Colletz

XKCD brings my attention to a mathematical conjecture called the Collatz Conjecture that claims that for a particular operation, all numbers have a chain that eventually leads back to one. Read the Wikipedia article for details.
While a definite proof would win one a cool $500, computer verification only suggests that the claim is true. No proof has actually been written. Mathematical proofs via computer are beyond me, but I did, for practice, write a verifying program, as they are very very short. Mine is 32 lines long, written in C.

#include <stdio.h>
void collatz(int);
int main(int argc, char *argv[])
{
if(argc==2)
{
int num=argv[1];
collatz(num);
}
else
{
printf("USAGE: collatz number\n");
}
return 0;
}
void collatz(int num)
{
int count=0;
while(num!=1)
{
if(num%2==0)
{
num=num/2;
}
else
{
num=num*3+1;
}
count++;
}
printf("Returned to 1 after %d cycles.\n",count);
}


The program accepts one number from you, the user, and runs a collatz chain until it reaches one. It then reports the length of this chain.
A trivial change to the main would produce a program that would report the length of ALL integers until it overflowed:

int main()
{
int num;
for(num=0;num<MAX_INT;num++)
{
printf("%d:",num);
collatz(num);
}
return 0;
}


The variable MAX_INT would be preset with a #define command according to the nature of the computer. Mine would be 2^64, as integers are 64-bits long on my computer.