defmodule LucasNumbers do
  defguardp is_positive(k) when is_integer(k) and k > 0
  @moduledoc """
  Lucas numbers are an infinite sequence of numbers which build progressively
  which hold a strong correlation to the golden ratio (φ or ϕ)

  E.g.: 2, 1, 3, 4, 7, 11, 18, 29, ...
  """
  def generate(1), do: [2]
  def generate(2), do: [2, 1]
  def generate(count) when is_positive(count) do
    Stream.iterate({2,1}, fn {x,y} -> {y, x+y} end)
    |> Stream.map(fn {x,_} -> x end) 
    |> Enum.take(count)
  end

  def generate(_), do: raise ArgumentError, "count must be specified as an integer >= 1"
end