login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 3
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

CROSSREFS

Cf. A101312, A188528.

Sequence in context: A291451 A323836 A062520 * A063741 A320227 A284780

Adjacent sequences:  A157959 A157960 A157961 * A157963 A157964 A157965

KEYWORD

nonn,tabf,easy

AUTHOR

Pierre CAMI, Mar 10 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 2 08:00 EDT 2020. Contains 334767 sequences. (Running on oeis4.)