Unlocking the Treasure Trove of Multiples: An Exploration of LeetCode 17.09, Unveiling the k-th Number

Preamble: Unveiling the Enigmatic k-th Number

In the vast expanse of numbers, there lies a captivating subset that intrigues mathematicians and computer scientists alike - numbers with prime factors restricted to 3, 5, and 7. These numbers possess a unique characteristic that distinguishes them from their brethren, and LeetCode 17.09 presents a tantalizing challenge to uncover the k-th number within this select group.

Stepping into the Arena: Deciphering the Problem Statement

The problem statement beckons us to devise an algorithm capable of identifying the k-th number with prime factors limited to 3, 5, and 7. However, the task is not as straightforward as it may seem. These numbers are not constrained to possessing all three prime factors; they can exhibit any combination of these factors or even lack them entirely.

Illuminating the Path: A Systematic Approach

To illuminate the path towards the solution, we embark on a structured approach that decomposes the problem into manageable steps:

1. Establishing a Foundation: We begin by defining a set of numbers that adhere to the given criteria. This set serves as the foundation upon which our algorithm will operate.

2. Discerning the Pattern: Immerse ourselves in the sequence of numbers that meet the criteria, seeking patterns and relationships that govern their formation. These patterns hold the key to unlocking the secrets of the k-th number.

3. Formulating an Algorithm: Armed with the insights gleaned from the patterns, we formulate an algorithm that systematically generates these numbers. This algorithm serves as the compass guiding us towards the elusive k-th number.

4. Unveiling the k-th Number: With the algorithm in place, we set about determining the k-th number. This number, hidden within the sequence, awaits discovery.

Conclusion: A Triumph of Perseverance and Ingenuity

The quest to uncover the k-th number with prime factors restricted to 3, 5, and 7 is a testament to the power of perseverance and ingenuity. By breaking down the problem, identifying patterns, and devising an algorithm, we illuminate the path towards the solution. This journey exemplifies the essence of problem-solving, where creativity and logical reasoning converge to reveal hidden truths.