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 October. Common years starting on Sunday share this characteristic, but also have another in January. From August of the year that precedes this year until October in this type of year is also the longest period (14 months) that occurs without a Friday the 13th. Common years starting on Tuesday share this characteristic, from July of the year that precedes it to September in that type of year. There are two other ways this 14 month interval can be formed, one involving a common year followed by a leap year and the other a leap year followed by a common year.
Calendars
Calendar for any leap year starting on Saturday, 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 Saturday (dominical letter BA)
January
Wk
Mo
Tu
We
Th
Fr
Sa
Su
52
01
02
01
03
04
05
06
07
08
09
02
10
11
12
13
14
15
16
03
17
18
19
20
21
22
23
04
24
25
26
27
28
29
30
05
31
February
Wk
Mo
Tu
We
Th
Fr
Sa
Su
05
01
02
03
04
05
06
06
07
08
09
10
11
12
13
07
14
15
16
17
18
19
20
08
21
22
23
24
25
26
27
09
28
29
March
Wk
Mo
Tu
We
Th
Fr
Sa
Su
09
01
02
03
04
05
10
06
07
08
09
10
11
12
11
13
14
15
16
17
18
19
12
20
21
22
23
24
25
26
13
27
28
29
30
31
April
Wk
Mo
Tu
We
Th
Fr
Sa
Su
13
01
02
14
03
04
05
06
07
08
09
15
10
11
12
13
14
15
16
16
17
18
19
20
21
22
23
17
24
25
26
27
28
29
30
May
Wk
Mo
Tu
We
Th
Fr
Sa
Su
18
01
02
03
04
05
06
07
19
08
09
10
11
12
13
14
20
15
16
17
18
19
20
21
21
22
23
24
25
26
27
28
22
29
30
31
June
Wk
Mo
Tu
We
Th
Fr
Sa
Su
22
01
02
03
04
23
05
06
07
08
09
10
11
24
12
13
14
15
16
17
18
25
19
20
21
22
23
24
25
26
26
27
28
29
30
July
Wk
Mo
Tu
We
Th
Fr
Sa
Su
26
01
02
27
03
04
05
06
07
08
09
28
10
11
12
13
14
15
16
29
17
18
19
20
21
22
23
30
24
25
26
27
28
29
30
31
31
August
Wk
Mo
Tu
We
Th
Fr
Sa
Su
31
01
02
03
04
05
06
32
07
08
09
10
11
12
13
33
14
15
16
17
18
19
20
34
21
22
23
24
25
26
27
35
28
29
30
31
September
Wk
Mo
Tu
We
Th
Fr
Sa
Su
35
01
02
03
36
04
05
06
07
08
09
10
37
11
12
13
14
15
16
17
38
18
19
20
21
22
23
24
39
25
26
27
28
29
30
October
Wk
Mo
Tu
We
Th
Fr
Sa
Su
39
01
40
02
03
04
05
06
07
08
41
09
10
11
12
13
14
15
42
16
17
18
19
20
21
22
43
23
24
25
26
27
28
29
44
30
31
November
Wk
Mo
Tu
We
Th
Fr
Sa
Su
44
01
02
03
04
05
45
06
07
08
09
10
11
12
46
13
14
15
16
17
18
19
47
20
21
22
23
24
25
26
48
27
28
29
30
December
Wk
Mo
Tu
We
Th
Fr
Sa
Su
48
01
02
03
49
04
05
06
07
08
09
10
50
11
12
13
14
15
16
17
51
18
19
20
21
22
23
24
52
25
26
27
28
29
30
31
Applicable years
Gregorian Calendar
Leap years that begin on Saturday, along with those that start on Monday or Thursday, occur least frequently: 13 out of 97 (≈ 13.402%) total leap years in a 400-year cycle of the Gregorian calendar. Their overall occurrence is thus 3.25% (13 out of 400).
Like all leap year types, the one starting with 1 January on a Saturday 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).