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

1,1

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

Table of n, a(n) for n=1..46.

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).

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 *)

Crossrefs

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

Sequence in context: A224941 A213116 A224942 * A233378 A083631 A224938

Adjacent sequences: A224947 A224948 A224949 * A224951 A224952 A224953

Keyword

nonn

Author

Aswini Vaidyanathan, Apr 21 2013

Status

approved