learn.howToCalculate
learn.whatIsHeading
The Collatz conjecture states that for any positive integer, repeatedly applying the rule: if even divide by 2, if odd multiply by 3 and add 1 — will always eventually reach 1. It remains one of mathematics' most famous unsolved problems.
공식
If n even: n → n/2; If n odd: n → 3n+1
- n
- positive integer — starting value for the sequence
- s
- stopping time — number of steps to reach 1
단계별 가이드
- 1If n is even: next = n / 2
- 2If n is odd: next = 3n + 1
- 3Continue until reaching 1
- 4The number of steps is called the "stopping time"
풀어진 예시
입력
n = 6
결과
6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1 (8 steps)
입력
n = 27
결과
111 steps, reaches maximum of 9,232
자주 묻는 질문
Is the Collatz conjecture proven?
No, it remains one of mathematics' great unsolved problems despite being tested for numbers up to 2⁶⁸.
Why does the Collatz sequence sometimes increase dramatically?
Odd numbers multiply by 3, creating larger values. But many steps follow: divide by 2 repeatedly until odd again.
What is the longest known Collatz stopping time?
For starting values tested, stopping times are in the hundreds. 27 requires 111 steps.
계산할 준비가 되셨나요? 무료 Collatz Sequence 계산기를 사용해 보세요
직접 시도해 보세요 →