Using F# Sequences to Count Instances of the 13th of the Month

Shortly after publishing yesterday’s post on the lazy evaluation of F# sequences, I came across this post by Dr. Drang about calculating the frequency by day of week of occurences of the 13th day of the month. His post was inspired by a Scientfic American article about why the 13th of the month falls on a Friday more than any other day of the week (like two days ago from when this post is published). Spoiler: while true, it’s not by much.

In his post, Dr. Drang offered up a short Python script that calculates the number of times the 13th falls on each day of the week across a 400-year span. He uses a simple imperative script consisting of nested for loops to iterate through the years and months and counting up the number of occurences by day in an array:

f13s = [0]*7
for y in range(1800, 2200):
  for m in range(1, 13):
    wd = date(y, m, 13).weekday()
    f13s[wd] += 1

Given the timeliness of his post as well as my recent forays into functional programming and the use of collections in F#, I thought it would be fun to see what I could come up with:

open System

let allDates (startDate: DateTime) (endDate: DateTime) =
    seq {
        let mutable theDate = startDate.Date
        while theDate <= endDate.Date do
            yield theDate
            theDate <- theDate.AddDays 1
    }

let startDate = DateTime(2000, 1, 1)
let endDate = DateTime(2399, 12, 31)

let myDates = allDates startDate endDate

myDates
|> Seq.filter (fun date -> date.Day = 13)
|> Seq.countBy (fun date -> date.DayOfWeek)
|> Seq.sort
|> Seq.iter (fun (dayOfWeek, count) -> printfn $"{dayOfWeek}: {count}")

While not as concise as the Python implementation, I thought I did ok.

I started with the now familiar allDates function from yesterday’s post to define a sequence consisting of all dates within the range we are interested in. Like the Scientific American article, I went for years 2000 through 2399. Once we have our dates, I apply a filter to find all occurrences of the 13th of the month and then count them by day of week. After sorting them by day of week, we print our results:

Sunday: 687
Monday: 685
Tuesday: 685
Wednesday: 687
Thursday: 684
Friday: 688
Saturday: 684

which match both the authors of the article and Dr. Drang!¹

While this past Friday was the second Friday the 13th of year, we’ll have one more in November. To learn more about why, look no further than the good Doctor!

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1. The only difference is in the order of the days. Whereas Python date.weekday() uses 0 for Monday and 6 for Sunday, .NET DayOfWeek uses 0 for Sunday and 6 for Saturday.↩︎