Python: n^th Hamming number

Last update on April 22 2025 12:51:18 (UTC/GMT +8 hours)

26. Nth Hamming Number

Write a Python program to find the nth Hamming number. Use the itertools module.

Hamming numbers are numbers of the form
H = 2ⁱ x 3^j x 5^k Where i, j, k ≥ 0
The sequence of Hamming numbers 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27. . . consists of all numbers of the form 2i.3j.5k where i, j and k are non-negative integers.

Sample Solution:

Python Code:

import itertools
from heapq import merge

def nth_hamming_number(n):
    def num_recur():
        last = 1
        yield last
        x, y, z = itertools.tee(num_recur(), 3)
        for n in merge((2 * i for i in x), (3 * i for i in y), (5 * i for i in z)):
            if n != last:
                yield n
                last = n
    result =  itertools.islice(num_recur(), n)
    return list(result)[-1]

print(nth_hamming_number(8))
print(nth_hamming_number(14))
print(nth_hamming_number(17))

Sample Output:

9
20
27

For more Practice: Solve these Related Problems:

• Write a Python program to compute the nth Hamming number using a generator and itertools.merge.
• Write a Python program to generate Hamming numbers in order and then use itertools.islice to select the nth element.
• Write a Python program to create an iterator for Hamming numbers and filter out numbers not matching the criteria until the nth is found.
• Write a Python program to build a Hamming number sequence using dynamic programming and itertools, then return the nth element.

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Python Code Editor:

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