Mathematic Algorithms

math_alg.py

def fibonacci(n):
    """A Fibonacci generator"""
    x_1, x = 1, 1
    while ( x < n ):
        yield x
        x_1, x = x, x + x_1

def erastothenes_sieve(n):
    """Get all the prime numbers below 'n'"""
    sqrtN = math.sqrt(n)
    A = [i for i in range(2, n + 1)]
    
    def mark_as_non_prime_value_at(i):
        A[i] = -1

    def only_prime_numbers():
        return [ A[i] for i in range(0, len(A)) if A[i] != -1 ]
    
    [ mark_as_non_prime_value_at(j) \
        for i in xrange(A.index(int(sqrtN + 1)) + 1) \
            for j in xrange(i, len(A), A[i]) \
                if A[i] != A[j] and A[j] % A[i] == 0 ]
    return only_prime_numbers()

def is_palindrome(x):
    x = str(x)
    k = len(x)
    for i in xrange(k/2):
        if x[i] != x[k-i-1]:
            return False
    return True

def triangular_number(n):
    """Return the 'n' Triangular Number"""
    return (n * (n+1)) * 0.5

def triangular_numbers(n):
    """Generate a list of 'n' Triangular Numbers"""
    i = 1
    k = 0
    while k < n:
        yield i + k
        k += 1
        i += k

def next_triangular_number():
    """Triangular Number Generator"""
    i = 1
    k = 0
    while True:
        yield i + k
        k += 1
        i += k