Common year starting on Friday

A common year starting on Friday is any non-leap year (i.e. a year with 365 days) that begins on Friday, 1 January, and ends on Friday, 31 December. Its dominical letter hence is C. The most recent year of such kind was 2010 and the next one will be 2021 in the Gregorian calendar,[1] or, likewise, 2011 and 2022 in the obsolete Julian calendar. The century year, 1700, was also a common year starting on Friday in the Gregorian calendar. See below for more. Any common year that starts on Wednesday, Friday or Saturday has only one Friday the 13th; the only Friday the 13th in this common year occurs in August. Leap years starting on Thursday share this characteristic, but also have another one in February.

Calendars

Calendar for any common year starting on Friday,
presented as common in many English-speaking areas – 2010

January
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31  
February
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
28  
 
March
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
April
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
252627282930
 
May
Su Mo Tu We Th Fr Sa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031  
June
Su Mo Tu We Th Fr Sa
0102030405
06070809101112
13141516171819
20212223242526
27282930  
 
July
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
August
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
293031  
 
September
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
2627282930  
 
October
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
31  
November
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
282930  
 
December
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
262728293031  
 

ISO 8601-conformant calendar with week numbers for
any common year starting on Friday (dominical letter C) – 2010

January
Wk Mo Tu We Th Fr Sa Su
53 010203
01 04050607080910
02 11121314151617
03 18192021222324
04 25262728293031
   
February
Wk Mo Tu We Th Fr Sa Su
05 01020304050607
06 08091011121314
07 15161718192021
08 22232425262728
 
   
March
Wk Mo Tu We Th Fr Sa Su
09 01020304050607
10 08091011121314
11 15161718192021
12 22232425262728
13 293031  
   
April
Wk Mo Tu We Th Fr Sa Su
13 01020304
14 05060708091011
15 12131415161718
16 19202122232425
17 2627282930  
   
May
Wk Mo Tu We Th Fr Sa Su
17 0102
18 03040506070809
19 10111213141516
20 17181920212223
21 24252627282930
22 31  
June
Wk Mo Tu We Th Fr Sa Su
22 010203040506
23 07080910111213
24 14151617181920
25 21222324252627
26 282930  
   
July
Wk Mo Tu We Th Fr Sa Su
26 01020304
27 05060708091011
28 12131415161718
29 19202122232425
30 262728293031  
   
August
Wk Mo Tu We Th Fr Sa Su
30 01
31 02030405060708
32 09101112131415
33 16171819202122
34 23242526272829
35 3031  
September
Wk Mo Tu We Th Fr Sa Su
35 0102030405
36 06070809101112
37 13141516171819
38 20212223242526
39 27282930  
   
October
Wk Mo Tu We Th Fr Sa Su
39 010203
40 04050607080910
41 11121314151617
42 18192021222324
43 25262728293031
   
November
Wk Mo Tu We Th Fr Sa Su
44 01020304050607
45 08091011121314
46 15161718192021
47 22232425262728
48 2930  
   
December
Wk Mo Tu We Th Fr Sa Su
48 0102030405
49 06070809101112
50 13141516171819
51 20212223242526
52 2728293031  
   

This is the only year type where the nth "Doomsday" (this year Sunday) is not in ISO week n; it is in ISO week n-1.

Applicable years

Gregorian Calendar

In the (currently used) Gregorian calendar, alongside Sunday, Monday, Wednesday 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 Friday. 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 Friday[1]
Decade 1st2nd3rd4th5th6th7th8th9th10th
16th century prior to first adoption (proleptic)15931599
17th century 1610—1621162716381649165516661677168316941700
18th century 1706171717231734174517511762177317791790—
19th century 1802181318191830—1841184718581869187518861897
20th century 19091915192619371943195419651971198219931999
21st century 2010—2021202720382049205520662077208320942100

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 4, 15 and 26 of the cycle are common years beginning on Friday. 2017 is year 10 of the cycle. Approximately 10.71% of all years are common years beginning on Friday.

Julian common years starting on Friday
Decade 1st2nd3rd4th5th6th7th8th9th10th
15th century 1406141714231434144514511462147314791490—
16th century 15011507151815291535154615571563157415851591
17th century 1602161316191630—1641164716581669167516861697
18th century 17031714172517311742175317591770—178117871798
19th century 18091815182618371843185418651871188218931899
20th century 1910—192119271938194919551966197719831994
21st century 200520112022203320392050—20612067207820892095
gollark: I think they're overused and not actually very good synchronization primitives. Please explain how you would use them.
gollark: Really? Hmm. Explain.
gollark: And it mutates some shared state.
gollark: As you can see, it has to explicitly manage a "waitgroup" for synchronization and whatnot.
gollark: ```go log.Println("Fetching feeds...") var feeds []*rss.Feed var wg sync.WaitGroup for _, source := range sources { wg.Add(1) src := source go func() { defer wg.Done() feed, err := rss.Fetch(src.String()) if err != nil { log.Printf("Error fetching %s: %s", src.String(), err.Error()) return } feeds = append(feeds, feed) log.Printf("Fetched %s", feed.Title) }() } wg.Wait()```So here is something which is meant to fetch a bunch of RSS feeds in parallel.

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