happy_numbers.rb

class Integer
  @@results = []

  def happy?
    value = digits_square_sum

    return false if @@results.include?(value)

    if value == 1
      @@results = []

      return true
    end

    @@results << value

    value.happy?
  end

  private

  def digits_square_sum
    self.to_s.chars.map { |num| num.to_i ** 2 }.reduce(:+)
  end
end

puts 19.happy? # => true

1.upto(30) do |n|
  puts "#{n} is #{n.happy? ? 'happy' : 'unhappy'}"
end

# 1 is happy
# 2 is unhappy
# 3 is unhappy
# 4 is unhappy
# 5 is unhappy
# 6 is unhappy
# 7 is happy
# 8 is unhappy
# 9 is unhappy
# 10 is happy
# 11 is unhappy
# 12 is unhappy
# 13 is happy
# 14 is unhappy
# 15 is unhappy
# 16 is unhappy
# 17 is unhappy
# 18 is unhappy
# 19 is happy
# 20 is unhappy
# 21 is unhappy
# 22 is unhappy
# 23 is happy
# 24 is unhappy
# 25 is unhappy
# 26 is unhappy
# 27 is unhappy
# 28 is happy
# 29 is unhappy
# 30 is unhappy