3.2 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
594ecc0d9a8cf816e3340187 | Taxicab numbers | 5 | 302337 | taxicab-numbers |
--description--
A taxicab 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:
13 + 123 and
93 + 103.
Taxicab numbers are also known as:
- taxi numbers
- taxi-cab numbers
- taxi cab numbers
- Hardy-Ramanujan numbers
--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:
- A001235 taxicab numbers on The On-Line Encyclopedia of Integer Sequences.
- taxicab number on Wikipedia.
--hints--
taxicabNumbers
should be a function.
assert(typeof taxicabNumbers === 'function');
taxicabNumbers
should return an array.
assert(typeof taxicabNumbers(2) === 'object');
taxicabNumbers
should return an array of numbers.
assert(typeof taxicabNumbers(100)[0] === 'number');
taxicabNumbers(4)
should return [1729, 4104, 13832, 20683].
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]
assert.deepEqual(taxicabNumbers(25), res25);
taxicabNumbers(39)
resulting numbers from 20 - 29 should be [314496,320264,327763,373464,402597,439101,443889,513000,513856].
assert.deepEqual(taxicabNumbers(39).slice(20, 29), res39From20To29);
--seed--
--after-user-code--
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--
function taxicabNumbers(n) {
return true;
}
--solutions--
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));
}