java - Use of integers and doubles give different answers when they shouldn't -

I am resolving a project using Java. I am not asking for help in solving the problem. I have already solved it, but I have something I can not understand.

The problem is similar:

The following repeated sequence set is defined for positive integers:

n = n / 2, if N is also n, then n = 3n + 1, if n is weird

Using the above rule and starting with 13, we generate the following sequence:

13 - Gt; 40 - & gt; 20 - & gt; 10 - & gt; 5 - & gt; 16 - & gt; 8 - & gt; 4 - & gt; 2 - & gt; 1. Here, the length of the series is 10 numbers.

Find the starting number starting at 1,000,000 which creates the longest chain.

Then I wrote this code:

  public class Euler014 {public static zero main (string [] args) {int maxChainCount = 0; Integer = 0; Int n; Int chainCount = 1; For (Int i = 0; I <1000000; i ++) {n = i; While (n> 1) {if (n% 2 == 0) {// even if check n / = 2; } And {// and: odd n = 3 * n + 1; } Chancount ++; } If (Chancet> Maximum ChainConnect) // Check whether this is the longest series ever, maxChainCount = chainCount; Answer = i; } Chancet = 1; } System.out.println ("\ n \ nLong series: i =" + answer); }}   
 This gives me the answer 910107, which is wrong.  
 However, if I type my n variable type  double n  it runs and gives me 8377 9 9, which is correct!  
 This really confuses me, because I do not know what the difference will be. I understand that if we use  int  and we divide it, then we can eliminate the rounding number when we do not intend it, but in this case, we should always check that What is divisble before dividing by  n  2? So I thought it would be completely safe to use the integer. What am I not seeing?  
 This is a complete code, copy, paste and run it in. If you want to see yourself, it runs in a few seconds despite it running too much. =)   
 
 
 Your problem is overflow if you enter  int n  to  If you change the long n , you will get the correct answer.  
 Remember: The number of   really big   in the sequence is not the limit of the overflow  int  but in this case (in this case)  double  s, or  long  s.  
 At one point in the series,  n  is  827,370,449  and you follow the  3n + 1  branch . This value wants to be  2,482,111,348 , but it exceeds the capacity of  int  (which is  2,147,483,647  in the positive area) and you  1812855 9 48. And things go from there to the south: -)  
 Then you want to correct your theory with integer (I should say  integral ) number is correct. But they have the ability to work.