Leap year starting on Sunday

A leap year starting on Sunday is any year with 366 days (i.e. it includes 29 February) that begins on Sunday, 1 January, and ends on Monday, 31 December. Its dominical letters hence are AG, such as the years 1888, 1928, 1956, 1984, 2012, 2040, 2068, 2096, 2108, 2136, 2164, and 2192 in the Gregorian calendar[1] or, likewise, 1996 and 2024 in the obsolete Julian calendar.

This leap year uniquely has the most occurrences of Friday the 13th. Any common year starting on Thursday shares this characteristic. The instances of Friday the 13th are three months (13 weeks) apart: in January, April, and July.

Calendars

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

January
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
293031  
 
February
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
26272829  
 
March
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
25262728293031
 
April
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
2930  
 
May
Su Mo Tu We Th Fr Sa
0102030405
06070809101112
13141516171819
20212223242526
2728293031  
 
June
Su Mo Tu We Th Fr Sa
0102
03040506070809
10111213141516
17181920212223
24252627282930
 
July
Su Mo Tu We Th Fr Sa
01020304050607
08091011121314
15161718192021
22232425262728
293031  
 
August
Su Mo Tu We Th Fr Sa
01020304
05060708091011
12131415161718
19202122232425
262728293031  
 
September
Su Mo Tu We Th Fr Sa
01
02030405060708
09101112131415
16171819202122
23242526272829
30  
October
Su Mo Tu We Th Fr Sa
010203040506
07080910111213
14151617181920
21222324252627
28293031  
 
November
Su Mo Tu We Th Fr Sa
010203
04050607080910
11121314151617
18192021222324
252627282930
 
December
Su Mo Tu We Th Fr Sa
01
02030405060708
09101112131415
16171819202122
23242526272829
3031  

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

January
Wk Mo Tu We Th Fr Sa Su
52 01
01 02030405060708
02 09101112131415
03 16171819202122
04 23242526272829
05 3031  
February
Wk Mo Tu We Th Fr Sa Su
05 0102030405
06 06070809101112
07 13141516171819
08 20212223242526
09 272829  
   
March
Wk Mo Tu We Th Fr Sa Su
09 01020304
10 05060708091011
11 12131415161718
12 19202122232425
13 262728293031  
   
April
Wk Mo Tu We Th Fr Sa Su
13 01
14 02030405060708
15 09101112131415
16 16171819202122
17 23242526272829
18 30  
May
Wk Mo Tu We Th Fr Sa Su
18 010203040506
19 07080910111213
20 14151617181920
21 21222324252627
22 28293031  
   
June
Wk Mo Tu We Th Fr Sa Su
22 010203
23 04050607080910
24 11121314151617
25 18192021222324
26 252627282930
   
July
Wk Mo Tu We Th Fr Sa Su
26 01
27 02030405060708
28 09101112131415
29 16171819202122
30 23242526272829
31 3031  
August
Wk Mo Tu We Th Fr Sa Su
31 0102030405
32 06070809101112
33 13141516171819
34 20212223242526
35 2728293031  
   
September
Wk Mo Tu We Th Fr Sa Su
35 0102
36 03040506070809
37 10111213141516
38 17181920212223
39 24252627282930
   
October
Wk Mo Tu We Th Fr Sa Su
40 01020304050607
41 08091011121314
42 15161718192021
43 22232425262728
44 293031  
   
November
Wk Mo Tu We Th Fr Sa Su
44 01020304
45 05060708091011
46 12131415161718
47 19202122232425
48 2627282930  
   
December
Wk Mo Tu We Th Fr Sa Su
48 0102
49 03040506070809
50 10111213141516
51 17181920212223
52 24252627282930
01 31  

Applicable years

Gregorian Calendar

Leap years that begin on Sunday, along with those that start on Friday, occur most frequently: 15 out of the 97 (≈ 15.46%) total leap years in a 400-year cycle of the Gregorian calendar. Thus, the overall occurrence is 3.75% (15 out of 400).

Gregorian leap years starting on Sunday[1]
Decade 1st2nd3rd4th5th6th7th8th9th10th
17th century 1612164016681696
18th century 1708173617641792
19th century 1804183218601888
20th century 192819561984
21st century 2012204020682096
22nd century 2108213621642192

Julian Calendar

Like all leap year types, the one starting with 1 January on a Sunday 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 Sunday
Decade 1st2nd3rd4th5th6th7th8th9th10th
15th century 1408143614641492
16th century 152015481576
17th century 1604163216601688
18th century 1716174417721800
19th century 182818561884
20th century 1912194019681996
21st century 202420522080
22nd century 2108213621642192
gollark: Thanks for the free OpenWeatherMap API key!
gollark: Apparently there's an OpenCL implementation for the Pi 3.
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gollark: https://news.sophos.com/en-us/2021/07/22/malware-increasingly-targets-discord-for-abuse/

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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