Python Program to Find Armstrong Number in an Interval

Introduction

An Armstrong number (or 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. For example, 153 is an Armstrong number because (1^3 + 5^3 + 3^3 = 153). These numbers are intriguing due to their self-representative nature and are often a popular subject in programming exercises to practice loops and conditionals.

In this article, you will learn how to write a Python program to find all Armstrong numbers in a given interval. This task will help you understand how to implement loops, conditional statements, and basic arithmetic operations in Python.

Finding Armstrong Numbers within an Interval

Determine if a Number is an Armstrong Number

1. Define a function to check if a number is an Armstrong number. The function takes a single integer as an argument.

2. Convert the number to a string to easily iterate over each digit.

3. Calculate the total number of digits in the number.

4. Sum the cubes (or powers corresponding to the digit length) of each digit.

5. Compare the sum to the original number and return True if they match, indicating it is an Armstrong number.

   python Copy

   def is_armstrong(num):
       str_num = str(num)
       power = len(str_num)
       sum_of_powers = sum(int(digit) ** power for digit in str_num)
       return sum_of_powers == num
   

   This function handles the task of calculating if a single number is an Armstrong number based on the definition. The digits are raised to the power of the total number of digits and then summed to see if they equal the original number.

Loop through an Interval to Find Armstrong Numbers

1. Accept two integers as the start and end of the interval.

2. Iterate through each number in this range.

3. Use the previously defined is_armstrong() function to check each number.

4. Append the number to a list if it is an Armstrong number.

5. Print the results after completing the loop through the range.

   python Copy

   def find_armstrong_numbers(start, end):
       armstrong_list = []
       for num in range(start, end + 1):
           if is_armstrong(num):
               armstrong_list.append(num)
       return armstrong_list
   

   This function performs a loop from start to end, checking each number to see if it's an Armstrong number via the is_armstrong() function. It collects all Armstrong numbers found within this interval.

Example Usage

To see the functions in action, define a range and find Armstrong numbers within it.

start_interval = 100
end_interval = 2000
armstrong_numbers = find_armstrong_numbers(start_interval, end_interval)
print("Armstrong numbers in interval:", armstrong_numbers)

This script sets an interval from 100 to 2000 and prints the Armstrong numbers found within this range. Adjust the interval values to explore other ranges.

Conclusion

Finding Armstrong numbers within a specified interval in Python offers a solid exercise in understanding loops, conditionals, and mathematical operations. Utilize the steps outlined to create efficient, readable Python scripts that accurately identify these unique numbers. This exercise not only helps in strengthening programming skills but also aids in grasping the practical applications of elementary mathematical concepts in computer science.