Number 1. Collatz Conjecture/ Collatz Sequence / Ulam Conjecture / 3n+1 Conjecture / Kakutani's Problem/ Thwaites Conjecture / Hasse's Algorithm /Syracuse Problem

So the Collatz sequence is basically a series of numbers that follows this pattern:

if it's even: divide it by two (if n is even: n/2)

if it's odd: multiply it by 3 and add 1 (if n is odd: 3n+1)

For example: if you were to start with 13, you get

13 --> 40 --> 20 --> 10 --> 5 --> 16 --> 8 --> 4 --> 2 --> 1

The Collatz Problem states that any sequence of these numbers will always equal 1 thought it has not been proven yet. This conjecture was proposed by Lothar Collatz in 1937. The Ulam part is named after Stanislaw Ulam, the Kakutani after Shizuo Kakutani, Thwaites after Sir Bryan Thwaites, Hasse's after Helmut Hasses.

Ahh yes one more thing: The longest Collatz sequence under 1 million (the numbers in between may exceed 1 mil) is 837799 which is an answer to an projecteuler question but please don't cheat, actually solve it yourself because that's the fun part.

So the Collatz sequence is basically a series of numbers that follows this pattern:

if it's even: divide it by two (if n is even: n/2)

if it's odd: multiply it by 3 and add 1 (if n is odd: 3n+1)

For example: if you were to start with 13, you get

13 --> 40 --> 20 --> 10 --> 5 --> 16 --> 8 --> 4 --> 2 --> 1

The Collatz Problem states that any sequence of these numbers will always equal 1 thought it has not been proven yet. This conjecture was proposed by Lothar Collatz in 1937. The Ulam part is named after Stanislaw Ulam, the Kakutani after Shizuo Kakutani, Thwaites after Sir Bryan Thwaites, Hasse's after Helmut Hasses.

Ahh yes one more thing: The longest Collatz sequence under 1 million (the numbers in between may exceed 1 mil) is 837799 which is an answer to an projecteuler question but please don't cheat, actually solve it yourself because that's the fun part.