npm package: @stdlib/math-base-special-nonfibonacci
Description: Compute the nth non-Fibonacci number.
Author: The Stdlib Authors
Latest version: 0.4.1

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# Non-Fibonacci

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

> Compute the nth [non-Fibonacci number][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@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/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-base-special-nonfibonacci
```

</section>

<section class="usage">

## Usage

```javascript
var nonfibonacci = require( '@stdlib/math-base-special-nonfibonacci' );
```

#### nonfibonacci( n )

Computes the nth [non-Fibonacci number][fibonacci-number].

```javascript
var v = nonfibonacci( 1 );
// returns 4

v = nonfibonacci( 2 );
// returns 6

v = nonfibonacci( 3 );
// returns 7
```

If provided either a non-integer or `n < 1`, the function returns `NaN`.

```javascript
var v = nonfibonacci( -1 );
// returns NaN

v = nonfibonacci( 3.14 );
// returns NaN
```

If provided `NaN`, the function returns `NaN`.

```javascript
var v = nonfibonacci( NaN );
// returns NaN
```

</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">

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var nonfibonacci = require( '@stdlib/math-base-special-nonfibonacci' );

var v;
var i;

for ( i = 1; i < 100; i++ ) {
    v = nonfibonacci( i );
    console.log( 'nonfibonacci(%d) = %d', i, v );
}
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

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<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/nonfibonacci.h"
```

#### stdlib_base_nonfibonacci( x )

Computes the nth non-Fibonacci number.

```c
double out = stdlib_base_nonfibonacci( 1.0 );
// returns 4.0

out = stdlib_base_nonfibonacci( 2.0 );
// returns 6.0
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.

```c
double stdlib_base_nonfibonacci( const double x );
```

</section>

<!-- /.usage -->

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

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/nonfibonacci.h"
#include <stdio.h>

int main( void ) {
    double i;
    double v;

    for ( i = 1.0; i < 12.0; i++ ) {
        v = stdlib_base_nonfibonacci( i );
        printf( "nonfibonacci(%lf) = %lf\n", i, v );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- 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/fibonacci`][@stdlib/math/base/special/fibonacci]</span><span class="delimiter">: </span><span class="description">compute the nth Fibonacci number.</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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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-nonfibonacci/main/LICENSE

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

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