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A224943
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Non-leap years beginning and ending on Friday.
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6
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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
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1,1
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COMMENTS
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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: August.
365 day ordinary year: 52 Sundays, 52 Mondays, 52 Tuesdays, 52 Wednesdays, 52 Thursdays, 53 Fridays, 52 Saturdays.
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LINKS
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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).
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MATHEMATICA
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Needs["Calendar`"]; 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, v9 or later *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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