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---
id: 594ecc0d9a8cf816e3340187
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title: Taxicab numbers
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challengeType: 5
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forumTopicId: 302337
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dashedName: taxicab-numbers
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---
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# --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 > .
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Taxicab numbers are also known as:
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< ul >
< li > taxi numbers< / li >
< li > taxi-cab numbers< / li >
< li > taxi cab numbers< / li >
< li > Hardy-Ramanujan numbers< / li >
< / ul >
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# --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:**
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< ul >
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< 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 >
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< / ul >
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# --hints--
`taxicabNumbers` should be a function.
```js
assert(typeof taxicabNumbers === 'function');
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```
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`taxicabNumbers` should return an array.
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```js
assert(typeof taxicabNumbers(2) === 'object');
```
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`taxicabNumbers` should return an array of numbers.
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```js
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assert(typeof taxicabNumbers(100)[0] === 'number');
```
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`taxicabNumbers(4)` should return [1729, 4104, 13832, 20683].
```js
assert.deepEqual(taxicabNumbers(4), res4);
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```
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`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);
```
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# --seed--
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## --after-user-code--
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```js
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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];
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```
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## --seed-contents--
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```js
function taxicabNumbers(n) {
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return true;
}
```
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# --solutions--
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```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));
}
```