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%I #20 Jul 26 2023 17:45:46
%S 1593,1599,1610,1621,1627,1638,1649,1655,1666,1677,1683,1694,1700,
%T 1706,1717,1723,1734,1745,1751,1762,1773,1779,1790,1802,1813,1819,
%U 1830,1841,1847,1858,1869,1875,1886,1897,1909,1915,1926,1937,1943,1954,1965,1971,1982,1993,1999
%N Non-leap years beginning and ending on Friday.
%C Gregorian calendar repeats after every 400 years because number of days in 400 years is 146097 which is a multiple of 7.
%C 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.
%C 43 occurrences in 400 years.
%C Months having Friday the 13th: August.
%C 365 day ordinary year: 52 Sundays, 52 Mondays, 52 Tuesdays, 52 Wednesdays, 52 Thursdays, 53 Fridays, 52 Saturdays.
%H Time and Date, <a href="http://www.timeanddate.com/calendar/gregorian-calendar.html">The Gregorian calendar</a>
%H Time and Date, <a href="http://www.timeanddate.com/calendar/?year=2010">2010</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Gregorian_calendar">Gregorian calendar</a>
%H <a href="/index/Ca#calendar">Index entries for sequences related to calendars</a>
%H <a href="/index/Rec#order_44">Index entries for linear recurrences with constant coefficients</a>, 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).
%t (* 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 *)
%t Select[Range[1590,2000],DayName[{#,1,1}]==DayName[{#,12,31}]==Friday && !LeapYearQ[ {#,1,1}]&] (* _Harvey P. Dale_, Apr 26 2016 *)
%Y Cf. A224938, A224939, A224940, A224941, A224942, A224944.
%K nonn
%O 1,1
%A _Aswini Vaidyanathan_, Apr 21 2013
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