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A119406 Years in which there are five Sundays in the month of February. 9
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
TimeAndDate.com, A calendar website
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).
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-François Alcover, Mar 27 2020 *)
CROSSREFS
Cf. A135795 (Mon), A143994 (Tue), A141039 (Wed), A143995 (Thu), A141287 (Fri), A176478 (Sat).
Sequence in context: A271747 A282480 A043436 * A204280 A252635 A213459
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 April 17 04:44 EDT 2024. Contains 371756 sequences. (Running on oeis4.)