Here is my simple solution, not thread safe, not optimize for finding
happiest number between 2 numbers.

happy? method returns false if the number is unhappy or happy list if
the number is happy.

class Integer
  def digits(base = 10)
    return [self] if self < base
    self.divmod(base).inject { |div, mod| div.digits(base) << mod }
  end

  def happy?(base = 10)
    @@happy_list = []
    _happy?(base) ? @@happy_list : false
  end

  protected

  def _happy?(base)
    return false if @@happy_list.include?(self)
    @@happy_list << self
    return true if self == 1
    self.digits(base).inject(0) { |n, d| n + d*d }._happy?(base)
  end
end


# some simple tests
if __FILE__ == $0
  p 7.happy?
  p 37.happy?
  p 25.happy?(2)  # base 2 is "happy base" all numbers(>0) on base 2
are happies.
  p 4394.happy?(16)
  p 367.happy?(100)
end