Check three consecutive numbers - JavaScript

We are required to write a JavaScript function that takes in a Number, say n, and we are required to check whether there exist such three consecutive natural numbers (not decimal/floating point) whose sum equals to n.

If there exist such numbers, our function should return them, otherwise it should return false. Following is the code ?

How It Works

For three consecutive numbers to sum to n, we need: x + (x+1) + (x+2) = n, which simplifies to 3x + 3 = n. Therefore, n must be divisible by 3 and greater than 5 (since the smallest three consecutive natural numbers are 1, 2, 3).

Example

const sum = 54;
const threeConsecutiveSum = sum => {
    if(sum < 6 || sum % 3 !== 0){
        return false;
    }
    // three numbers will be of the form:
    // x + x + 1 + x + 2 = 3 * x + 3
    const residue = sum - 3;
    const num = residue / 3;
    return [num, num+1, num+2];
};
console.log(threeConsecutiveSum(sum));

Output

Following is the output in the console ?

[ 17, 18, 19 ]

Testing Different Cases

console.log(threeConsecutiveSum(6));   // [1, 2, 3]
console.log(threeConsecutiveSum(15));  // [4, 5, 6]
console.log(threeConsecutiveSum(30));  // [9, 10, 11]
console.log(threeConsecutiveSum(5));   // false (too small)
console.log(threeConsecutiveSum(7));   // false (not divisible by 3)

[ 1, 2, 3 ]
[ 4, 5, 6 ]
[ 9, 10, 11 ]
false
false

Key Points

• The sum must be at least 6 (minimum consecutive numbers: 1, 2, 3)
• The sum must be divisible by 3
• The first number is calculated as (sum - 3) / 3

Conclusion

This function efficiently determines if a number can be expressed as the sum of three consecutive natural numbers by checking divisibility and calculating the starting number mathematically.