A348924 Paschal full moon dates expressed as days after March 21 (Gregorian calendar).
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, 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, 21, 10, 28, 18, 7, 26, 15, 4, 23, 12, 1, 20, 9, 27, 16, 5, 24, 13, 2
Offset: 0
Examples
For year 2021: n=2021, m=7, c=20, q=5, d=13. For the Julian calendar: a(m)=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. For the Gregorian calendar: x=7, a(n)=7, and s=7, so the GPFM is March 28 and Gregorian Easter Sunday is April 4, which corresponds to March 22 in the Julian calendar.
References
- Byron Lawrence Gurnette and Richard van der Riet Woolley, Explanatory Supplement to the Astronomical Ephemeris, H. M. Stationery Office, London, 1961, pages 420-429.
- Donald Ervin Knuth, The Art of Computer Programming, Stanford University, 1968. Volume 1, Chapter 1.3.2, Exercise #14.
- Thomas Hay O'Beirne, Puzzles and Paradoxes, Oxford University, London, 1965, Chapter 10, pages 168-184. Reprinted by Dover Publications, New York, 1984.
- Edward Graham Richards, Mapping Time, Oxford University, London, 1998. Part IV, especially pages 364, 375-376.
- Paul Kenneth Seidelmann and Leroy Elsworth Doggett, Explanatory Supplement to the Astronomical Almanac, Mill Valley, 1992, pages 581-582.
Links
- Anonymous, The Date of Easter, Nature, Vol. 13 (24 February 1876), pp. 326-327. Reproduces Gauss's Easter algorithm.
- Anonymous, To Find Easter, Nature, Vol. 13 (20 April 1876), p. 487. Still often cited.
- Christoph Clavius, Romani Kalendarii a Gregorio XIII P.M. Restituti Explicatio, Rome, 1603, 680 pages (in Latin).
- P. K. Seidelmann, Gregorian Calendar Ecclesiastical Rules, Explanatory Supplement 1992.
- Index entries for sequences related to calendars
Programs
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Mathematica
a[n_] := Module[{c = Floor[n/100], q = Floor[n/400], m = Mod[n, 19], x}, x = Mod[19*m + 15 + Floor[(c*17 + 11)/25 - q], 30]; If[(m > 10 && x == 28) || x == 29, x - 1, x]]; Array[a, 120, 0] (* Amiram Eldar, Nov 05 2021 *)
Formula
For both Julian and Gregorian calendars:
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 dates to convert to Gregorian
= days to subtract from Gregorian to convert to Julian
For the Julian calendar (repeats cycle a(0) through a(18):
a(m) = days from March 21 to the JPFM (0 to 28 days)
= (19*m+15) mod 30
s = days from JPFM to next Sunday (1 to 7 days)
= 7 - ((a(m)+floor(n*5/4)) mod 7)
Note that a(m) never equals 29, so Easter Sunday never falls on April 26.
For the Gregorian calendar (repeats cycle a(0) through a(5699999):
x = (19*m+15+floor((c*17+11)/25)-q) mod 30
a(n) = days from March 21 to the GPFM (0 to 28 days)
= x-1 if (x=29) or (x=28 and m>10)
= x otherwise
s = days from GPFM to next Sunday (0 to 7 days)
= 7 - ((a(n)+floor(n*5/4)-c+q+2) mod 7)
For compatibility with Julian calendar, Gregorian a(n) never equals 29.
Comments