In this post, we’ll explore a classic beginner programming problem: Armstrong Numbers.
What is an Armstrong Number?
An Armstrong number (also known as a Narcissistic number) is a number that is equal to the sum of its own digits each raised to the power of the number of digits.
Formula: If a number $N$ has $d$ digits ($a, b, c, …$), then: $$N = a^d + b^d + c^d + …$$
Examples
1. Number: 153 * Digits: 1, 5, 3 * Number of digits ($d$): 3 * Calculation: $1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153$ * Result: Yes, 153 is an Armstrong number.
2. Number: 1634 * Digits: 1, 6, 3, 4 * Number of digits ($d$): 4 * Calculation: $1^4 + 6^4 + 3^4 + 4^4 = 1 + 1296 + 81 + 256 = 1634$ * Result: Yes, 1634 is an Armstrong number.
3. Number: 123 * Digits: 1, 2, 3 * Number of digits ($d$): 3 * Calculation: $1^3 + 2^3 + 3^3 = 1 + 8 + 27 = 36$ * Result: No, 123 is not an Armstrong number (36 != 123).
Python Implementation
Here is a Python script to find all Armstrong numbers up to 1,000,000.
def is_armstrong(number):
# Convert number to string to easily iterate digits
num_str = str(number)
num_digits = len(num_str)
sum_of_powers = 0
for digit in num_str:
sum_of_powers += int(digit) ** num_digits
return sum_of_powers == number
# Find Armstrong numbers in a range
print("Finding Armstrong numbers up to 1,000,000:")
for i in range(1000000):
if is_armstrong(i):
print(f"{i} is an Armstrong number")
How it Works
str(number): Converting the integer to a string allows us to easily count the digits (len()) and iterate through them.int(digit) ** num_digits: We convert each character back to an integer and raise it to the power of the total count of digits.- Comparison: Finally, we check if our calculated sum equals the original number.
Try running this code and see which numbers pop up! It’s a great exercise for practicing loops and type conversions.
Written by
Abdur-Rahmaan Janhangeer
Chef
Python author of 7+ years having worked for Python companies around the world
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