# What is 3n 1 conjecture - Definition and Meaning

### 3n 1 Conjecture :

3n 1 Conjecture is otherwise called as Collatz conjecture, Ulam conjecture, Kakutani's problem, Thwaites conjecture, Hasse's algorithm or Syracuse problem. It is discovered by Lothar Collatz in 1937. This conjecture consider the following operation. **n / 2** - If the number is even, divide it by two **3n + 1** - If the number is odd, triple it and add one. The conjecture states, you can start with any number but the sequence will always end with one.

#### Example :

Lets consider n= 12.
12 is a even number, so divide by 2, **12/2 = 6**
6 is even, again divide by 2,** 6/2 = 3**
3 is odd, so triple it and add one, **3(3)+1 = 9+1= 10**
10 is even, so **10/2 = 5**
5 is odd, so **3(5) + 1 = 15 + 1 = 16**
16 is even, **16/2 = 8**
8 is even, **8/2 = 4**
4 is even, **4/2= 2**
2 is even, *2/2=1*
The sequence of numbers are **6, 3, 10, 5, 16, 8, 4, 2,1**

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