From Wikipedia, the free encyclopedia:

 A happy number is defined by the following process:
 Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals   1   (where it will stay),   or it loops endlessly in a cycle which does not include   1.   


 Those numbers for which this process end in   1   are       happy   numbers,   
 while   those numbers   that   do   not   end in   1   are   unhappy   numbers. 


Task

Find and print the first   8   happy numbers.

Display an example of your output here on this page.



See also

   The OEIS entry:   The     happy numbers:   A007770
   The OEIS entry:   The unhappy numbers;   A031177


def happy?(n)
  past = [] of Int32 | Int64
  until n == 1
    sum = 0; while n > 0; sum += (n % 10) ** 2; n //= 10 end
    return false if past.includes? (n = sum)
    past << n
  end
  true
end
 
i = count = 0
until count == 8; (puts i; count += 1) if happy?(i += 1) end
puts
(99999999999900..99999999999999).each { |i| puts i if happy?(i) }