Leap year starting on Tuesday

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Template:Short description 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. The most recent year of such kind was 2008, and the next one will be 2036 in the Gregorian calendar<ref name="math">Template:Cite web</ref> or, likewise 2020 and 2048 in the obsolete Julian calendar.

Any leap year that starts on Tuesday has only one Friday the 13th; the only one in this leap year occurs in June. Common years starting on Wednesday share this characteristic.

Any leap year that starts on Tuesday has only one Tuesday the 13th: the only one in this leap year occurs in May.

Any leap year that starts on Tuesday has only one Friday the 17th: 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 17th.

This year has three months (March, June and November) which begin on a weekend-day.

Calendars

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Applicable years

Gregorian Calendar

Leap years that begin on Tuesday, along with those starting on Wednesday, occur at a rate of approximately 14.43% (14 out of 97) of all total leap years in a 400-year cycle of the Gregorian calendar. Thus, their overall occurrence is 3.5% (14 out of 400).

Gregorian leap years starting on Tuesday<ref name=math/>
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
23rd century 2228 2256 2284
24th century 2324 2352 2380
25th century 2408 2436 2464 2492
26th century 2504 2532 2560 2588
400-year cycle
0–99 8 36 64 92
100–199 104 132 160 188
200–299 228 256 284
300–399 324 352 380

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

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References

Template:Reflist Template:List of calendars