Wednesday, June 16, 2010

Problem 37: Find the sum of all eleven primes that are both truncatable from left to right and right to left.

Kind of a variation on Problem 35.  I was surprised by how fast it ran!

let problem37a =
    let isTruncatablePrime n =
        if n |> isPrime |> not then false
            let digs = n |> Digits.fromInt
            let truncations =
                seq { for i in 1..(Seq.length digs)-1 -> 
                          digs |> Seq.take i |> Digits.toInt
                      for i in 1..(Seq.length digs)-1 -> 
                          digs |> Seq.skip i |> Digits.toInt }
            Seq.forall isPrime truncations
    let rec odds n = seq {yield n; yield! odds (n+2)}
    odds 11 //skip the single digit primes
    |> Seq.filter isTruncatablePrime
    |> Seq.take 11 //we are given there are only 11
    |> Seq.sum

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