Non-Fibonacci
Compute the nth non-Fibonacci number.
The nth non-Fibonacci number is given by
where φ is the golden ratio.
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_tinput 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>.