time-to-botec

README.md (5164B)

---

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 # iterNonFibonacciSeq
 
 > Create an iterator which generates a [non-Fibonacci integer sequence][fibonacci-number].
 
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 <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>
 
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 <!-- Package usage documentation. -->
 
 <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>
 
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 <!-- 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 -->
 
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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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