Happy numbers

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 ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers.

Task: Find and print the first 8 happy numbers.

Forth

next ( n -- n )

 0 swap begin 10 /mod >r  dup * +  r> ?dup 0= until ;

cycle? ( n -- ? )

 here dup @ cells +
 begin dup here >
 while 2dup @ = if 2drop true exit then
       1 cells -
 repeat
 1 over +!  dup @ cells + !  false ;

happy? ( n -- ? )

 0 here !  begin next dup cycle? until  1 = ;

happy-numbers ( n -- )

 0 swap 0 do
   begin 1+ dup happy? until dup .
 loop drop ;

8 happy-numbers \ 1 7 10 13 19 23 28 31 </lang>

JavaScript

<lang javascript> function happy(number) {

   var m, digit ;
   var cycle = new Array() ;

   while(number != 1 && cycle[number] != true) {
       cycle[number] = true ;
       m = 0 ;
       while (number > 0) {
           digit = number % 10 ;
           m += digit * digit ;
           number = (number  - digit) / 10 ;
       }
       number = m ;
   }
   return (number == 1) ;

} ;

var cnt = 8 ; var number = 1 ;

while(cnt-- > 0) {

   while(!happy(number))
       number++ ;
   document.write(number + " ") ;
   number++ ;

} </lang>

Python

Includes a cache of precomputed values. <lang python>>>> def happy(number):

   cycle = set()
   while number != 1 and number not in cycle:
       if number in happy.cache:
           number = 1 if happy.cache[number] else 0
           break
       cycle.add(number)
       newnumber = 0
       while number > 0:
           digit = number %10
           newnumber += digit*digit
           number = (number - digit) / 10
       number = newnumber
   happiness = number==1
   for n in cycle:     # all in cycle share the same happiness
       happy.cache.setdefault(n, happiness)
   return happiness

>>> happy.cache={} >>> [x for x in range(1,50) if happy(x)] # First few happy numbers [1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49] >>> </lang>

Tcl

using code from Sum of squares#Tcl <lang tcl>proc is_happy n {

   set seen [list]
   while {$n > 1 && [lsearch -exact $seen $n] == -1} {
       lappend seen $n
       set n [sum_of_squares [split $n ""]]
   }
   return [expr {$n == 1}]

}

set happy [list] set n -1 while {[llength $happy] < 8} {

   if {[is_happy $n]} {lappend happy $n}
   incr n

} puts "the first 8 happy numbers are: [list $happy]"</lang>

the first 8 happy numbers are: {1 7 10 13 19 23 28 31}