A224944 Non-leap years beginning and ending on Saturday.

1583, 1594, 1605, 1611, 1622, 1633, 1639, 1650, 1661, 1667, 1678, 1689, 1695, 1701, 1707, 1718, 1729, 1735, 1746, 1757, 1763, 1774, 1785, 1791, 1803, 1814, 1825, 1831, 1842, 1853, 1859, 1870, 1881, 1887, 1898, 1910, 1921, 1927, 1938, 1949, 1955, 1966, 1977, 1983, 1994

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.

43 occurrences in 400 years.

Months having Friday the 13th: May.

365 day ordinary year: 52 Sundays, 52 Mondays, 52 Tuesdays, 52 Wednesdays, 52 Thursdays, 52 Fridays, 53 Saturdays.

Links

Table of n, a(n) for n=1..45.

Time and Date, The Gregorian calendar

Time and Date, 2011

Wikipedia, Gregorian calendar

Index entries for sequences related to calendars

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Mathematica

Select[Range[1583, 2600], DayOfWeek[{#, 1, 1}, Calendar -> Gregorian] == Saturday && DaysBetween[{#, 1, 1}, {# + 1, 1, 1}, Calendar -> Gregorian] == 365 &, 50] (* T. D. Noe, Apr 22 2013 *)
Select[Range[1583, 2500], !LeapYearQ[{#}]&&DayName[{#, 1, 1}]==DayName[{#, 12, 31}]==Saturday&] (* Harvey P. Dale, Aug 14 2022 *)

Crossrefs

Cf. A224938, A224939, A224940, A224941, A224942, A224943.

Sequence in context: A216064 A182409 A350027 * A222164 A242539 A224945

Adjacent sequences: A224941 A224942 A224943 * A224945 A224946 A224947

Keyword

nonn

Author

Aswini Vaidyanathan, Apr 21 2013

Status

approved