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A188528 First month in year n with a "Friday the 13th", starting from 1901.

%I A188528 #34 Feb 16 2025 08:33:14
%S A188528 9,6,2,5,1,4,9,3,8,5,1,9,6,2,8,10,4,9,6,2,5,1,4,6,2,8,5,1,9,6,2,5,1,4,
%T A188528 9,3,8,5,1,9,6,2,8,10,4,9,6,2,5,1,4,6,2,8,5,1,9,6,2,5,1,4,9,3,8,5,1,9,
%U A188528 6,2,8,10,4,9,6,2,5,1,4,6,2,8,5,1,9
%N A188528 First month in year n with a "Friday the 13th", starting from 1901.
%C A188528 A101312(n) > 0, therefore a(n) is defined for all n.
%D A188528 Chr. Zeller, Kalender-Formeln, Acta mathematica, 9 (1886), 131-136.
%H A188528 Reinhard Zumkeller, <a href="/A188528/b188528.txt">Table of n, a(n) for n = 1901..3000</a>
%H A188528 J. R. Stockton, <a href="https://web.archive.org/web/20140111181708/http://www.merlyn.demon.co.uk/zel-86px.htm">Rektor Chr. Zeller's 1886 Paper "Kalender-Formeln"</a>
%H A188528 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Triskaidekaphobia.html">Triskaidekaphobia</a>
%H A188528 Wikipedia, <a href="http://en.wikipedia.org/wiki/Triskaidekaphobia">Triskaidekaphobia</a>
%H A188528 <a href="/index/Ca#calendar">Index entries for sequences related to calendars</a>
%e A188528 Number of times all months occur on "Friday the 13th" in the past century and the current one:
%e A188528           | Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
%e A188528 ----------+------------------------------------------------
%e A188528 1991-2000 |  14  14   4  10  14  14   0  11  15   4   0   0
%e A188528 2000-2100 |  14  15   3  11  14  15   0  11  14   3   0   0
%e A188528 The table doesn't say that there are no "Friday the 13ths" in July, November, and December: just first occurrences are considered, e.g. Nov 13 2009 is on a Friday, but a(2009) = 2; Jul 13 2012 is on a Friday, but a(2012) = 1; and Dec 13 2024 is on a Friday, but a(2024) = 9.
%t A188528 << Calendar`;
%t A188528 Table[Select[ Table[ {yr,n,13},{n,12}],DayOfWeek[#]==Friday&,1][[1,2]],{yr,1901,2011}] (* _Harvey P. Dale_, Oct 26 2011 *)
%o A188528 (Haskell)
%o A188528 import Data.List (findIndex)
%o A188528 import Data.Maybe (fromJust)
%o A188528 a188528 n = succ $ fromJust $
%o A188528   findIndex (\m -> h n m 13 == 6) [1..12] where
%o A188528     h year month day  -- cf. Zeller reference.
%o A188528       | month <= 2 = h  (year - 1)  (month + 12)  day
%o A188528       | otherwise  = (day + 26 * (month + 1) `div` 10 + y + y `div` 4
%o A188528                      + century `div` 4 - 2 * century) `mod` 7
%o A188528         where (century, y) = divMod year 100
%o A188528 b188528 = bFileFun "A188528" a188528 1991 3000
%o A188528 -- For statistics (see example) ...
%o A188528 ff13_perMonth ys m = length $ filter (== m) (map a188528 ys)
%o A188528 century20 = map (ff13_perMonth [1901..2000]) [1..12]
%o A188528 century21 = map (ff13_perMonth [2001..2100]) [1..12]
%o A188528 (Python)
%o A188528 from datetime import date
%o A188528 def a(n):
%o A188528     for month in range(1, 13):
%o A188528         if date.isoweekday(date(n, month, 13)) == 5: return month
%o A188528 print([a(n) for n in range(1901, 1986)]) # _Michael S. Branicky_, Sep 06 2021
%Y A188528 Cf. A101312, A157962.
%K A188528 nonn
%O A188528 1901,1
%A A188528 _Reinhard Zumkeller_, May 16 2011