Collatz Conjecture

The conjecture use the following algorithm: If n is even, divide it by 2, else multiply by 3 and add 1. Start over until you get 1.

Example: n=10, 10 is even, divide it by 2 and get 5,
5 is odd, multiply it by 3 and add 1 to get 16,
The sequence is continued by 8, 4, 2 and 1.

No, nobody has found a number for which it does not work but nobody has found any mathematical proof that the conjecture is always true.

A number never appears twice in the sequence.

Any sequence ends with a series of powers of 2.

An odd number is always followed by an even number.

The numbers 5 and 32 give the same result.

// Javascript Algorithm
function step(n) {
if (n%2 == 0) return n/2;
return 3*n+1;
}
function collatz(n) {
var nb = 1;
while (n != 1) {
n = step(n);
nb++;
}
return nb;
}
// Python Code Algo
def collatz(x):
while x != 1:
if x % 2 > 0:
x =((3 * x) + 1)
list_.append(x)
else:
x = (x / 2)
list_.append(x)
return list_


The Collatz conjecture is also known as

- 3n + 1 conjecture

- Ulam conjecture

- Kakutani's problem

- Thwaites conjecture

- Hasse's algorithm

- Syracuse problem

This table is for numbers until 1000 (total time => numbers)

This table shows numbers until 1000 (max number reached => numbers)

Formulated in 1937 it remains unsolved: nobody has been able to prove this conjecture always ends with 1.