A224951 - OEIS

%I #15 Jul 21 2024 20:15:44

%S 1600,1628,1656,1684,1724,1752,1780,1820,1848,1876,1916,1944,1972,

%T 2000,2028,2056,2084,2124,2152,2180,2220,2248,2276,2316,2344,2372,

%U 2400,2428,2456,2484,2524,2552,2580,2620,2648,2676,2716,2744,2772

%N Leap years having 53 Saturdays and Sundays.

%C Gregorian calendar repeats after every 400 years because number of days in 400 years is 146097 which is a multiple of 7.

%C Non-century years are leap years if and only if they are multiples of 4 while century years are leap years if and only if they are multiples of 400.

%C 13 occurrences in 400 years.

%C Months having Friday the 13th: October.

%C February 29th falls on Tuesday.

%C 366 day leap year: 53 Sundays, 52 Mondays, 52 Tuesdays, 52 Wednesdays, 52 Thursdays, 52 Fridays, 53 Saturdays.

%H Time and Date, <a href="http://www.timeanddate.com/calendar/gregorian-calendar.html">The Gregorian calendar</a>

%H Time and Date, <a href="http://www.timeanddate.com/calendar/?year=2000">2000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Gregorian_calendar">Gregorian calendar</a>

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

%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

%t Needs["Calendar`"]; Select[Range[1583, 2800], DayOfWeek[{#, 1, 1}, Calendar -> Gregorian] == Saturday && DaysBetween[{#, 1, 1}, {# + 1, 1, 1}, Calendar -> Gregorian] == 366 &, 50] (* _T. D. Noe_, Apr 22 2013 *)

%t Select[Range[1583,3000],LeapYearQ[{#}]&&DayName[{#,1,1}]==Saturday&] (* _Ray Chandler_, Jul 26 2023, v9 or later, after _Harvey P.Dale_ at A224945 *)

%Y Cf. A224945, A224946, A224947, A224948, A224949, A224950.

%K nonn

%O 1,1

%A _Aswini Vaidyanathan_, Apr 21 2013