A224949 Leap years having 53 Thursdays and Fridays.

1604, 1632, 1660, 1688, 1728, 1756, 1784, 1824, 1852, 1880, 1920, 1948, 1976, 2004, 2032, 2060, 2088, 2128, 2156, 2184, 2224, 2252, 2280, 2320, 2348, 2376, 2404, 2432, 2460, 2488, 2528, 2556, 2584, 2624, 2652, 2680, 2720, 2748, 2776

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: February and August.

February 29th falls on Sunday.

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

Links

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

Time and Date, The Gregorian calendar

Time and Date, 2004

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

Select[Range[1583, 2800], DayOfWeek[{#, 1, 1}, Calendar -> Gregorian] == Thursday && DaysBetween[{#, 1, 1}, {# + 1, 1, 1}, Calendar -> Gregorian] == 366 &, 50] (* T. D. Noe, Apr 22 2013 *)
Select[Range[1583, 3000], LeapYearQ[{#}]&&DayName[{#, 1, 1}]==Thursday&] (* Ray Chandler, Jul 26 2023, Version 10, after _Harvey P.Dale_ at A224945 *)

Crossrefs

Cf. A224945, A224946, A224947, A224948, A224950, A224951.

Sequence in context: A293370 A352092 A252439 * A171466 A205267 A210364

Adjacent sequences: A224946 A224947 A224948 * A224950 A224951 A224952

Keyword

nonn

Author

Aswini Vaidyanathan, Apr 21 2013

Status

approved