

A119406


Years in which there are five Sundays in the month of February.


7



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, 2804, 2832, 2860, 2888, 2928, 2956, 2984, 3024
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OFFSET

1,1


COMMENTS

"The Gregorian calendar has been in use in the Western world since 1582 by Roman Catholic countries and since 1752 by English speaking countries. The Gregorian calendar counts leap years every year divisible by 4, except for centuries not divisible by 400, which are not leap years."  The Mathematica Book
Because the days of the week of the Gregorian calendar repeat every 400 years, the first differences of this sequence have period 13: [28, 40, 28, 28, 40, 28, 28, 28, 28, 28, 28, 40, 28].  Nathaniel Johnston, May 30 2011


REFERENCES

George G. Szpiro, The Secret Life Of Numbers, 50 Easy Pieces On How Mathematicians Work And Think, Joseph Henry Press, Washington, D.C., 2006, Chapter 1, "Lopping Leap Years", pages 35.


LINKS

Table of n, a(n) for n=1..42.
TimeAndDate.com, A calendar website
Index entries for sequences related to calendars


MAPLE

A119406 := proc(n) local s: s:=[0, 28, 68, 96, 124, 164, 192, 220, 248, 276, 304, 332, 372]: return 1756 + 400*floor((n1)/13) + s[((n1) mod 13) + 1]: end: seq(A119406(n), n=1..42); # Nathaniel Johnston, May 30 2011


MATHEMATICA

(* first do *) Needs["Miscellaneous`Calendar`"] (* then *) fQ[y_] := Mod[y, 4] == 0 && Mod[y, 400] ? 0 && DayOfWeek[{y, 2, 1}] == Sunday; Select[ Range[1582, 3051], fQ@# &]
(* Second program, needing Mma version >= 9.0 *)
okQ[y_] := Mod[y, 4] == 0 && DayCount[{y, 1, 31}, DatePlus[{y, 3, 1}, 1], Sunday] == 5;
Select[Range[1752, 3051, 4], okQ] (* JeanFrançois Alcover, Mar 27 2020 *)


CROSSREFS

Cf. A008685, A011763, A011770.
Cf. A135795, A143994, A141039, A143995, A141287.  J. Lowell, Oct 06 2008
Sequence in context: A271747 A282480 A043436 * A204280 A252635 A213459
Adjacent sequences: A119403 A119404 A119405 * A119407 A119408 A119409


KEYWORD

nonn,easy


AUTHOR

George G. Szpiro (george(AT)netvision.net.il) and Robert G. Wilson v, Jul 05 2006


STATUS

approved



