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 A188528 First month in year n with a "Friday the 13th", starting from 1901. 3
 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, 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, 6, 2, 8, 10, 4, 9, 6, 2, 5, 1, 4, 6, 2, 8, 5, 1, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1901,1 COMMENTS A101312(n) > 0, therefore a(n) is defined for all n. REFERENCES Chr. Zeller, Kalender-Formeln, Acta mathematica, 9 (1886), 131-136. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1901..3000 J. R. Stockton, Rektor Chr. Zeller's 1886 Paper "Kalender-Formeln" Eric Weisstein's World of Mathematics, Triskaidekaphobia Wikipedia, Triskaidekaphobia EXAMPLE Number of times all months occur on "Friday the 13th" in the past century and the current one:           | Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec ----------+------------------------------------------------ 1991-2000 |  14  14   4  10  14  14   0  11  15   4   0   0 2000-2100 |  14  15   3  11  14  15   0  11  14   3   0   0 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. MATHEMATICA {* First execute *) << Calendar`; (* then execute *) Table[Select[ Table[ {yr, n, 13}, {n, 12}], DayOfWeek[#]==Friday&, 1][[1, 2]], {yr, 1901, 2011}] (* Harvey P. Dale, Oct 26 2011 *) PROG (Haskell) import Data.List (findIndex) import Data.Maybe (fromJust) a188528 n = succ \$ fromJust \$   findIndex (\m -> h n m 13 == 6) [1..12] where     h year month day  -- cf. Zeller reference.       | month <= 2 = h  (year - 1)  (month + 12)  day       | otherwise  = (day + 26 * (month + 1) `div` 10 + y + y `div` 4                      + century `div` 4 - 2 * century) `mod` 7         where (century, y) = divMod year 100 b188528 = bFileFun "A188528" a188528 1991 3000 -- For statistics (see example) ... ff13_perMonth ys m = length \$ filter (== m) (map a188528 ys) century20 = map (ff13_perMonth [1901..2000]) [1..12] century21 = map (ff13_perMonth [2001..2100]) [1..12] CROSSREFS Cf. A101312, A157962. Sequence in context: A154899 A011219 A202543 * A243257 A194182 A019961 Adjacent sequences:  A188525 A188526 A188527 * A188529 A188530 A188531 KEYWORD nonn AUTHOR Reinhard Zumkeller, May 16 2011 STATUS approved

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Last modified January 28 22:40 EST 2020. Contains 331328 sequences. (Running on oeis4.)