A008685 Lengths of months in the Gregorian calendar.

31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31, 31, 28, 31

Offset

1,1

Comments

To make the definition unambiguous, consider these as starting from January 2001 (or, equivalently, AD 1 in the proleptic Gregorian calendar). [Charles R Greathouse IV, Sep 28 2011]

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Index entries for sequences related to calendars

Index entries for linear recurrences with constant coefficients, order 4800.

Formula

a(n) = a(n-4800). [Charles R Greathouse IV, Sep 28 2011]

Mathematica

year1 = 2001; year2 = 2100;
PreviousDate[#, "Day"][[1, 3]]& /@ Flatten[Table[{#, m, 1}, {m, Append[ Range[2, 12], 1]}]& /@ Range[year1, year2], 1] (* Jean-François Alcover, Aug 01 2018 *)

Prog

(PARI) v=[]; for(n=1, 50, v=concat(v, [31, if(n%4||(n%100==0&&n%400), 28, 29), 31, 30, 31, 30, 31, 31, 30, 31, 30, 31])); v
(Haskell)
a008685 n = a008685_list !! (n-1)
a008685_list = concatMap t [1..] where
   t y = [31, 28 + leap, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
         where leap = if mod y 4 == 0 &&
                         (mod y 100 > 0 || mod y 400 == 0) then 1 else 0
-- Reinhard Zumkeller, Jun 19 2015
(Python)
def a(n):
    y, m = 1 + (n-1)//12, (n-1)%12
    leap = int((y%4 == 0 and y%100 != 0) or y%400 == 0)
    return [31, 28+leap, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31][m]
print([a(n) for n in range(1, 64)]) # Michael S. Branicky, Feb 04 2024

Crossrefs

Cf. A061251.

Sequence in context: A361315 A291471 A276992 * A162156 A141529 A022987

Adjacent sequences: A008682 A008683 A008684 * A008686 A008687 A008688

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved