A190652 Years with exactly two "Friday the 13ths", starting from 1901.

1901, 1905, 1906, 1907, 1908, 1911, 1912, 1917, 1918, 1920, 1922, 1923, 1929, 1933, 1934, 1935, 1936, 1939, 1940, 1945, 1946, 1948, 1950, 1951, 1957, 1961, 1962, 1963, 1964, 1967, 1968, 1973, 1974, 1976, 1978, 1979, 1985, 1989, 1990, 1991, 1992, 1995, 1996

Offset: 1

Author

Reinhard Zumkeller, May 16 2011

Keywords

• nonn

Examples

			2004 is a term, since only Feb 13 2004 and Aug 13 2004 fell on a Friday.
		

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, A190653.

Programs

Haskell

a190652 n = a190652_list !! (n-1)
a190652_list = filter ((== 2) . a101312) [1901..]

Mathematica

Select[Range[1901,2020],Count[Table[{#,m,13},{m,12}],?(DayName[#] == Friday&)] == 2&] (* _Harvey P. Dale, Oct 02 2018 *)

Python

from datetime import date
def ok(n): return sum(date.isoweekday(date(n, m, 13)) == 5 for m in range(1, 13)) == 2
print(list(filter(ok, range(1901, 2000)))) # Michael S. Branicky, Sep 12 2021

Formula

A101312(a(n)) = 2, 1 <= A101312(n) <= 3.