Lucas Number Calculator
Calculate the nth Lucas number and list the sequence. Lucas numbers follow the same rule as Fibonacci but start with 2 and 1.
Last reviewed by the Radiatus Cloud team
Generate the Lucas sequence, a cousin of the Fibonacci numbers.
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Generate Lucas numbers
The Lucas numbers are a sequence closely related to the Fibonacci numbers, following the exact same rule that each term is the sum of the previous two, but starting from two and one instead of zero and one. This gives the sequence two, one, three, four, seven, eleven, eighteen, twenty-nine, and so on. This calculator generates as many terms as you request. Like Fibonacci, the ratio of consecutive Lucas numbers approaches the golden ratio.
The tenth Lucas number is one hundred and twenty-three.
Fibonacci companion
Lucas numbers and Fibonacci numbers are deeply intertwined, satisfying many elegant identities, and together they illuminate the mathematics of the golden ratio. Named after the mathematician Edouard Lucas, who also studied Fibonacci numbers, the Lucas sequence appears in number theory and in primality testing. Every Lucas number can be expressed in terms of the golden ratio, just like its Fibonacci counterpart.
Exploring Lucas numbers alongside Fibonacci reveals how the same recurrence produces different but related patterns depending on the starting values. All calculation happens locally in your browser.
About this tool
Because the lucas number calculator runs entirely in your browser, you can use it as many times as you like for free, with nothing uploaded and no sign-up required. Everything is computed locally on your own device, so it is fast and private.
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Frequently Asked Questions
What are Lucas numbers?
A sequence following the same add-the-previous-two rule as Fibonacci, but starting from two and one, giving two, one, three, four, seven and so on.
How do they relate to Fibonacci?
They use the identical recurrence and share many identities, and both have consecutive ratios that approach the golden ratio.
Who are they named after?
Edouard Lucas, a nineteenth-century mathematician who studied the Fibonacci sequence and gave it its modern name.
Where are Lucas numbers used?
In number theory, in identities linking them to Fibonacci and the golden ratio, and in some primality-testing methods.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Enter how many terms to generate.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.