A190653 Years with exactly three "Friday the 13ths", starting from 1901.

1903, 1914, 1925, 1928, 1931, 1942, 1953, 1956, 1959, 1970, 1981, 1984, 1987, 1998, 2009, 2012, 2015, 2026, 2037, 2040, 2043, 2054, 2065, 2068, 2071, 2082, 2093, 2096, 2099, 2105, 2108, 2111, 2122, 2133, 2136, 2139, 2150, 2161, 2164, 2167, 2178, 2189, 2192

Offset: 1

Author

Reinhard Zumkeller, May 16 2011

Keywords

• nonn

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Triskaidekaphobia
• Wikipedia, Triskaidekaphobia
• Index entries for sequences related to calendars

Crossrefs

Cf. A101312, A190651, A190652.

Programs

Haskell

a190653 n = a190653_list !! (n-1)
a190653_list = filter ((== 3) . a101312) [1901..]

Mathematica

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 *)

Python

from datetime import date
def ok(n): return sum(date.isoweekday(date(n, m, 13)) == 5 for m in range(1, 13)) == 3
print(list(filter(ok, range(1901, 2193)))) # Michael S. Branicky, Sep 12 2021

Formula

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