A104019 Years in the Gregorian calendar for which Easter falls on the 25th day of the month.

1663, 1666, 1674, 1731, 1734, 1742, 1883, 1886, 1894, 1943, 1951, 2035, 2038, 2046, 2103, 2187, 2190, 2198, 2255, 2258, 2266, 2323, 2326, 2334, 2407, 2410, 2418, 2491, 2559, 2570, 2573, 2581, 2627, 2630, 2638, 2779, 2782, 2790, 2874, 2877, 2885, 2931

Offset

1,1

Comments

The starting point for the sequence is explained by the fact that the Gregorian calendar was only introduced in 1582.

The complete Easter cycle lasts 5700000 years. In this cycle, Mar 25 occurs 110200 times and Apr 25 occurs 42000 times for a total of 152200 times. This reduces to 761 occurrences every 28500 years (~2.67%). - Hans Havermann, Jan 27 2008

Links

Table of n, a(n) for n=1..42.

Holger Oertel, Calculation of Easter. [Via Wayback Machine]

M. Montes, Frequency of the Date of Easter over one complete Gregorian Easter Cycle.

Index entries for sequences related to calendars

Formula

The formula is based on the algorithm of Oudin (1940) taken from the link.

Mathematica

(* first do *) Needs["Miscellaneous`Calendar`"] (* then *) Select[ Range[1582, 2941], EasterSunday[ # ][[3]] == 25 &] (* Robert G. Wilson v, Apr 06 2005 *)

Prog

(PARI) edate(yr1, yr2, day) = { local(flag=1, d, y, y2, ct, dt); for(d=day, day, ct=0; for(y=yr1, yr2, dt=oudin(y); if(eval(mid(dt, 4, 2))==d, if(flag, y2=y; flag=0); ct++; \ print(ct" "dt" "y-y2); print1(y", "); if(y2<>y, y2=y); ); ); \ print1(ct", "); ) } oudin(y) = \This is based on the algorithm of Oudin (1940) { local(c, n, k, i1, i2, i3, a1, a2, m, d, l, dt, dat=""); c=floor(y/100); n=y-19*floor(y/19); k=floor((c-17)/25); i1=c-floor(c/4)-floor((c-k)/3)+19*n+15; i2=i1-30*floor(i1/30); i3=i2-floor(i2/28)*(1-floor(i2/28)*floor(29/(i2+1))*floor((21-n)/11)); a1=y+floor(y/4)+i3+2-c+floor(c/4); a2=a1-7*floor(a1/7); l=i3-a2; m=3+floor((l+40)/44); d=l+28-31*floor(m/4); dat = concat(dat, right(Str(m+100), 2)); dat = concat(dat, " "); dat = concat(dat, right(Str(d+100), 2)); dat = concat(dat, " "); dat = concat(dat, Str(y)); return(dat); }

Crossrefs

Cf. A104034.

Sequence in context: A236042 A163273 A340923 * A054810 A251888 A251785

Adjacent sequences: A104016 A104017 A104018 * A104020 A104021 A104022

Keyword

nonn

Author

Cino Hilliard, Mar 31 2005

Extensions

More terms from Robert G. Wilson v, Apr 06 2005

Status

approved