Non-Fibonacci

Compute the nth non-Fibonacci number.

The nth non-Fibonacci number is given by

where φ is the golden ratio.

Installation

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

Usage

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

nonfibonacci( n )

Computes the nth non-Fibonacci number.

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.

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

v = nonfibonacci( 3.14 );
// returns NaN

If provided NaN, the function returns NaN.

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

Examples

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 );
}

C APIs

Usage

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

stdlib_base_nonfibonacci( x )

Computes the nth non-Fibonacci number.

double out = stdlib_base_nonfibonacci( 1 );
// returns 4

out = stdlib_base_nonfibonacci( 2 );
// returns 6

The function accepts the following arguments:

• x: [in] int32_t input value.

double stdlib_base_nonfibonacci( const int32_t x );

Examples

#include "stdlib/math/base/special/nonfibonacci.h"
#include <stdio.h>
#include <stdlib.h>
int main( void ) {
    int i;
    for ( i = 1; i < 12; i++ ) {
        double result = stdlib_base_nonfibonacci( i );
        printf( "x: %i => result: %lf", i , result );
    }
}

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>.

See Also

• @stdlib/math-base/special/fibonacci: compute the nth Fibonacci number.

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

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.