Collatz Calculator

✓ Reviewed by David Chen, CFA | Mathematical Logic & Finance Specialist

Explore the mysteries of the $3n+1$ problem with our Collatz Calculator. Simply input any positive integer to visualize its path to unity and discover the total stopping time and peak values of the sequence.

Collatz Calculator

Collatz Calculator Formula:

For any positive integer n:

• If n is even: n = n / 2
• If n is odd: n = 3n + 1

Formula Source: Wolfram MathWorld | Wikipedia

Variables:

• Starting Number (n): Any positive integer you wish to test.
• Total Steps: The number of iterations required for the sequence to reach 1.
• Peak Value: The highest number achieved during the sequence.

Related Calculators:

• Prime Factorization Tool
• Fibonacci Sequence Generator
• Arithmetic Progression Solver
• Number Base Converter

What is Collatz Calculator?

The Collatz Calculator is a tool designed to process the Collatz Conjecture, also known as the $3n+1$ problem. This mathematical mystery suggests that regardless of the starting positive integer, the sequence will always eventually reach the number 1.

Despite its simple rules, the conjecture remains one of the most famous unsolved problems in mathematics. Our calculator helps researchers and students visualize the “hailstone numbers”—so-called because the values rise and fall like hailstones in a cloud before falling to earth (the number 1).

How to Calculate Collatz Calculator (Example):

Let’s calculate the sequence for n = 6:

1. 6 is even: 6 / 2 = 3
2. 3 is odd: (3 * 3) + 1 = 10
3. 10 is even: 10 / 2 = 5
4. 5 is odd: (5 * 3) + 1 = 16
5. 16 is even: 16 / 2 = 8
6. 8 is even: 8 / 2 = 4
7. 4 is even: 4 / 2 = 2
8. 2 is even: 2 / 2 = 1 (Stop)

Total steps: 8. Peak value: 16.

Frequently Asked Questions (FAQ):

Is there a number that doesn’t reach 1? No such number has been found yet, even though billions of numbers have been tested by computers.

Why is it called the “Hailstone” sequence? Because the numbers fluctuate wildly up and down before reaching the ground state of 1.

Can I input negative numbers? No, the Collatz Conjecture specifically applies to positive integers.

Who invented the Collatz Conjecture? It was introduced by Lothar Collatz in 1937, though it is also known as Ulam’s conjecture or Kakutani’s problem.