803181418251831184218531859-187018811898
20th century1910192119271938194919551966197719831994
21st century20052011202220332039205020612067207820892095
22nd century21012107211821292135214621572163217421852191
23rd century2203221422252231224222532259-227022812298
24th century2310232123272338234923552366237723832394
25th century24052411242224332439245024612467247824892495
400-year cycle
0–99511223339506167788995
100–199101107118129135146157163174185191
200–299203214225231242253259270281287298
300–399310321327338349355366377383394

Julian Calendar

[edit]

In the now-obsolete Julian calendar, the fourteen types of year (seven common, seven leap) repeat in a28-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 10, 16 and 27 of the cycle are common years beginning on Saturday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years starting on Saturday.

Julian common years starting on Saturday
Decade1st2nd3rd4th5th6th7th8th9th10th
15th century14011407141814291435144614571463147414851491
16th century15021513151915301541154715581569157515861597
17th century16031614162516311642165316591670168116871698
18th century17091715172617371743175417651771178217931799
19th century1810182118271838184918551866187718831894
20th century19051911192219331939195019611967197819891995
21st century2006201720232034204520512062207320792090

Holidays

[edit]

International

[edit]

Roman Catholic Solemnities

[edit]

Australia and New Zealand

[edit]

British Isles

[edit]

Canada

[edit]

Denmark

[edit]

Germany

[edit]

United States

[edit]

References

[edit]
  1. ^Robert van Gent (2017)."The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved20 July 2017.
Gregorian year types per leap cycle byDominical letter (DL) andDoomsday (DD)
Year startsCommon yearsLeap years
1 JanCountRatio31 DecDLDDCountRatio31 DecDLDDCountRatio
Sun5814.50 %SunATue4310.75 %MonAGWed153.75 %
Mon5614.00 %MonGWed4310.75 %TueGFThu133.25 %
Tue5814.50 %TueFThu4411.00 %WedFEFri143.50 %
Wed5714.25 %WedEFri4310.75 %ThuEDSat143.50 %
Thu5714.25 %ThuDSat4411.00 %FriDCSun133.25 %
Fri5814.50 %FriCSun4310.75 %SatCBMon153.75 %
Sat5614.00 %SatBMon4310.75 %SunBATue133.25 %
400100.0 %30375.75 %9724.25 %
Source:Robert van Gent (2017)."The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved20 July 2017.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Common_year_starting_on_Saturday&oldid=1310938309"
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