Prime Number Detection in a Range

start = int(input("Enter the lower bound: "))
end = int(input("Enter the upper bound: "))

for candidate in range(start + 1, end):
    if candidate < 2:
        continue
    is_prime = True
    for divisor in range(2, int(candidate ** 0.5) + 1):
        if candidate % divisor == 0:
            is_prime = False
            break
    if is_prime:
        print(candidate)

Generating Arithmetic Progrestions

values = input("Enter start, step, count (comma-separated): ").split(',')
first, delta, length = [eval(v) for v in values]
sequence = [first + i * delta for i in range(length)]
print(sequence)

Buildding Geometric Progressions

parts = input("Enter first term, common ratio, number of terms: ").split(',')
a, r, n = [eval(x) for x in parts]
terms_as_str = [str(a * (r ** i)) for i in range(n)]
print(','.join(terms_as_str))

Computing Logarithms Safely

import math

try:
    base_val = float(input("Logarithm base: "))
    num_val = float(input("Logarithm argument: "))
    if base_val <= 0 or num_val <= 0:
        print("Both base and argument must be greater than zero.")
    else:
        res = math.log(num_val, base_val)
        print(res)
except ValueError:
    print("Invalid numeric input.")
except ZeroDivisionError:
    print("Base cannot be 1.")

Fibonacci Sequence Up to a Limit

limit = 50
prev, curr = 0, 1
while prev <= limit:
    print(prev, end=', ')
    prev, curr = curr, prev + curr
print()

Custom Count

n_terms = int(input("How many Fibonacci numbers? "))
a, b = 0, 1
for _ in range(n_terms):
    print(a, end=' ')
    a, b = b, a + b

Pascal's Triangle

def generate_pascal(rows):
    triangle = []
    for i in range(rows):
        row = [1] * (i + 1)
        for j in range(1, i):
            row[j] = triangle[i-1][j-1] + triangle[i-1][j]
        triangle.append(row)
    return triangle

def print_right(tri):
    for row in tri:
        for val in row:
            print(f"{val:3d}", end=" ")
        print()

def print_centered(tri):
    n = len(tri)
    for i, row in enumerate(tri):
        print('  ' * (n - i - 1), end='')
        for val in row:
            print(f"{val:3d}", end=" ")
        print()

# Example with 8 rows
triangle = generate_pascal(8)
print("Right-aligned:")
print_right(triangle)
print("\nCentered:")
print_centered(triangle)