5-hamming-numbers.md

Problem:

A *Hamming number* is a positive integer of the form 2ⁱ3^j5^k, for some non-negative integers i, j, and k.

Write a function that computes the nth smallest Hamming number.

Specifically:

• The first smallest Hamming number is 1 = 2⁰3⁰5⁰
• The second smallest Hamming number is 2 = 2¹3⁰5⁰
• The third smallest Hamming number is 3 = 2⁰3¹5⁰
• The fourth smallest Hamming number is 4 = 2²3⁰5⁰
• The fifth smallest Hamming number is 5 = 2⁰3⁰5¹

The 20 smallest Hamming numbers are given in example test fixture.

Your code should be able to compute all of the smallest 5,000 (Clojure: 2000) Hamming numbers without timing out.

Solution