A leap year starting on Tuesday is any year with 366 days (i.e. it includes 29 February) that begins on Tuesday, 1 January, and ends on Wednesday, 31 December. Its dominical letters hence are FE, such as the years 1884, 1924, 1952, 1980, 2008, 2036, 2064, 2092, and 2104 in the Gregorian calendar[1] or, likewise, 1964, 1992, and 2020 in the obsolete Julian calendar. Any leap year that starts on Tuesday, Friday or Saturday has only one Friday the 13th; The only Friday the 13th in this leap year occurs in June. Common years starting on Wednesday share this characteristic.
Contents
1Calendars
2Applicable years
2.1Gregorian Calendar
2.2Julian Calendar
3References
Calendars
Calendar for any leap year starting on Tuesday, presented as common in many English-speaking areas
January
Su
Mo
Tu
We
Th
Fr
Sa
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
February
Su
Mo
Tu
We
Th
Fr
Sa
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
March
Su
Mo
Tu
We
Th
Fr
Sa
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
April
Su
Mo
Tu
We
Th
Fr
Sa
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
May
Su
Mo
Tu
We
Th
Fr
Sa
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
June
Su
Mo
Tu
We
Th
Fr
Sa
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
July
Su
Mo
Tu
We
Th
Fr
Sa
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
August
Su
Mo
Tu
We
Th
Fr
Sa
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
September
Su
Mo
Tu
We
Th
Fr
Sa
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
October
Su
Mo
Tu
We
Th
Fr
Sa
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
November
Su
Mo
Tu
We
Th
Fr
Sa
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
December
Su
Mo
Tu
We
Th
Fr
Sa
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
ISO 8601-conformant calendar with week numbers for any leap year starting on Tuesday (dominical letter FE)
January
Wk
Mo
Tu
We
Th
Fr
Sa
Su
01
01
02
03
04
05
06
02
07
08
09
10
11
12
13
03
14
15
16
17
18
19
20
04
21
22
23
24
25
26
27
05
28
29
30
31
April
Wk
Mo
Tu
We
Th
Fr
Sa
Su
14
01
02
03
04
05
06
15
07
08
09
10
11
12
13
16
14
15
16
17
18
19
20
17
21
22
23
24
25
26
27
18
28
29
30
July
Wk
Mo
Tu
We
Th
Fr
Sa
Su
27
01
02
03
04
05
06
28
07
08
09
10
11
12
13
29
14
15
16
17
18
19
20
30
21
22
23
24
25
26
27
31
28
29
30
31
October
Wk
Mo
Tu
We
Th
Fr
Sa
Su
40
01
02
03
04
05
41
06
07
08
09
10
11
12
42
13
14
15
16
17
18
19
43
20
21
22
23
24
25
26
44
27
28
29
30
31
February
Wk
Mo
Tu
We
Th
Fr
Sa
Su
05
01
02
03
06
04
05
06
07
08
09
10
07
11
12
13
14
15
16
17
08
18
19
20
21
22
23
24
09
25
26
27
28
29
May
Wk
Mo
Tu
We
Th
Fr
Sa
Su
18
01
02
03
04
19
05
06
07
08
09
10
11
20
12
13
14
15
16
17
18
21
19
20
21
22
23
24
25
22
26
27
28
29
30
31
August
Wk
Mo
Tu
We
Th
Fr
Sa
Su
31
01
02
03
32
04
05
06
07
08
09
10
33
11
12
13
14
15
16
17
34
18
19
20
21
22
23
24
35
25
26
27
28
29
30
31
November
Wk
Mo
Tu
We
Th
Fr
Sa
Su
44
01
02
45
03
04
05
06
07
08
09
46
10
11
12
13
14
15
16
47
17
18
19
20
21
22
23
48
24
25
26
27
28
29
30
March
Wk
Mo
Tu
We
Th
Fr
Sa
Su
09
01
02
10
03
04
05
06
07
08
09
11
10
11
12
13
14
15
16
12
17
18
19
20
21
22
23
13
24
25
26
27
28
29
30
14
31
June
Wk
Mo
Tu
We
Th
Fr
Sa
Su
22
01
23
02
03
04
05
06
07
08
24
09
10
11
12
13
14
15
25
16
17
18
19
20
21
22
26
23
24
25
26
27
28
29
27
30
September
Wk
Mo
Tu
We
Th
Fr
Sa
Su
36
01
02
03
04
05
06
07
37
08
09
10
11
12
13
14
38
15
16
17
18
19
20
21
39
22
23
24
25
26
27
28
40
29
30
December
Wk
Mo
Tu
We
Th
Fr
Sa
Su
49
01
02
03
04
05
06
07
50
08
09
10
11
12
13
14
51
15
16
17
18
19
20
21
52
22
23
24
25
26
27
28
01
29
30
31
Applicable years
Gregorian Calendar
Leap years that begin on Tuesday, like those that start on Wednesday, occur at a rate of approximately 14.4% of all total leap years in a 400-year cycle of the Gregorian calendar. Their overall occurrence is 3.5% (14 out of 400).
Gregorian leap years starting on Tuesday[1]
Decade
1st
2nd
3rd
4th
5th
6th
7th
8th
9th
10th
17th century
1608
1636
1664
1692
18th century
1704
1732
1760
1788
19th century
1828
1856
1884
20th century
1924
1952
1980
21st century
2008
2036
2064
2092
22nd century
2104
2132
2160
2188
Gregorian year types per leap cycle by Dominical letter (DL)[1] and Doomsday (DD)
Year starts
Common years
Leap years
1 Jan
Count
Ratio
31 Dec
DL
DD
Count
Ratio
31 Dec
DL
DD
Count
Ratio
Sun
58
14.50 %
Sun
A
Tue
43
10.75 %
Mon
AG
Wed
15
03.75 %
Sat
56
14.00 %
Sat
B
Mon
43
10.75 %
Sun
BA
Tue
13
03.25 %
Fri
58
14.50 %
Fri
C
Sun
43
10.75 %
Sat
CB
Mon
15
03.75 %
Thu
57
14.25 %
Thu
D
Sat
44
11.00 %
Fri
DC
Sun
13
03.25 %
Wed
57
14.25 %
Wed
E
Fri
43
10.75 %
Thu
ED
Sat
14
03.50 %
Tue
58
14.50 %
Tue
F
Thu
44
11.00 %
Wed
FE
Fri
14
03.50 %
Mon
56
14.00 %
Mon
G
Wed
43
10.75 %
Tue
GF
Thu
13
03.25 %
∑
400
100.0 %
303
75.75 %
97
24.25 %
Julian Calendar
Like all leap year types, the one starting with 1 January on a Tuesday 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 Tuesday
Decade
1st
2nd
3rd
4th
5th
6th
7th
8th
9th
10th
14th century
1320
1348
1376
15th century
1404
1432
1460
1488
16th century
1516
1544
1572
1600
17th century
1628
1656
1684
18th century
1712
1740
1768
1796
19th century
1824
1852
1880
20th century
1908
1936
1964
1992
21st century
2020
2048
2076
22nd century
2104
2132
2160
2188
References
^ abcRobert van Gent (2017). "The Mathematics of the ISO 8601 Calendar". Utrecht University, Department of Mathematics. Retrieved 20 July 2017..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"""""""'""'"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}
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