time-to-botec/squiggle/node_modules/@stdlib/math/iter/sequences/nonfibonacci/README.md

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# iterNonFibonacciSeq

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

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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>

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<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>

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<!-- 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>

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<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 -->

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* * *

<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>

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<section class="links">

[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

</section>

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