The Simplest Math Problem No One Can Solve

Context

See The Simplest Math Problem No One Can Solve

defmodule ThreeXplusone do
  def run(x) do
    loop(x, [])
  end

  def loop(x, res) when x <= 1 do
    res ++ [x]
  end

  def loop(x, res) when rem(x, 2) == 0 do
    new_x = div(x, 2)
    loop(new_x, res ++ [x])
  end

  def loop(x, res) do
    new_x = 3 * x + 1
    loop(new_x, res ++ [x])
  end
end

ThreeXplusone.run(7)

Graph the results

Mix.install([
  {:vega_lite, "~> 0.1.0"},
  {:kino, "~> 0.2.0"}
])

alias VegaLite, as: Vl

data =
  ThreeXplusone.run(7)
  |> Enum.with_index()
  |> Enum.map(fn {val, indx} -> %{"x" => indx, "y" => val} end)

Vl.new(width: 400, height: 300)
|> Vl.data_from_values(data)
|> Vl.mark(:line)
|> Vl.encode_field(:x, "x", type: :quantitative)
|> Vl.encode_field(:y, "y", type: :quantitative)

start_n = IO.gets("start_n") |> String.trim() |> String.to_integer()
end_n = IO.gets("end_n") |> String.trim() |> String.to_integer()

data =
  start_n..end_n
  |> Enum.flat_map(fn n ->
    ThreeXplusone.run(n)
    |> Enum.with_index()
    |> Enum.map(fn {val, indx} -> %{"x" => indx, "y" => val, "n" => n} end)
  end)

Vl.new(width: 400, height: 300)
|> Vl.data_from_values(data)
|> Vl.mark(:line)
|> Vl.encode_field(:x, "x", type: :quantitative)
|> Vl.encode_field(:y, "y", type: :quantitative)
|> Vl.encode_field(:color, "n", type: :nominal)