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A349710
Paschal full moon dates expressed as days after March 21 (Julian calendar).
2
15, 4, 23, 12, 1, 20, 9, 28, 17, 6, 25, 14, 3, 22, 11, 0, 19, 8, 27, 15, 4, 23, 12, 1, 20, 9, 28, 17, 6, 25, 14, 3, 22, 11, 0, 19, 8, 27, 15, 4, 23, 12, 1, 20, 9, 28, 17, 6, 25, 14, 3, 22, 11, 0, 19, 8, 27, 15, 4, 23, 12, 1, 20, 9, 28, 17, 6, 25, 14, 3, 22, 11, 0, 19, 8
OFFSET
0,1
COMMENTS
The date of the Julian Paschal (Ecclesiastical) Full Moon (JPFM) in year n is a(n) days after March 21. Julian Easter Sunday is the first Sunday after (never on) the JPFM. The complete JPFM cycle is a repeating sequence of 19 terms, a(0) through a(18). The year 0 AD (conventionally denoted as 1 BC) is used as a starting point for a(0) solely as a computational convenience. The complete Julian Easter Sunday cycle is 19*4*7 = 532 years. For details on Easter and the Paschal Full Moon, in both Julian and Gregorian calendars, see A348924.
REFERENCES
Byron Lawrence Gurnette and Richard van der Riet Woolley, Explanatory Supplement to the Astronomical Ephemeris, H. M. Stationery Office, London, 1961. Pages 420-422. The 1992 edition omits Julian Easter calculation.
Edward Graham Richards, Mapping Time, Oxford University, London, 1998. Part IV, especially page 364.
FORMULA
n = calendar year (4 digits)
m = n mod 19 = position of n in the 19-year Metonic Lunar cycle
c = floor(n/100) = calendar century
q = floor(n/400) = calendar quad-century
d = c-q+2 = days to add to Julian calendar dates to convert to Gregorian
a(n) = days from March 21 to the JPFM (0 to 28 days)
= (19*m+15) mod 30
s = days from JPFM to next (Easter) Sunday (1 to 7 days)
= 7 - ((a(n)+floor(n*5/4)) mod 7)
Note that a(n) never equals 29, so Easter Sunday never falls on April 26.
EXAMPLE
For year 2021: n = 2021, m = 7, c = 20, q = 5, d = 13.
a(n) = 28 and s = 1, so the JPFM is April 18 and Julian Easter Sunday is April 19, which corresponds to May 2 in the Gregorian calendar.
MATHEMATICA
a[n_] := Mod[19 * Mod[n, 19] + 15, 30]; Array[a, 100, 0] (* Amiram Eldar, Jan 05 2022 *)
CROSSREFS
Cf. A348924.
Sequence in context: A330361 A291157 A040216 * A348924 A278872 A278900
KEYWORD
easy,nonn
AUTHOR
Robert B Fowler, Jan 05 2022
STATUS
approved