OFFSET
1,1
COMMENTS
Gregorian calendar repeats after every 400 years because number of days in 400 years is 146097 which is a multiple of 7.
Non-century years are leap years if and only if they are multiples of 4 while century years are leap years if and only if they are multiples of 400.
13 occurrences in 400 years.
Months having Friday the 13th: October.
February 29th falls on Tuesday.
366 day leap year: 53 Sundays, 52 Mondays, 52 Tuesdays, 52 Wednesdays, 52 Thursdays, 52 Fridays, 53 Saturdays.
LINKS
Time and Date, The Gregorian calendar
Time and Date, 2000
Wikipedia, Gregorian calendar
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).
FORMULA
G.f.: x*(1600 + 28*x + 28*x^2 + 28*x^3 + 40*x^4 + 28*x^5 + 28*x^6 + 40*x^7 + 28*x^8 + 28*x^9 + 40*x^10 + 28*x^11 + 28*x^12 - 1572*x^13)/(1 - x - x^13 + x^14). - Charles R Greathouse IV, May 15 2026
MATHEMATICA
Needs["Calendar`"]; Select[Range[1583, 2800], DayOfWeek[{#, 1, 1}, Calendar -> Gregorian] == Saturday && DaysBetween[{#, 1, 1}, {# + 1, 1, 1}, Calendar -> Gregorian] == 366 &, 50] (* T. D. Noe, Apr 22 2013 *)
Select[Range[1583, 3000], LeapYearQ[{#}]&&DayName[{#, 1, 1}]==Saturday&] (* Ray Chandler, Jul 26 2023, v9 or later, after _Harvey P.Dale_ at A224945 *)
PROG
(PARI) a(n)=1600+((n-1)\13)*400+[372, 0, 28, 56, 84, 124, 152, 180, 220, 248, 276, 316, 344][n%13+1] \\ Charles R Greathouse IV, May 15 2026
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Aswini Vaidyanathan, Apr 21 2013
STATUS
approved