A224946 Leap years having 53 Mondays and Tuesdays.

1596, 1624, 1652, 1680, 1720, 1748, 1776, 1816, 1844, 1872, 1912, 1940, 1968, 1996, 2024, 2052, 2080, 2120, 2148, 2176, 2216, 2244, 2272, 2312, 2340, 2368, 2396, 2424, 2452, 2480, 2520, 2548, 2576, 2616, 2644, 2672, 2712, 2740, 2768, 2796

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: September and December.

February 29th falls on Thursday.

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

Links

Table of n, a(n) for n=1..40.

Time and Date, The Gregorian calendar

Time and Date, 1996

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

Crossrefs

Cf. A224945, A224947, A224948, A224949, A224950, A224951.

Sequence in context: A029561 A015281 A132654 * A316335 A179248 A068131

Adjacent sequences: A224943 A224944 A224945 * A224947 A224948 A224949

Keyword

nonn

Author

Aswini Vaidyanathan, Apr 21 2013

Status

approved