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Finding the k-prime numbers with a specific distance in a range in JavaScript
K-Prime Numbers
A natural number is called k-prime if it has exactly k prime factors, counted with multiplicity.
Which means even though the only prime factor of 4 is 2 it will be a 2-prime number because −
4 = 2 * 2 and both 2s will be counted separately taking the count to 2.
Similarly, 8 is 3-prime because 8 = 2 * 2 * 2 taking the count to 3.
Problem
We are required to write a JavaScript function that takes in a number k, a distance and a range.
Our function should return an array of arrays containing k-prime numbers within the range the distance between whom is exactly equal to the distance specified.
Example
Following is the code −
const k = 2;
const step = 2;
const range = [0, 50];
const kPrimeSteps = (k = 1, step = 1, [start, end]) => {
const res = [];
let i = start;
const findLen = (n = 1) => {
let count = 0, i = 2;
while (i * i <= n) {
while (n % i === 0) {
count++;
n /= i;
}
i++;
}
if (n > 1) count++;
return count;
}
while (i <= end - step) {
if ((findLen(i) == k && findLen(i+step) == k))
res.push([i, i+step]);
i++;
}
return res;
};
console.log(kPrimeSteps(k, step, range));Output
Following is the console output −
[ [ 4, 6 ], [ 33, 35 ] ]
Updated on: 20-Apr-2021
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