A224950 Leap years having 53 Fridays and Saturdays.

1588, 1616, 1644, 1672, 1712, 1740, 1768, 1796, 1808, 1836, 1864, 1892, 1904, 1932, 1960, 1988, 2016, 2044, 2072, 2112, 2140, 2168, 2196, 2208, 2236, 2264, 2292, 2304, 2332, 2360, 2388, 2416, 2444, 2472, 2512, 2540, 2568, 2596, 2608, 2636, 2664, 2692, 2704, 2732, 2760, 2788

Offset: 1

Author

Aswini Vaidyanathan, Apr 21 2013

Keywords

• nonn

Comments

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

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.

15 occurrences in 400 years.

Months having Friday the 13th: May.

February 29th falls on Monday.

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

Links

• Time and Date, The Gregorian calendar
• Time and Date, 2016
• Wikipedia, Gregorian calendar
• Index entries for sequences related to calendars
• Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Crossrefs

Cf. A224945, A224946, A224947, A224948, A224949, A224951.

Programs

Mathematica

Needs["Calendar`"]; Select[Range[1583, 2800], DayOfWeek[{#, 1, 1}, Calendar -> Gregorian] == Friday && DaysBetween[{#, 1, 1}, {# + 1, 1, 1}, Calendar -> Gregorian] == 366 &, 50] (* T. D. Noe, Apr 22 2013 *)
ly53Q[y_]:=LeapYearQ[{y}]&&Count[DayRange[{y,1,1},{y,12,31}],?(DayName[ #]==Friday&)]==53&&Count[DayRange[{y,1,1},{y,12,31}],?(DayName[#] == Saturday&)] ==53; Select[Range[1570,2800],ly53Q] (* Harvey P. Dale, Oct 14 2021, v9 or later *)