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


(include-book "arithmetic-3/top" :dir :system)
 
(defun sum-of-digit-squares (n)
   (if (zp n)
       0
       (+ (expt (mod n 10) 2)
          (sum-of-digit-squares (floor n 10)))))
 
(defun is-happy-r (n seen)
   (let ((next (sum-of-digit-squares n)))
        (cond ((= next 1) t)
              ((member next seen) nil)
              (t (is-happy-r next (cons next seen))))))
 
(defun is-happy (n)
   (is-happy-r n nil))
 
(defun first-happy-nums-r (n i)
   (cond ((zp n) nil)
         ((is-happy i)
          (cons i (first-happy-nums-r (1- n) (1+ i))))
         (t (first-happy-nums-r n (1+ i)))))
 
(defun first-happy-nums (n)
   (first-happy-nums-r n 1))