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Non-Fibonacci

Compute the nth non-Fibonacci single-precision floating-point number.

The nth non-Fibonacci number is given by

$$f(n) = \left \lfloor{ n + 1 + \log_\varphi \biggl( \sqrt{5}( n + 1 + \log_\varphi(\sqrt{5}(n+1))) - 5 + \tfrac{3}{n+1} \biggr) - 2 } \right \rfloor$$

where φ is the golden ratio.

Installation

npm install @stdlib/math-base-special-nonfibonaccif

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var nonfibonaccif = require( '@stdlib/math-base-special-nonfibonaccif' );

nonfibonaccif( n )

Computes the nth non-Fibonacci single-precision floating-point number.

var v = nonfibonaccif( 1 );
// returns 4

v = nonfibonaccif( 2 );
// returns 6

v = nonfibonaccif( 3 );
// returns 7

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

var v = nonfibonaccif( -1 );
// returns NaN

v = nonfibonaccif( 3.14 );
// returns NaN

If provided NaN, the function returns NaN.

var v = nonfibonaccif( NaN );
// returns NaN

Examples

var nonfibonaccif = require( '@stdlib/math-base-special-nonfibonaccif' );

var i;
for ( i = 1; i < 100; i++ ) {
    console.log( 'nonfibonaccif(%d) = %d', i, nonfibonaccif( i ) );
}

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C APIs

Usage

#include "stdlib/math/base/special/nonfibonaccif.h"

stdlib_base_nonfibonaccif( x )

Computes the nth non-Fibonacci single-precision floating-point number.

float out = stdlib_base_nonfibonaccif( 1 );
// returns 4.0f

out = stdlib_base_nonfibonaccif( 2 );
// returns 6.0f

The function accepts the following arguments:

• x: [in] int32_t input value.

float stdlib_base_nonfibonaccif( const int32_t x );

Examples

#include "stdlib/math/base/special/nonfibonaccif.h"
#include <stdio.h>

int main( void ) {
    int i;
    
    for ( i = 1; i < 12; i++ ) {
        printf( "x: %i => result: %f", i , stdlib_base_nonfibonaccif( i ) );
    }
}

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References

• Gould, H.W. 1965. "Non-Fibonacci Numbers." Fibonacci Quarterly, no. 3: 177–83. <http://www.fq.math.ca/Scanned/3-3/gould.pdf>.
• Farhi, Bakir. 2011. "An explicit formula generating the non-Fibonacci numbers." arXiv abs/1105.1127 [Math.NT] (May): 1–5. <https://arxiv.org/abs/1105.1127>.

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Notice

This package is part of 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, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.