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Leap years having 53 Mondays and Tuesdays.
6

%I #16 Jul 21 2024 20:10:08

%S 1596,1624,1652,1680,1720,1748,1776,1816,1844,1872,1912,1940,1968,

%T 1996,2024,2052,2080,2120,2148,2176,2216,2244,2272,2312,2340,2368,

%U 2396,2424,2452,2480,2520,2548,2576,2616,2644,2672,2712,2740,2768,2796

%N Leap years having 53 Mondays and Tuesdays.

%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: September and December.

%C February 29th falls on Thursday.

%C 366 day leap year: 52 Sundays, 53 Mondays, 53 Tuesdays, 52 Wednesdays, 52 Thursdays, 52 Fridays, 52 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=1996">1996</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] == Monday && 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}]==Monday&] (* _Ray Chandler_, Jul 26 2023, v9 or later, after _Harvey P.Dale_ at A224945 *)

%Y Cf. A224945, A224947, A224948, A224949, A224950, A224951.

%K nonn

%O 1,1

%A _Aswini Vaidyanathan_, Apr 21 2013