I often have to generate Lucas numbers so I created this simple online utility that does it for me. It lets you generate however many Lucas numbers you need starting from any position or value. It works in the browser and is powered by alien technology from the future.

Lucas Number Generator Options

Starting Position or Value
Count and Separator
Base

Lucas Number Generator Examples (click to try!)

Lucas Numbers from a Specific Position
In this example, we've selected the option that calculates Lucas numbers from a specified position. The starting number is set to 12 and it starts the Lucas series from L12. The 12th Lucas number is 322 so the series starts from this number. We generate 10 terms and separate them by the newline.
322
521
843
1364
2207
3571
5778
9349
15127
24476
Start from a Position
Find Lucas numbers starting from this position.
How many values to generate?
Separate Lucas numbers with this character.
Decimal Base
Lucas Numbers from a Specific Value
In this example, we've selected the option for computing Lucas sequence from the specified value. The starting value is set to 12 but this is not a Lucas number. To start generating the sequence, this tool finds the next largest value Ln that is a Lucas number. This value is 18 so the sequence starts from this value. This tool calculates 30 sequence values and separates them with a semicolon.
18; 29; 47; 76; 123; 199; 322; 521; 843; 1364; 2207; 3571; 5778; 9349; 15127; 24476; 39603; 64079; 103682; 167761; 271443; 439204; 710647; 1149851; 1860498; 3010349; 4870847; 7881196; 12752043; 20633239
Start from a Value
Find Lucas numbers bigger or equal to this value.
How many values to generate?
Separate Lucas numbers with this character.
Decimal Base
Large Hex Lucas Numbers
In this example, we generate 20 Lucas numbers in hexadecimal base. We start with Lucas number L100 and find the next 20 sequence members. The 100th Lucas number is huge as Ln is very close to 1.61n (or more precisely φn). In this case, L100 is about 1.61100. This number has 21 digits in base-10 and 18 digits in base-16.
2af030e8455b8bb1c7
4579bd1cc61bb9b84b
7069ee050b77456a12
b5e3ab21d192ff225d
1264d9926dd0a448c6f
1dc314448ae9d43aecc
3027edd6f8ba7883b3b
4deb021b83a44cbea07
7e12eff27c5ec542542
cbfdf20e00031200f49
14a10e2007c61d74348b
2160ed40e7c64e9443d4
3601fb60ef8c6c08785f
5762e8a1d752ba9cbc33
8d64e402c6df26a53492
e4c7cca49e31e141f0c5
1722cb0a7651107e72557
256f47d4c0342e929161c
3c9212df36853f1103b73
62015ab3f6b96da39518f
Start from a Position
Find Lucas numbers starting from this position.
How many values to generate?
Separate Lucas numbers with this character.
Hexadecimal Base

How Does This Lucas Number Generator Work?

This Lucas number generator works entirely in your browser and is written in JavaScript. It starts the sequence by creating two variables lucasPrev and lucasCurrent, and initializing them to 2 and 1, which are the first two Lucas numbers. It also creates an empty terms array that will hold the computed Lucas numbers. Each next Lucas number is calculated as a sum of lucasPrev and lucasCurrent. To generate count terms (specified in options), it creates a while() loop that keeps adding the last two Lucas values together until it finds the start position or value (specified in options). At this moment it starts terms.push()ing the Lucas numbers to the terms array. The while() loop keeps doing this until terms.length is less than count (sequence length; specified in options). When terms.length reaches count, the loop breaks and it runs base conversion code on the terms array and calls the terms.join(separator) function that joins all Lucas numbers by the separator character. This function returns a string that is then printed to your screen.

Created by Browserling

This lucas number generator was created by me and my team at Browserling. Behind the scenes, it's actually powered by our programmer tools that are used by millions of people every month. Browserling itself is an online cross-browser testing service powered by alien technology. Check it out!

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