A224110 Easter occurrences on March 22, March 23, ..., April 25 during a 5,700,000-year Gregorian Easter cycle.

27550, 54150, 81225, 110200, 133000, 165300, 186200, 192850, 189525, 189525, 192850, 186200, 192850, 186200, 192850, 189525, 189525, 192850, 186200, 192850, 186200, 192850, 189525, 189525, 192850, 186200, 192850, 197400, 220400, 189525, 162450, 137750, 106400, 82650, 42000

Offset: 1

Author

Rick L. Shepherd, Mar 31 2013

Keywords

• nonn
• fini
• full

Comments

For the Gregorian calendar, the most common Easter Sunday date is the 19th of April and the least common is the 22nd of March with frequencies 3.867% and 0.483%. Among these 35 possible Easter dates there are only 16 distinct frequencies as there are sets of 6, 7, and 9 dates with equal frequencies for each date within the set (the larger the set the larger the frequency for each individual date).

The 16 distinct a(n) frequencies share many common factors. All are multiples of 25. All are multiples of either 56, 57, or 58. Except for a(28) and a(35), all are multiples of 19 (but the sum a(28)+a(35) is a multiple of 19). - Robert B Fowler, Jul 28 2024

Examples

			In an entire Gregorian Easter cycle, Easter Sunday occurs on March 22 exactly a(1) = 27550 times, so the frequency of occurrence of Easter on March 22 over the entire cycle is calculated simply as 27550/5700000 = 0.0048333..., rounding to 0.483%.  (Of course, these frequencies can vary within more-limited time periods.)  The van Gent link displays these frequencies as percentages and contains similar information for the Julian calendar.
The van Gent link does not currently contain these frequencies. The 35 a(n) values have been verified using A348924 for years 1 AD through 5700000 AD. - _Robert B Fowler_, Jul 28 2024
		

Links

• R. H. van Gent, Frequency of Easter Sundays. This link currently does not contain the actual frequencies, nor any algorithms to derive them; see A348924 below. - _Robert B Fowler_, Jul 28 2024
• Ch. Zeller, Problema duplex calendarii fundamentale, Bulletin de la S. M. F., tome 11 (1883), pp. 59-61.

Crossrefs

Cf. A348924 (algorithms for Paschal Full Moon and Easter Sunday in both Julian and Gregorian Calendars). - Robert B Fowler, Jul 28 2024

Cf. A375027 (frequencies for Julian Easter dates). - Robert B Fowler, Jul 29 2024

Formula

See the FORMULA at A348924.