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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 (list; graph; refs; listen; history; text; internal format)
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 3-5.

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((n-1)/13) + s[((n-1) 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] (* Jean-Fran├žois 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

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Last modified November 24 01:40 EST 2020. Contains 338603 sequences. (Running on oeis4.)