A224951 Leap years having 53 Saturdays and Sundays.

1600, 1628, 1656, 1684, 1724, 1752, 1780, 1820, 1848, 1876, 1916, 1944, 1972, 2000, 2028, 2056, 2084, 2124, 2152, 2180, 2220, 2248, 2276, 2316, 2344, 2372, 2400, 2428, 2456, 2484, 2524, 2552, 2580, 2620, 2648, 2676, 2716, 2744, 2772

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.

13 occurrences in 400 years.

Months having Friday the 13th: October.

February 29th falls on Tuesday.

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

Links

Table of n, a(n) for n=1..39.

Time and Date, The Gregorian calendar

Time and Date, 2000

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, 1, -1).

Mathematica

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

Crossrefs

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

Sequence in context: A260245 A282158 A252110 * A260499 A309562 A043412

Adjacent sequences: A224948 A224949 A224950 * A224952 A224953 A224954

Keyword

nonn

Author

Aswini Vaidyanathan, Apr 21 2013

Status

approved