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


function digits(n)
  if n > 0 then return n % 10, digits(math.floor(n/10)) end
end
function sumsq(a, ...)
  return a and a ^ 2 + sumsq(...) or 0
end
local happy = setmetatable({true, false, false, false}, {
      __index = function(self, n)
         self[n] = self[sumsq(digits(n))]
         return self[n]
      end } )
i, j = 0, 1
repeat
   i, j = happy[j] and (print(j) or i+1) or i, j + 1
until i == 8