141 lines
3.2 KiB
Markdown
141 lines
3.2 KiB
Markdown
---
|
||
id: 594ecc0d9a8cf816e3340187
|
||
title: Taxicab numbers
|
||
challengeType: 5
|
||
forumTopicId: 302337
|
||
dashedName: taxicab-numbers
|
||
---
|
||
|
||
# --description--
|
||
|
||
A [taxicab number](<https://en.wikipedia.org/wiki/Hardy–Ramanujan number> "wp: Hardy–Ramanujan number") (the definition that is being used here) is a positive integer that can be expressed as the sum of two positive cubes in more than one way.
|
||
|
||
The first taxicab number is `1729`, which is:
|
||
|
||
1<sup>3</sup> + 12<sup>3</sup> and
|
||
|
||
9<sup>3</sup> + 10<sup>3</sup>.
|
||
|
||
Taxicab numbers are also known as:
|
||
|
||
<ul>
|
||
<li>taxi numbers</li>
|
||
<li>taxi-cab numbers</li>
|
||
<li>taxi cab numbers</li>
|
||
<li>Hardy-Ramanujan numbers</li>
|
||
</ul>
|
||
|
||
# --instructions--
|
||
|
||
Write a function that returns the lowest `n` taxicab numbers. For each of the taxicab numbers, show the number as well as its constituent cubes.
|
||
|
||
**See also:**
|
||
|
||
<ul>
|
||
<li><a href='https://oeis.org/A001235' target='_blank'>A001235 taxicab numbers</a> on The On-Line Encyclopedia of Integer Sequences.</li>
|
||
<li><a href='https://en.wikipedia.org/wiki/Taxicab_number' target='_blank'>taxicab number</a> on Wikipedia.</li>
|
||
</ul>
|
||
|
||
# --hints--
|
||
|
||
`taxicabNumbers` should be a function.
|
||
|
||
```js
|
||
assert(typeof taxicabNumbers === 'function');
|
||
```
|
||
|
||
`taxicabNumbers` should return an array.
|
||
|
||
```js
|
||
assert(typeof taxicabNumbers(2) === 'object');
|
||
```
|
||
|
||
`taxicabNumbers` should return an array of numbers.
|
||
|
||
```js
|
||
assert(typeof taxicabNumbers(100)[0] === 'number');
|
||
```
|
||
|
||
`taxicabNumbers(4)` should return [1729, 4104, 13832, 20683].
|
||
|
||
```js
|
||
assert.deepEqual(taxicabNumbers(4), res4);
|
||
```
|
||
|
||
`taxicabNumbers(25)` should return [1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, 65728, 110656, 110808, 134379, 149389, 165464, 171288, 195841, 216027, 216125, 262656, 314496, 320264, 327763, 373464, 402597]
|
||
|
||
```js
|
||
assert.deepEqual(taxicabNumbers(25), res25);
|
||
```
|
||
|
||
`taxicabNumbers(39)` resulting numbers from 20 - 29 should be [314496,320264,327763,373464,402597,439101,443889,513000,513856].
|
||
|
||
```js
|
||
assert.deepEqual(taxicabNumbers(39).slice(20, 29), res39From20To29);
|
||
```
|
||
|
||
# --seed--
|
||
|
||
## --after-user-code--
|
||
|
||
```js
|
||
const res4 = [1729, 4104, 13832, 20683];
|
||
const res25 = [
|
||
1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, 65728, 110656,
|
||
110808, 134379, 149389, 165464, 171288, 195841, 216027, 216125, 262656, 314496, 320264, 327763,
|
||
373464, 402597
|
||
];
|
||
|
||
const res39From20To29 = [314496, 320264, 327763, 373464, 402597, 439101, 443889, 513000, 513856];
|
||
```
|
||
|
||
## --seed-contents--
|
||
|
||
```js
|
||
function taxicabNumbers(n) {
|
||
|
||
return true;
|
||
}
|
||
```
|
||
|
||
# --solutions--
|
||
|
||
```js
|
||
function taxicabNumbers(nNumbers) {
|
||
const cubeN = [];
|
||
const s3s = {};
|
||
|
||
const e = 100;
|
||
for (let n = 1; n < e; n += 1) {
|
||
cubeN[n] = n * n * n;
|
||
}
|
||
|
||
for (let a = 1; a < e - 1; a += 1) {
|
||
const a3 = cubeN[a];
|
||
for (let b = a; b < e; b += 1) {
|
||
const b3 = cubeN[b];
|
||
const s3 = a3 + b3;
|
||
|
||
let abs = s3s[s3];
|
||
if (!abs) {
|
||
s3s[s3] = abs = [];
|
||
}
|
||
abs.push([a, b]);
|
||
}
|
||
}
|
||
|
||
let i = 0;
|
||
const res = [];
|
||
Object.keys(s3s).forEach(s3 => {
|
||
const abs = s3s[s3];
|
||
if (abs.length >= 2) { // No two cube pairs found
|
||
i += 1;
|
||
if (i <= nNumbers) {
|
||
res.push(s3);
|
||
}
|
||
}
|
||
});
|
||
return res.map(item => parseInt(item, 10));
|
||
}
|
||
```
|