From Wikipedia, the free encyclopedia
A leap year starting on Saturday is any year with 366 days (i.e. it includes 29 February) that begins on Saturday , 1 January, and ends on Sunday , 31 December. Its dominical letters hence are BA . The most recent year of such kind was 2000 and the next one will be 2028 in the Gregorian calendar or, likewise 2012 and 2040 in the obsolescent Julian calendar . In the Gregorian calendar , years divisible by 400 are always leap years starting on Saturday. The most recent such occurrence was 2000 and the next one will be 2400 , see below for more .[ 1]
Any leap year that starts on Tuesday , Friday or Saturday has only one Friday the 13th : the only one in this leap year occurs in October . From August of the common year preceding that 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.
This is the only type of year in which all dates (except 29 February) fall on their respective weekdays the minimal 56 times in the 400 year Gregorian Calendar cycle. Additionally, these types of years are the only ones which contain 54 different calendar weeks (2 partial, 52 in full) in areas of the world where Sunday is considered the first day of the week, and also the only type of year to contain 53 Saturdays and Sundays.
Calendar for any leap year starting on Saturday, presented as common in many English-speaking areas
January
Su
Mo
Tu
We
Th
Fr
Sa
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
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
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
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
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
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
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
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
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
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
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
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
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
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
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
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
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
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
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
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
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
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
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0 9
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
Leap years that begin on Saturday, along with those starting on Monday and 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).
400-year cycle
0–99
0
28
56
84
100–199
124
152
180
200–299
220
248
276
300–399
316
344
372
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
0 3.75 %
Sat
56
14.00 %
Sat
B
Mon
43
10.75 %
Sun
BA
Tue
13
0 3.25 %
Fri
58
14.50 %
Fri
C
Sun
43
10.75 %
Sat
CB
Mon
15
0 3.75 %
Thu
57
14.25 %
Thu
D
Sat
44
11.00 %
Fri
DC
Sun
13
0 3.25 %
Wed
57
14.25 %
Wed
E
Fri
43
10.75 %
Thu
ED
Sat
14
0 3.50 %
Tue
58
14.50 %
Tue
F
Thu
44
11.00 %
Wed
FE
Fri
14
0 3.50 %
Mon
56
14.00 %
Mon
G
Wed
43
10.75 %
Tue
GF
Thu
13
0 3.25 %
∑
400
100.0 %
303
75.75 %
97
24.25 %
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).
Roman Catholic Solemnities [ edit ]
Australia and New Zealand [ edit ]
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
0 3.75 %
Sat
56
14.00 %
Sat
B
Mon
43
10.75 %
Sun
BA
Tue
13
0 3.25 %
Fri
58
14.50 %
Fri
C
Sun
43
10.75 %
Sat
CB
Mon
15
0 3.75 %
Thu
57
14.25 %
Thu
D
Sat
44
11.00 %
Fri
DC
Sun
13
0 3.25 %
Wed
57
14.25 %
Wed
E
Fri
43
10.75 %
Thu
ED
Sat
14
0 3.50 %
Tue
58
14.50 %
Tue
F
Thu
44
11.00 %
Wed
FE
Fri
14
0 3.50 %
Mon
56
14.00 %
Mon
G
Wed
43
10.75 %
Tue
GF
Thu
13
0 3.25 %
∑
400
100.0 %
303
75.75 %
97
24.25 %