1.8 KiB
1.8 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f3891000cf542c50fe9c | Problem 29: Distinct powers | 5 | 301941 | problem-29-distinct-powers |
--description--
Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
22=4, 23=8, 24=16, 25=32
32=9, 33=27, 34=81, 35=243
42=16, 43=64, 44=256, 45=1024
52=25, 53=125, 54=625, 55=3125
32=9, 33=27, 34=81, 35=243
42=16, 43=64, 44=256, 45=1024
52=25, 53=125, 54=625, 55=3125
If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
How many distinct terms are in the sequence generated by ab
for 2 ≤ a
≤ n
and 2 ≤ b
≤ n
?
--hints--
distinctPowers(15)
should return a number.
assert(typeof distinctPowers(15) === 'number');
distinctPowers(15)
should return 177.
assert.strictEqual(distinctPowers(15), 177);
distinctPowers(20)
should return 324.
assert.strictEqual(distinctPowers(20), 324);
distinctPowers(25)
should return 519.
assert.strictEqual(distinctPowers(25), 519);
distinctPowers(30)
should return 755.
assert.strictEqual(distinctPowers(30), 755);
--seed--
--seed-contents--
function distinctPowers(n) {
return n;
}
distinctPowers(30);
--solutions--
const distinctPowers = (n) => {
let list = [];
for (let a=2; a<=n; a++) {
for (let b=2; b<=n; b++) {
let term = Math.pow(a, b);
if (list.indexOf(term)===-1) list.push(term);
}
}
return list.length;
};