# Collatz conjecture

The Collatz conjecture is a conjecture (an idea which many people think is likely) in mathematics. It is named after Lothar Collatz. He first proposed it in 1937.[1] It is about what happens when something is done repeatedly (over and over) starting at some number n:[1][2]

• If n is even (divisible by two), n is halved (divide by two = take its half).
• If n is odd (not divisible by two), n is changed to $3n+1$.

The conjecture states that n will always reach one. Here is an example sequence:

• 9
• 28 (9 is odd, so we triple it and add one)
• 14 (28 is even; 14 is half of 28)
• 7 (14 is even, 7 is its half)
• 22 ($22 = 3 \times 7 + 1$)
• 11
• 34
• 17
• 52
• 26
• 13
• 40
• 20
• 10
• 5
• 16 (16 is a power of two, so it will lead to 1, halving each time)
• 8
• 4
• 2
• 1 (after 1 comes 4, 2, 1, 4, 2, 1, etc.)