

A224943


Nonleap years beginning and ending on Friday.


0



1593, 1599, 1610, 1621, 1627, 1638, 1649, 1655, 1666, 1677, 1683, 1694, 1700, 1706, 1717, 1723, 1734, 1745, 1751, 1762, 1773, 1779, 1790, 1802, 1813, 1819, 1830, 1841, 1847, 1858, 1869, 1875, 1886, 1897, 1909, 1915, 1926, 1937, 1943, 1954, 1965, 1971, 1982, 1993, 1999
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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.
Noncentury 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: August.
365 day ordinary year: 52 Sundays, 52 Mondays, 52 Tuesdays, 52 Wednesdays, 52 Thursdays, 53 Fridays, 52 Saturdays.


LINKS

Table of n, a(n) for n=1..45.
Time and Date, The Gregorian calendar
Time and Date, 2010
Wikipedia, Gregorian calendar


MATHEMATICA

(* This first program no longer works in Mathematica version 10 because the relevant functions in that version have changed names. The second program, below, uses the functions now in Mathematica version 10 *) Select[Range[1583, 2600], DayOfWeek[{#, 1, 1}, Calendar > Gregorian] == Friday && DaysBetween[{#, 1, 1}, {# + 1, 1, 1}, Calendar > Gregorian] == 365 &, 50] (* T. D. Noe, Apr 22 2013 *)
Select[Range[1590, 2000], DayName[{#, 1, 1}]==DayName[{#, 12, 31}]==Friday && !LeapYearQ[ {#, 1, 1}]&] (* Harvey P. Dale, Apr 26 2016 *)


CROSSREFS

Sequence in context: A224948 A238075 A250959 * A045273 A316336 A028893
Adjacent sequences: A224940 A224941 A224942 * A224944 A224945 A224946


KEYWORD

nonn


AUTHOR

Aswini Vaidyanathan, Apr 21 2013


STATUS

approved



