npm package: @stdlib/math-iter-sequences-lucas
Description: Create an iterator which generates a Lucas sequence.
Author: The Stdlib Authors
Latest version: 0.2.3

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# iterLucasSeq

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> Create an iterator which generates a [Lucas sequence][lucas-number].

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

The [Lucas numbers][lucas-number] are the integer sequence

<!-- <equation class="equation" label="eq:lucas_sequence" align="center" raw="2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, \ldots" alt="Lucas sequence"> -->

<div class="equation" align="center" data-raw-text="2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, \ldots" data-equation="eq:lucas_sequence">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@aa77a2f6e76d2e9da5b49bffa45ee5167d6c16e1/lib/node_modules/@stdlib/math/iter/sequences/lucas/docs/img/equation_lucas_sequence.svg" alt="Lucas sequence">
    <br>
</div> -->

<!-- </equation> -->

The sequence is defined by the recurrence relation

<!-- <equation class="equation" label="eq:lucas_recurrence_relation" align="center" raw="L_n = \begin{cases}2 & \textrm{if}\ n = 0\\1 & \textrm{if}\ n = 1\\L_{n-1} + L_{n-2} & \textrm{if}\ n > 1\end{cases}" alt="Lucas sequence recurrence relation"> -->

<!-- <div class="equation" align="center" data-raw-text="L_n = \begin{cases}2 &amp; \textrm{if}\ n = 0\\1 &amp; \textrm{if}\ n = 1\\L_{n-1} + L_{n-2} &amp; \textrm{if}\ n &gt; 1\end{cases}" data-equation="eq:lucas_recurrence_relation">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@aa77a2f6e76d2e9da5b49bffa45ee5167d6c16e1/lib/node_modules/@stdlib/math/iter/sequences/lucas/docs/img/equation_lucas_recurrence_relation.svg" alt="Lucas sequence recurrence relation">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-iter-sequences-lucas
```

</section>

<section class="usage">

## Usage

```javascript
var iterLucasSeq = require( '@stdlib/math-iter-sequences-lucas' );
```

#### iterLucasSeq( \[options] )

Returns an iterator which generates a [Lucas sequence][lucas-number].

```javascript
var it = iterLucasSeq();
// returns <Object>

var v = it.next().value;
// returns 2

v = it.next().value;
// returns 1

v = it.next().value;
// returns 3

// ...
```

The returned iterator protocol-compliant object has the following properties:

-   **next**: function which returns an iterator protocol-compliant object containing the next iterated value (if one exists) assigned to a `value` property and a `done` property having a `boolean` value indicating whether the iterator is finished.
-   **return**: function which closes an iterator and returns a single (optional) argument in an iterator protocol-compliant object.

The function supports the following `options`:

-   **iter**: number of iterations. Default: `77`.

The returned iterator can only generate the first `77` [Lucas numbers][lucas-number], as larger [Lucas numbers][lucas-number] cannot be safely represented in [double-precision floating-point format][ieee754]. By default, the function returns an iterator which generates all `77` numbers. To limit the number of iterations, set the `iter` option.

```javascript
var opts = {
    'iter': 2
};
var it = iterLucasSeq( opts );
// returns <Object>

var v = it.next().value;
// returns 2

v = it.next().value;
// returns 1

var bool = it.next().done;
// returns true
```

</section>

<!-- /.usage -->

<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

## Notes

-   If an environment supports `Symbol.iterator`, the returned iterator is iterable.

</section>

<!-- /.notes -->

<!-- Package usage examples. -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var iterLucasSeq = require( '@stdlib/math-iter-sequences-lucas' );

// Create an iterator:
var it = iterLucasSeq();

// Perform manual iteration...
var v;
while ( true ) {
    v = it.next();
    if ( v.done ) {
        break;
    }
    console.log( v.value );
}
```

</section>

<!-- /.examples -->

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<section class="references">

</section>

<!-- /.references -->

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<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math-base/special/lucas`][@stdlib/math/base/special/lucas]</span><span class="delimiter">: </span><span class="description">compute the nth Lucas number.</span>
-   <span class="package-name">[`@stdlib/math-iter/sequences/fibonacci`][@stdlib/math/iter/sequences/fibonacci]</span><span class="delimiter">: </span><span class="description">create an iterator which generates a Fibonacci sequence.</span>
-   <span class="package-name">[`@stdlib/math-iter/sequences/negalucas`][@stdlib/math/iter/sequences/negalucas]</span><span class="delimiter">: </span><span class="description">create an iterator which generates a negaLucas sequence.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[lucas-number]: https://en.wikipedia.org/wiki/Lucas_number

[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985

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[@stdlib/math/base/special/lucas]: https://www.npmjs.com/package/@stdlib/math-base-special-lucas

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