Discussion on: Write a program or script to find Lucky Numbers

foo> dotnet build -c Release
...

foo> dotnet bin\Release\netcoreapp2.0\MyConsoleApp.dll
Count: 71918
Elapsed Milliseconds: 456
Memory Usage: 916208 bytes
Garbage Collections: 0 gen0, 0 gen1, 0 gen2

open System

// Max is the number of items to wait before removal
// Count is items seen since last removal
type Filter() =
    [<DefaultValue>] val mutable public Max : int
    [<DefaultValue>] val mutable public Count : int

[<EntryPoint>]
let main args =

    // pre-allocating capacity
    let results =
        Array.zeroCreate<int> 71918
    // 1 is a given
    results.[0] <- 1
    // index to place the next result
    let mutable nextResult = 1

    let iterationCount = 1_000_000
    // experimentally determined 6507 filters for 1,000,000
    // first filter (odd numbers) built into looping logic
    let filterCount = 6506 

    let filters =
        Array.zeroCreate<Filter> filterCount
    // index to place the next filter
    let mutable nextFilter = 0

    let timer =
        System.Diagnostics.Stopwatch()


    timer.Start()


    let mutable n = 3
    while n < iterationCount do
        let mutable i = 0
        let mutable survived = true
        // check each filter to see if it will discard the number
        // stop as soon as it is discarded
        while i < nextFilter && survived do
            let filter = filters.[i]
            let newCount = filter.Count + 1
            // update filter state... this is much faster than modulo
            if filter.Max = newCount then
                filter.Count <- 0
                survived <- false
            else
                filter.Count <- newCount
                survived <- true
            i <- i + 1

        // survived the guantlet
        if survived then
            results.[nextResult] <- n
            nextResult <- nextResult + 1
            //printfn " %i" i

            // create a new filter, if there is room
            if nextFilter < filterCount then
                filters.[nextFilter] <- Filter(Max=n, Count=nextResult)
                nextFilter <- nextFilter + 1

        n <- n + 2 // odds


    timer.Stop()


    printfn "Count: %i" nextResult
    printfn "Elapsed Milliseconds: %i" timer.ElapsedMilliseconds
    printfn "Memory Usage: %i bytes" <| GC.GetTotalMemory(false)
    printfn "Garbage Collections: %i gen0, %i gen1, %i gen2"
        <| GC.CollectionCount(0)
        <| GC.CollectionCount(1)
        <| GC.CollectionCount(2)

    0 // exit code