A224938 Non-leap years beginning and ending on Sunday.

1589, 1595, 1606, 1617, 1623, 1634, 1645, 1651, 1662, 1673, 1679, 1690, 1702, 1713, 1719, 1730, 1741, 1747, 1758, 1769, 1775, 1786, 1797, 1809, 1815, 1826, 1837, 1843, 1854, 1865, 1871, 1882, 1893, 1899, 1905, 1911, 1922, 1933, 1939, 1950, 1961, 1967, 1978, 1989, 1995

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: January and October.

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

Links

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

Time and Date, The Gregorian calendar

Time and Date, 2006

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

Needs["Calendar`"]; Select[Range[1583, 2600], DayOfWeek[{#, 1, 1}, Calendar -> Gregorian] == Sunday && 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}]==Sunday&](* Ray Chandler, Jul 26 2023, v9 or later, after _Harvey P.Dale_ at A224942 *)

Crossrefs

Cf. A224939, A224940, A224941, A224942, A224943, A224944.

Sequence in context: A224950 A233378 A083631 * A083632 A224939 A049520

Adjacent sequences: A224935 A224936 A224937 * A224939 A224940 A224941

Keyword

nonn

Author

Aswini Vaidyanathan, Apr 21 2013

Status

approved