🔁 考拉兹猜想（3n+1）计算器Collatz Conjecture Calculator
输入正整数 n，按「偶数除以 2、奇数乘 3 加 1」反复迭代，给出到达 1 的步数、过程中的最大值、奇偶步数和完整序列；用大整数计算，支持最多 100 位的起始数。Enter a positive whole number n and apply 'halve if even, 3n + 1 if odd' until it reaches 1 — with the number of steps, the highest value reached, the odd and even step counts and the full sequence. Big integers allow starting numbers up to 100 digits.
使用说明与常见问题How-to & FAQ
「考拉兹猜想（3n+1）计算器」是什么？What is the Collatz Conjecture Calculator tool?
输入正整数 n，按「偶数除以 2、奇数乘 3 加 1」反复迭代，给出到达 1 的步数、过程中的最大值、奇偶步数和完整序列；用大整数计算，支持最多 100 位的起始数。Enter a positive whole number n and apply 'halve if even, 3n + 1 if odd' until it reaches 1 — with the number of steps, the highest value reached, the odd and even step counts and the full sequence. Big integers allow starting numbers up to 100 digits.
如何使用「考拉兹猜想（3n+1）计算器」？How do I use the Collatz Conjecture Calculator tool?
在「考拉兹猜想（3n+1）计算器」中，填写「起始数 n」等参数，结果会随输入实时计算并显示在下方。In the Collatz Conjecture Calculator: Fill in "Starting number n"; results are recalculated instantly as you type.
考拉兹猜想是什么？What is the Collatz conjecture?
任取正整数 n：偶数就除以 2，奇数就乘 3 再加 1，如此反复。猜想认为无论从哪个数开始，最终都会到达 1（之后进入 4 → 2 → 1 循环）。这一猜想至今未被证明，但已用计算机验证到约 2⁶⁸。Take any positive whole number n: halve it if even, otherwise triple it and add 1, and repeat. The conjecture says every starting number eventually reaches 1 (then cycles 4 → 2 → 1). It is still unproved, but computers have checked it up to about 2⁶⁸.
步数是怎么数的？How are steps counted?
每做一次「÷2」或「×3+1」算一步，到达 1 时停止，即「总停止时间」。例如 6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1 共 8 步；27 需要 111 步，途中最高到 9,232。Each halving or 3n + 1 counts as one step, stopping at 1 (the total stopping time). For example 6 → 3 → 10 → 5 → 16 → 8 → 4 → 2 → 1 takes 8 steps; 27 takes 111 steps and peaks at 9,232.
有什么限制？Are there limits?
起始数最多 100 位，用 BigInt 精确计算；超过 1,000,000 步会停止（实际上 100 位以内的数远用不了这么多步）。序列超过 120 项时只显示前 60 项和结尾。Starting numbers can have up to 100 digits and are computed exactly with BigInt; the run stops after 1,000,000 steps (far more than any 100-digit number needs in practice). Sequences longer than 120 terms show the first 60 terms and the ending.
计算精度如何？How precise are the results?
「考拉兹猜想（3n+1）计算器」使用 JavaScript 双精度浮点数（约 15–16 位有效数字），部分功能使用 BigInt 处理大整数。The Collatz Conjecture Calculator uses double-precision floating point (about 15–16 significant digits); some features use BigInt for large integers.
「考拉兹猜想（3n+1）计算器」免费吗？需要注册吗？Is the Collatz Conjecture Calculator free? Do I need an account?
「考拉兹猜想（3n+1）计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Collatz Conjecture Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.