Collatz Conjecture Calculator

The 3n+1 problem

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About Collatz Conjecture Calculator

A Collatz conjecture calculator exploring the 3n+1 problem. If n is even, divide by 2; if odd, compute 3n+1. Shows sequence, stopping time, maximum value reached, and odd/even step counts. All calculations are client-side.

Collatz Conjecture Calculator Features

  • Sequence
  • Stopping time
  • Max value
  • Step counts
  • Table
Collatz: if n even → n/2, if n odd → 3n+1. Conjecture: every positive integer eventually reaches 1. Verified up to ~10²⁰. Stopping time: steps to reach 1. Record high trajectories at n=27 (111 steps, max 9232).

How to Use

Enter starting value:

  • n: Positive integer
  • Steps: To reach 1
  • Sequence: Full trajectory

Records

n=27: 111 steps, peak 9232. n=871: 178 steps. n=6171: 262 steps. The longest trajectories don't always come from the largest starting values.

Theory

Unsolved since 1937. Erdős: 'Mathematics is not yet ready for such problems.' Tao (2019): 'almost all' orbits reach values below any function f(n)→∞. No counterexample found.

Step-by-Step Instructions

  1. 1Enter n.
  2. 2View sequence.
  3. 3Count steps.
  4. 4Find max value.
  5. 5Compare records.

Collatz Conjecture Calculator — Frequently Asked Questions

Has the Collatz conjecture been proven?+

No! It remains one of the most famous unsolved problems. Verified computationally for all n up to about 10²⁰. Terence Tao (2019) proved that 'almost all' starting values eventually reach small values, but a complete proof remains elusive. Paul Erdős offered $500 for a proof.

Why is it so hard to prove?+

The sequence mixes multiplication (3n+1) and division (n/2) in an unpredictable pattern. There's no obvious structure to exploit. Some orbits go very high before descending (n=27 reaches 9232). The problem connects to dynamics, number theory, and computability theory.

Are there generalizations?+

Yes! 5n+1 has cycles not reaching 1 (e.g., 13→66→33→166→83→416→208→104→52→26→13). The qn+1 problem for various q has been studied. In negative integers, the 3n+1 map has several known cycles.

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