𝑳 生成卢卡斯数Generate Lucas Numbers
生成卢卡斯数列：L0=2，L1=1，之后每项为前两项之和。可设项数与起点下标，本地处理。Generate Lucas numbers: L0=2, L1=1, then each term is the sum of the previous two. Set count and start index. Processed locally.
使用说明与常见问题How-to & FAQ
「生成卢卡斯数」是什么？What is the Generate Lucas Numbers tool?
生成卢卡斯数列：L0=2，L1=1，之后每项为前两项之和。可设项数与起点下标，本地处理。Generate Lucas numbers: L0=2, L1=1, then each term is the sum of the previous two. Set count and start index. Processed locally.
如何使用「生成卢卡斯数」？How do I use the Generate Lucas Numbers tool?
在「生成卢卡斯数」中，按需设置「项数」、「起点下标」，结果会实时显示在下方，点击「复制结果」即可复制。In the Generate Lucas Numbers: Adjust "Terms", "Start index"; the result appears below instantly — click "Copy result" to copy it.
卢卡斯数和斐波那契数有什么关系？How are Lucas numbers related to Fibonacci numbers?
递推规则相同（每项等于前两项之和），只是起始值为 L0 = 2、L1 = 1，而斐波那契是 0、1。两者满足 L_n = F_{n−1} + F_{n+1}，例如 L5 = 3 + 8 = 11。They use the same rule (each term is the sum of the previous two) but start from L0 = 2, L1 = 1 instead of 0, 1. They are linked by L_n = F_{n−1} + F_{n+1}, e.g. L5 = 3 + 8 = 11.
输入和输出是什么样的？What does the input and output look like?
例如在「生成卢卡斯数」中把「项数」设为 5，「起点下标」设为 0，输出为：2 ⏎ 1 ⏎ 3 ⏎ 4 ⏎ 7（⏎ 表示换行）。For example, in the Generate Lucas Numbers with "Terms" set to 5, "Start index" set to 0, the output is: 2 ⏎ 1 ⏎ 3 ⏎ 4 ⏎ 7 (⏎ marks a line break).
有哪些选项可以调整？What options can I adjust?
「生成卢卡斯数」的设置：「项数」默认 15；「起点下标」默认 0。每次生成结果都按当前设置处理。Settings in the Generate Lucas Numbers — "Terms" default 15; "Start index" default 0. The result always uses the current settings.
计算精度如何？How precise are the results?
「生成卢卡斯数」中的整数都用大整数（BigInt）精确计算，不经过浮点，所以再长的项也不会丢失位数；输入超出页面说明的范围时会给出提示，而不是悄悄截断。Integers in the Generate Lucas Numbers are computed exactly with big integers (BigInt), with no floating-point step, so even very long terms keep every digit; values outside the stated ranges give a message instead of being silently cut off.
「生成卢卡斯数」免费吗？需要注册吗？Is the Generate Lucas Numbers free? Do I need an account?
「生成卢卡斯数」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 Generate Lucas Numbers is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.