Lucas Number Calculator
Find any Lucas number exactly, using big integers past term 76.
What is Lucas Numbers?
The Lucas sequence is the Fibonacci sequence's twin: it starts 2, 1 instead of 0, 1 and otherwise adds the previous two terms — 2, 1, 3, 4, 7, 11, 18, … Because both obey the same recurrence, L(n) = F(n − 1) + F(n + 1), and the ratio of consecutive Lucas terms converges on the same golden ratio φ ≈ 1.6180339887.
How it works
Values are computed as exact integers with BigInt, from the same fast-doubling pair that backs the Fibonacci page — L(n) = 2F(n + 1) − F(n) — so term 100,000 is instant and no least-significant digit is ever guessed at. L(76) is the last Lucas number a JavaScript number holds exactly, one term before F(78), and the page says which side of that line you are on.
- Enter your input. Type or paste your input into the field above — the tool responds instantly.
- Review the result. Output updates live as you type. Everything runs entirely in your browser.
- Copy or download. Use the Copy button to grab the result, or Download to save it as a file.
Examples
Realistic sample
Type or paste any realistic input — the tool computes the result locally and instantly.
Common mistakes
Expecting a server round-trip
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