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

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# iterNonFibonacciSeq

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Create an iterator which generates a [non-Fibonacci integer sequence][fibonacci-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 nth [non-Fibonacci number][fibonacci-number] is given by

<!-- <equation class="equation" label="eq:nonfibonacci_number" align="center" raw="f(n) = \left \lfloor{ n + 1 + \log_\varphi \biggl( \sqrt{5}( n + 1 + \log_\varphi(\sqrt{5}(n+1))) - 5 + \tfrac{3}{n+1} \biggr) - 2 } \right \rfloor" alt="Formula to compute the nth non-Fibonacci number."> -->

<div class="equation" align="center" data-raw-text="f(n) = \left \lfloor{ n + 1 + \log_\varphi \biggl( \sqrt{5}( n + 1 + \log_\varphi(\sqrt{5}(n+1))) - 5 + \tfrac{3}{n+1} \biggr) - 2 } \right \rfloor" data-equation="eq:nonfibonacci_number">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@aa77a2f6e76d2e9da5b49bffa45ee5167d6c16e1/lib/node_modules/@stdlib/math/iter/sequences/nonfibonacci/docs/img/equation_nonfibonacci_number.svg" alt="Formula to compute the nth non-Fibonacci number.">
    <br>
</div>

<!-- </equation> -->

where `φ` is the [golden ratio][golden-ratio].

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### iterNonFibonacciSeq( \[options] )

Returns an iterator which generates a [non-Fibonacci integer sequence][fibonacci-number].

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

var v = it.next().value;
// returns 4

v = it.next().value;
// returns 6

v = it.next().value;
// returns 7

// ...
```

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: `1e308`.

By default, the function returns an infinite iterator (i.e., an iterator which never ends). To limit the number of iterations, set the `iter` option.

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

var v = it.next().value;
// returns 4

v = it.next().value;
// returns 6

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 iterNonFibonacciSeq = require( '@stdlib/math-iter-sequences-nonfibonacci' );

// Create an iterator:
var opts = {
    'iter': 100
};
var it = iterNonFibonacciSeq( opts );

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

</section>

<!-- /.examples -->

<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

* * *

<section class="references">

## References

-   Gould, H.W. 1965. "Non-Fibonacci Numbers." _Fibonacci Quarterly_, no. 3: 177–83. [&lt;http://www.fq.math.ca/Scanned/3-3/gould.pdf>][@gould:1965a].
-   Farhi, Bakir. 2011. "An explicit formula generating the non-Fibonacci numbers." _arXiv_ abs/1105.1127 \[Math.NT] (May): 1–5. [&lt;https://arxiv.org/abs/1105.1127>][@farhi:2011a].

</section>

<!-- /.references -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math-base/special/nonfibonacci`][@stdlib/math/base/special/nonfibonacci]</span><span class="delimiter">: </span><span class="description">compute the nth non-Fibonacci 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>

</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

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

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

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[fibonacci-number]: https://en.wikipedia.org/wiki/Fibonacci_number

[golden-ratio]: https://en.wikipedia.org/wiki/Golden_ratio

[@gould:1965a]: http://www.fq.math.ca/Scanned/3-3/gould.pdf

[@farhi:2011a]: https://arxiv.org/abs/1105.1127

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

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