A104019 - OEIS

%I #22 Aug 15 2020 08:48:07

%S 1663,1666,1674,1731,1734,1742,1883,1886,1894,1943,1951,2035,2038,

%T 2046,2103,2187,2190,2198,2255,2258,2266,2323,2326,2334,2407,2410,

%U 2418,2491,2559,2570,2573,2581,2627,2630,2638,2779,2782,2790,2874,2877,2885,2931

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

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

%C 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

%H Holger Oertel, <a href="https://web.archive.org/web/20120314005924/http://www.ortelius.de/kalender/east_en.php">Calculation of Easter</a>. [Via Wayback Machine]

%H M. Montes, <a href="http://www.smart.net/~mmontes/freq1.html">Frequency of the Date of Easter over one complete Gregorian Easter Cycle</a>.

%H <a href="/index/Ca#calendar">Index entries for sequences related to calendars</a>

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

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

%o (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); }

%Y Cf. A104034.

%K nonn

%O 1,1

%A _Cino Hilliard_, Mar 31 2005

%E More terms from _Robert G. Wilson v_, Apr 06 2005