Number Pattern Generator

def arithmetic(a1, d, n):
    """Arithmetic sequence: a1, a1+d, a1+2d, ..."""
    return [a1 + i * d for i in range(n)]

def geometric(a1, r, n):
    """Geometric sequence: a1, a1*r, a1*r^2, ..."""
    return [a1 * (r ** i) for i in range(n)]

def fibonacci_like(a1, a2, n):
    """Fibonacci-like: starts with a1, a2; each term = sum of previous two."""
    seq = [a1, a2]
    for _ in range(n - 2):
        seq.append(seq[-1] + seq[-2])
    return seq[:n]

def primes(n):
    """First n prime numbers using trial division."""
    result = []
    candidate = 2
    while len(result) < n:
        if all(candidate % p != 0 for p in result if p * p <= candidate):
            result.append(candidate)
        candidate += 1
    return result

# Examples
print("Arithmetic (a=3, d=4):", arithmetic(3, 4, 8))
# [3, 7, 11, 15, 19, 23, 27, 31]

print("Geometric (a=2, r=3):", geometric(2, 3, 6))
# [2, 6, 18, 54, 162, 486]

print("Fibonacci-like (1,1):", fibonacci_like(1, 1, 8))
# [1, 1, 2, 3, 5, 8, 13, 21]

print("First 8 primes:", primes(8))
# [2, 3, 5, 7, 11, 13, 17, 19]

print("Squares:", [i**2 for i in range(1, 9)])
# [1, 4, 9, 16, 25, 36, 49, 64]