leap year starting on Sunday

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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. The most recent year of such kind was 2012, and the next one will be 2040 in the Gregorian calendar{{cite web|url=https://webspace.science.uu.nl/~gent0113/calendar/isocalendar.htm |author=Robert van Gent |title=The Mathematics of the ISO 8601 Calendar |publisher=Utrecht University, Department of Mathematics |date=2017 |access-date=20 July 2017}} or, likewise 2024 and 2052 in the obsolete Julian calendar.

This is the only leap year with three occurrences of Friday the 13th: those three in this leap year occur three months (13 weeks) apart: in January, April, and July. Common years starting on Thursday share this characteristic, in the months of February, March, and November.

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 Monday is considered the first day of the week.

This year has five months (January, April, July, September and December) which begin on a weekend-day. This is the greatest possible number of months to begin on a weekend-day in a given year; this is the only kind of year in which this occurs.

Calendars

{{calendar|year=2012|show_year=off|title=Calendar for any leap year starting on Sunday,
presented as common in many English-speaking areas}}

{{calendar|year=2012|show_year=off|format=iso|row=3|zero=0|title=ISO 8601-conformant calendar with week numbers for
any leap year starting on Sunday (dominical letter AG)}}

Applicable years

=Gregorian Calendar=

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

class="wikitable"

|+ Gregorian leap years starting on Sunday

!scope=row| Decade

! 1st !! 2nd !! 3rd !! 4th !! 5th !! 6th !! 7th !! 8th !! 9th !! 10th

style="opacity: 0.5;"

! style="background-color:#efefef;" | 16th century

| colspan="8" | prior to first adoption (proleptic)

1584
17th century

|

|1612

|

|1640

|

|

|1668

|

|

|1696

style="background-color:#efefef;" | 18th century

| 1708 || || || 1736 || || || 1764 || || || 1792

style="background-color:#efefef;" | 19th century

| 1804 || || || 1832 || || 1860 || || || 1888 ||

style="background-color:#efefef;" | 20th century

| || || 1928 || || || 1956 || || || 1984 ||

style="background-color:#efefef;" | 21st century

| || 2012 || || 2040 || || || 2068 || || || 2096

style="background-color:#efefef;" | 22nd century

| 2108 || || || 2136 || || || 2164 || || || 2192

style="background-color:#efefef;" | 23rd century

| 2204 || || || 2232 || || 2260 || || || 2288 ||

style="background-color:#efefef;" | 24th century

| || || 2328 || || || 2356 || || || 2384 ||

style="background-color:#efefef;" | 25th century

| || 2412 || || 2440 || || || 2468 || || || 2496

style="background-color:#efefef;" | 26th century

| 2508 || || || 2536 || || || 2564 || || || 2592

style="background-color:#efefef;" | 27th century

| 2604 || || || 2632 || || 2660 || || || 2688 ||

class="wikitable"

|+ 400-year cycle

0–99

| 12 || 40 || 68 || 96

100–199

| 108 || 136 || 164 || 192

200–299

| 204 || 232 || 260 || 288

300–399

| 328 || 356 || 384 ||

=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, it will also repeat after 700 years, i.e., 25 cycles. The formula gives the year's position in the cycle ((year + 8) mod 28) + 1).

class="wikitable"

|+ Julian leap years starting on Sunday

!scope=row| Decade

! 1st !! 2nd !! 3rd !! 4th !! 5th !! 6th !! 7th !! 8th !! 9th !! 10th

style="background-color:#efefef;" | 15th century

| 1408 || || || 1436 || || || 1464 || || || 1492

style="background-color:#efefef;" | 16th century

| || 1520 || || || 1548 || || || 1576 || ||

style="background-color:#efefef;" | 17th century

| 1604 || || || 1632 || || 1660 || || || 1688 ||

style="background-color:#efefef;" | 18th century

| || 1716 || || || 1744 || || || 1772 || || 1800

style="background-color:#efefef;" | 19th century

| || || 1828 || || || 1856 || || || 1884 ||

style="background-color:#efefef;" | 20th century

| || 1912 || || 1940 || || || 1968 || || || 1996

style="background-color:#efefef;" | 21st century

| || || 2024 || || || 2052 || || 2080 || ||

style="background-color:#efefef;" | 22nd century

| 2108 || || || 2136 || || || 2164 || || || 2192

Holidays

= International =

= Roman Catholic Solemnities =

= Australia and New Zealand =

= British Isles =

= Canada =

= United States =

References

{{Commons category}}

{{Reflist}}

{{List of calendars}}

{{DEFAULTSORT:Leap Year Starting On Sunday}}

Category:Gregorian calendar

Category:Julian calendar

Category:Sunday