Python: Find the value of n where n degrees of number 2 are written sequentially in a line without spaces

Last update on April 17 2025 13:05:59 (UTC/GMT +8 hours)

Sequential Powers of Two

Write a Python program that finds the value of n when n degrees of number 2 are written sequentially on a line without spaces between them.

Visual Presentation:

Python: Find the value of n where n degrees of number 2 are written sequentially in a line without spaces

Sample Solution:

Python Code:

# Define a function 'ndegrees' that calculates the highest power of a number 'n'
# such that the resulting number is found within a given input string 'num'.
def ndegrees(num):
    ans = True  # Initialize a boolean variable 'ans' to True.
    n, tempn, i = 2, 2, 2  # Initialize variables 'n', 'tempn', and 'i'.
    
    # Use a while loop to check conditions.
    while ans:
        # Check if the string representation of 'tempn' is found within 'num'.
        if str(tempn) in num:
            i += 1  # Increment 'i'.
            tempn = pow(n, i)  # Update 'tempn' with the next power of 'n'.
        else:
            ans = False  # Set 'ans' to False if 'tempn' is not found in 'num'.
    
    return i - 1  # Return the highest power (i-1).

# Test the 'ndegrees' function with different input strings and print the results.
print(ndegrees("2481632"))
print(ndegrees("248163264"))

Sample Output:

5
6

Explanation:

The above Python code defines a function "ndegrees()" that calculates the highest power of a number 'n' such that the resulting number is found within a given input string 'num'. Here's a brief explanation:

Function Definition:

def ndegrees(num):: Define a function named "ndegrees()" that takes a string num as input.

Initialization:

ans = True: Initialize a boolean variable 'ans' to 'True'.
n, tempn, i = 2, 2, 2: Initialize variables 'n' (base number), 'tempn' (temporary result), and i (exponent) to 2.

While Loop:

while ans:: Enter a while loop that continues as long as 'ans' is 'True'.

if str(tempn) in num:: Check if the string representation of 'tempn' is found within the input string 'num'.

i += 1: Increment the exponent i.
tempn = pow(n, i): Update 'tempn' with the next power of 'n'.

else:: If 'tempn' is not found in 'num', set 'ans' to 'False' to exit the loop.

Return Result:

return i - 1: Return the highest exponent (i-1) that satisfies the condition.>

Function Testing:

print(ndegrees("2481632")): Test the function with the input string "2481632" and print the result.
print(ndegrees("248163264")): Test the function with the input string "248163264" and print the result.

Flowchart:

For more Practice: Solve these Related Problems:

Write a Python program to find the smallest n such that concatenating the powers of 3 produces a number divisible by a given integer.
Write a Python program to compute the sum of digits of the number formed by writing sequential powers of 2.
Write a Python program to multiply consecutive numbers until the product reaches a specified digit length.
Write a Python program to determine the smallest n for which the concatenation of the first n natural numbers is divisible by a given divisor.

Go to:

Previous: Write a Python program to find the median among three given numbers
Next: Write a Python program to find the number of zeros at the end of a factorial of a given positive number.

Python Code Editor:

Have another way to solve this solution? Contribute your code (and comments) through Disqus.