#! /usr/bin/ruby

require 'test/unit'

def sylvester(ct)
  o = [ 2 ]
  2.upto(ct) do
    o.push(1 + (o[-1] * (o[-1] - 1)))
  end
  return o
end

class TestSylvester < Test::Unit::TestCase

  def test_ex1
    assert_equal([
                   2,
                   3,
                   7,
                   43,
                   1807,
                   3263443,
                   10650056950807,
                   113423713055421844361000443,
                   12864938683278671740537145998360961546653259485195807,
                   165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
                 ],sylvester(10))
  end

end