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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A061251.

Programs

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

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 *)

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

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

Formula

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