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A349710
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Paschal full moon dates expressed as days after March 21 (Julian calendar).
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1
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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
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OFFSET
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0,1
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COMMENTS
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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.
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REFERENCES
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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.
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LINKS
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FORMULA
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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.
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EXAMPLE
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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.
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MATHEMATICA
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a[n_] := Mod[19 * Mod[n, 19] + 15, 30]; Array[a, 100, 0] (* Amiram Eldar, Jan 05 2022 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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