A157962 - OEIS

A157962

Table read by rows: Occurrences of Friday the 13th, T(n,1)=month (1 for January), T(n,2)=year-2000, starting year 2000.

10, 0, 4, 1, 7, 1, 9, 2, 12, 2, 6, 3, 2, 4, 8, 4, 5, 5, 1, 6, 10, 6, 4, 7, 7, 7, 6, 8, 2, 9, 3, 9, 11, 9, 8, 10, 5, 11, 1, 12, 4, 12, 7, 12, 9, 13, 12, 13, 6, 14, 2, 15, 3, 15, 11, 15, 5, 16, 1, 17, 10, 17, 4, 18, 7, 18, 9, 19, 12, 19, 3, 20, 11, 20, 8, 21, 5, 22, 1, 23, 10, 23, 9, 24, 12, 24

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Uses the Gregorian calendar.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..3442

J. R. Stockton, Rektor Chr. Zeller's 1886 Paper "Kalender-Formeln" [Wayback Machine link from Felix Fröhlich, Sep 23 2019]

Eric Weisstein's World of Mathematics, Triskaidekaphobia

Wikipedia, Triskaidekaphobia

Chr. Zeller, Kalender-Formeln, Acta Mathematica, 9 (1886), 131-136.

Index entries for linear recurrences with constant coefficients, order 1376.

Index entries for sequences related to calendars

FORMULA

a(2n+1) = a(2n + 1377), a(2n) = a(2n + 1376) + 400. - Charles R Greathouse IV, May 17 2011

EXAMPLE

a(39) = 1, a(40) = 12 -> Jan 2012,

a(41) = 4, a(42) = 12 -> Apr 2012,

a(43) = 7, a(44) = 12 -> Jul 2012,

a(45) = 9, a(46) = 13 -> Sep 2013.

MATHEMATICA

<< Calendar`; {y, m} = {2000, 1}; A157962 = {}; Do[ If[ m == 12, y = y + 1; m = 1, m = m + 1]; If[ DayOfWeek[ {y, m, 13}] == Friday, AppendTo[ A157962, {m , y - 2000}]] , {300}]; Flatten[A157962] (* Jean-François Alcover, Dec 16 2011 *)

Flatten[Table[If[DateValue[{2000+n, m, 13}, "DayName"]==Friday, {m, n}, {}], {n, 0, 25}, {m, 12}]/.{}->Nothing] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 10 2017 *)

PROG

(VBA) jo = 6 For a = 2000 To 2399 For b = 1 To 31 jo = jo + 1: If jo = 7 Then jo = 0 If jo = 6 And b = 13 Then ll = ll + 1: Cells(ll, 1) = 1: Cells(ll, 2) = a - 2000 Next b If a - 4 * Int(a / 4) = 0 Then GoTo 10 For c = 1 To 28 jo = jo + 1: If jo = 7 Then jo = 0 If jo = 6 And c = 13 Then ll = ll + 1: Cells(ll, 1) = 2: Cells(ll, 2) = a - 2000 Next c GoTo 20 10 For c = 1 To 29 jo = jo + 1: If jo = 7

Then jo = 0 If jo = 6 And c = 13 Then ll = ll + 1: Cells(ll, 1) = 2: Cells(ll, 2) = a - 2000 Next c 20 For d = 1 To 31 jo = jo + 1: If jo = 7 Then jo = 0 If jo = 6 And d = 13 Then ll = ll + 1: Cells(ll, 1) = 3: Cells(ll, 2) = a - 2000 Next d For e = 1 To 30 jo = jo + 1: If jo = 7 Then jo = 0 If jo = 6 And e = 13 Then ll = ll + 1: Cells(ll, 1) = 4: Cells(ll, 2) = a - 2000 Next e For f = 1 To 31 jo = jo + 1: If jo = 7 Then jo = 0 If jo = 6 And f = 13 Then ll = ll + 1: Cells(ll, 1) = 5: Cells(ll, 2) = a - 2000 Next f For g = 1 To 30 jo = jo + 1: If jo = 7 Then jo = 0 If jo = 6 And g = 13 Then ll = ll + 1: Cells(ll, 1) = 6: Cells(ll, 2) = a - 2000 Next g For h = 1 To 31 jo = jo + 1: If jo = 7 Then jo = 0 If jo = 6 And h = 13 Then ll = ll + 1: Cells(ll, 1) = 7: Cells(ll, 2) = a - 2000 Next h For i = 1 To 31 jo = jo + 1: If jo = 7 Then jo = 0 If jo = 6 And i = 13

Then ll = ll + 1: Cells(ll, 1) = 8: Cells(ll, 2) = a - 2000 Next i For j = 1 To 30 jo = jo + 1: If jo = 7 Then jo = 0 If jo = 6 And j = 13 Then ll = ll + 1: Cells(ll, 1) = 9: Cells(ll, 2) = a - 2000 Next j For k = 1 To 31 jo = jo + 1: If jo = 7 Then jo = 0 If jo = 6 And k = 13 Then ll = ll + 1: Cells(ll, 1) = 10: Cells(ll, 2) = a - 2000 Next k For l = 1 To 30 jo = jo + 1: If jo = 7 Then jo = 0 If jo = 6 And l = 13 Then ll = ll + 1: Cells(ll, 1) = 11: Cells(ll, 2) = a - 2000 Next l For m = 1 To 31 jo = jo + 1: If jo = 7 Then jo = 0 If jo = 6 And m = 13 Then ll = ll + 1: Cells(ll, 1) = 12: Cells(ll, 2) = a - 2000 Next m Next a End Sub

(Haskell)

a157962 n = a157962_list !! (n-1)

a157962_list = concat $ map (t 1 {- January -}) [0..] where

t 13 _ = []

t m n | h (n+2000) m 13 == 6 = m : n : t (succ m) n

| otherwise = t (succ m) n

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

-- Reinhard Zumkeller, May 17 2011