Pronic numbers in JavaScript

A Pronic number is a number which is the product of two consecutive integers, that is, a number of the form n(n + 1). For example, 6 is a Pronic number because 6 = 2 × 3, and 12 is Pronic because 12 = 3 × 4.

We are required to write a JavaScript function that takes in a number and returns true if it is a Pronic number otherwise returns false.

Understanding Pronic Numbers

The first few Pronic numbers are: 0, 2, 6, 12, 20, 30, 42, 56, 72, 90...

Method 1: Using Square Root Approach

Since a Pronic number is n(n+1), we can find n by taking the square root and checking nearby integers:

const num = 90;
const isPronic = num => {
    let nearestSqrt = Math.floor(Math.sqrt(num));
    
    // Check if nearestSqrt * (nearestSqrt + 1) equals num
    if (nearestSqrt * (nearestSqrt + 1) === num) {
        return true;
    }
    
    // Check the previous integer as well
    nearestSqrt = nearestSqrt - 1;
    if (nearestSqrt * (nearestSqrt + 1) === num) {
        return true;
    }
    
    return false;
};

console.log(`Is ${num} a Pronic number?`, isPronic(num));
console.log(`Is 12 a Pronic number?`, isPronic(12));
console.log(`Is 15 a Pronic number?`, isPronic(15));

Is 90 a Pronic number? true
Is 12 a Pronic number? true
Is 15 a Pronic number? false

Method 2: Optimized Single Check

A more efficient approach checks only the floor of the square root:

const isPronicOptimized = (num) => {
    let n = Math.floor(Math.sqrt(num));
    return n * (n + 1) === num;
};

// Test multiple numbers
const testNumbers = [0, 2, 6, 12, 15, 20, 25, 30, 42];

testNumbers.forEach(num => {
    console.log(`${num}: ${isPronicOptimized(num)}`);
});

0: true
2: true
6: true
12: true
15: false
20: true
25: false
30: true
42: true

Method 3: Finding All Pronic Numbers Up to N

Generate all Pronic numbers up to a given limit:

function findPronicNumbers(limit) {
    const pronicNumbers = [];
    let n = 0;
    let pronic = n * (n + 1);
    
    while (pronic 

Pronic numbers up to 100:
[0, 2, 6, 12, 20, 30, 42, 56, 72, 90]


Performance Comparison

Conclusion

Pronic numbers follow the pattern n(n+1) and can be efficiently identified using the square root method. The optimized single check approach provides O(1) time complexity for determining if a number is Pronic.