Solution for https://www.youtube.com/watch?v=1lHDCAIsyb8

Math_WhatPositiveNumberDoublesWhenMovingLastDigit.fs

// Runs in https://fable.io/repl/#
open System

type Intermediate = { Digit : int; Flow: int; LastWasZero : bool }

let t = [ 1 .. 9 ] |> List.map (fun i -> { Digit = i; Flow = 0; LastWasZero = false })
let nextRound (intermediate) =
    let sum = intermediate.Digit * 2 + intermediate.Flow
    let digit = sum % 10
    let nextFlow = sum / 10
    { Digit = digit; Flow = nextFlow; LastWasZero = intermediate.Digit = 0 }

let checkFoundSingle startNum intermediate =
    let ok = startNum = intermediate.Digit && intermediate.Flow = 0 && not intermediate.LastWasZero
    if ok then Console.WriteLine(sprintf "Found OK: %A" intermediate)
    ok

let checkFound list =
    list
    |> List.mapi (fun idx intermediate -> (idx, intermediate))
    |> List.tryFind (fun (idx, intermediate) ->
        checkFoundSingle (idx + 1) intermediate)
    |> Option.map (fun (idx, _) -> idx + 1)

let y_0 = t |> List.map nextRound

//Fable.Core.JS.console.log(y_0)
//Console.WriteLine(y_0)
let mutable next = y_0
let mutable found = None
let mutable i = 0
while found.IsNone do
    i <- i + 1
    next <- next |> List.map nextRound
    match checkFound next with
    | Some num ->
        Console.WriteLine(sprintf "%d worked in round %d" num i)
        found <- Some num
    | _ -> ()
    Console.WriteLine(sprintf "Testing round %d" i)

match found with
| Some num ->
    let start = { Digit = num; Flow = 0; LastWasZero = false }
    let mutable start = [ nextRound start; start ]
    while not (checkFoundSingle num start.Head) do
        start <- nextRound start.Head :: start

    let sol = start.Tail |> List.map (fun i -> i.Digit)
    Console.WriteLine (sprintf "Solution %A" sol)
    
    let num = 
        sol
        |> List.rev
        |> List.mapi (fun idx num -> bigint num * (System.Numerics.BigInteger.Pow(10I, idx)))
        |> List.sum
    Console.WriteLine (sprintf "Solution %A" num)
    Console.WriteLine (sprintf "Times 2: %A" (num * 2I))

| _ -> ()