

A224950


Leap years having 53 Fridays and Saturdays.


6



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
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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.
Noncentury 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

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



KEYWORD

nonn,changed


AUTHOR



STATUS

approved



