README.md

About stdlib...

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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.

Usage

import nonfibonaccif from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-nonfibonaccif@deno/mod.js';

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

import nonfibonaccif from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-nonfibonaccif@deno/mod.js';

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