Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 | 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x | /**
* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MODULES //
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var isInteger = require( '@stdlib/math/base/assert/is-integer' );
var ln = require( '@stdlib/math/base/special/ln' );
var floor = require( '@stdlib/math/base/special/floor' );
var PHI = require( '@stdlib/constants/float64/phi' );
var PINF = require( '@stdlib/constants/float64/pinf' );
// VARIABLES //
var SQRT_5 = 2.23606797749979;
var LN_PHI = ln( PHI );
// MAIN //
/**
* Computes the nth non-Fibonacci number.
*
* ## 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>.
*
* @param {NonNegativeInteger} n - the non-Fibonacci number to compute
* @returns {NonNegativeInteger} non-Fibonacci number
*
* @example
* var v = nonfibonacci( 1 );
* // returns 4
*
* @example
* var v = nonfibonacci( 2 );
* // returns 6
*
* @example
* var v = nonfibonacci( 3 );
* // returns 7
*
* @example
* var v = nonfibonacci( NaN );
* // returns NaN
*
* @example
* var v = nonfibonacci( 3.14 );
* // returns NaN
*
* @example
* var v = nonfibonacci( -1 );
* // returns NaN
*/
function nonfibonacci( n ) {
var a;
var b;
if (
isnan( n ) ||
isInteger( n ) === false ||
n < 1 ||
n === PINF
) {
return NaN;
}
n += 1;
a = ln( n * SQRT_5 ) / LN_PHI;
b = ln( (SQRT_5 * (n+a)) - 5.0 + (3.0/n) ) / LN_PHI;
return floor( n + b - 2.0 );
}
// EXPORTS //
module.exports = nonfibonacci;
|