%I #20 Sep 12 2021 12:50:24

%S 1903,1914,1925,1928,1931,1942,1953,1956,1959,1970,1981,1984,1987,

%T 1998,2009,2012,2015,2026,2037,2040,2043,2054,2065,2068,2071,2082,

%U 2093,2096,2099,2105,2108,2111,2122,2133,2136,2139,2150,2161,2164,2167,2178,2189,2192

%N Years with exactly three "Friday the 13ths", starting from 1901.

%H Reinhard Zumkeller, <a href="/A190653/b190653.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Triskaidekaphobia.html">Triskaidekaphobia</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Triskaidekaphobia">Triskaidekaphobia</a>

%H <a href="/index/Ca#calendar">Index entries for sequences related to calendars</a>

%F A101312(a(n)) = 3, 1 <= A101312(n) <= 3.

%e 2012 is a term, since only Jan 13 2012, Apr 13 2012 and Jul 13 2012 fell on Fridays.

%t Module[{mos={#[[1]],Length[#]}&/@(Flatten[Take[#,1]&/@DateSelect[ DateRange[ {1900,1,1},{2200,12,1}],#Day==13&&#DayName== Friday&]]// Split)},Select[ mos,#[[2]]>2&][[All,1]]] (* Requires Mathematica version 12 or later *) (* _Harvey P. Dale_, Jan 17 2021 *)

%o (Haskell)

%o a190653 n = a190653_list !! (n-1)

%o a190653_list = filter ((== 3) . a101312) [1901..]

%o (Python)

%o from datetime import date

%o def ok(n): return sum(date.isoweekday(date(n, m, 13)) == 5 for m in range(1, 13)) == 3

%o print(list(filter(ok, range(1901, 2193)))) # _Michael S. Branicky_, Sep 12 2021

%Y Cf. A101312, A190651, A190652.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, May 16 2011