cp's OEIS Frontend

A349710 Paschal full moon dates expressed as days after March 21 (Julian calendar).

%I A349710 #58 Jan 27 2025 17:52:32
%S A349710 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,
%T A349710 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,
%U A349710 11,0,19,8,27,15,4,23,12,1,20,9,28,17,6,25,14,3,22,11,0,19,8
%N A349710 Paschal full moon dates expressed as days after March 21 (Julian calendar).
%C A349710 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.
%D A349710 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.
%D A349710 Edward Graham Richards, Mapping Time, Oxford University, London, 1998. Part IV, especially page 364.
%H A349710 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F A349710 n = calendar year (4 digits)
%F A349710 m = n mod 19 = position of n in the 19-year Metonic Lunar cycle
%F A349710 c = floor(n/100) = calendar century
%F A349710 q = floor(n/400) = calendar quad-century
%F A349710 d = c-q+2 = days to add to Julian calendar dates to convert to Gregorian
%F A349710 a(n) = days from March 21 to the JPFM (0 to 28 days)
%F A349710      = (19*m+15) mod 30
%F A349710 s = days from JPFM to next (Easter) Sunday (1 to 7 days)
%F A349710   = 7 - ((a(n)+floor(n*5/4)) mod 7)
%F A349710 Note that a(n) never equals 29, so Easter Sunday never falls on April 26.
%e A349710 For year 2021: n = 2021, m = 7, c = 20, q = 5, d = 13.
%e A349710 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.
%t A349710 a[n_] := Mod[19 * Mod[n, 19] + 15, 30]; Array[a, 100, 0] (* _Amiram Eldar_, Jan 05 2022 *)
%Y A349710 Cf. A348924.
%K A349710 easy,nonn
%O A349710 0,1
%A A349710 _Robert B Fowler_, Jan 05 2022