# Printing powers of base
# from j=0 oto j=n
def powers(base, n):
    for i in range(n):
        print(base**i, end=" ")
    print()

powers(3, 10)


# Prints divisors of n
def divisors(n):
    # The cycle runs to n+1, since n also divides itself!
    for i in range(1, n + 1):
        if n % i == 0:
            print(i, end=" ")
    print()

divisors(14)


# Printing subsequence
# 1 1 2 1 2 3 1 2 3 4...
def subsequences(n):
    count = 0
    sub = 1  # Number of the subsequence
    while count < n:
        for i in range(sub):  # Prints subsequence
            print(i + 1, end=" ")
            count += 1
            if count == n:  # We jump out of cycle if we reach desired length os sequence
                break
        sub += 1
    print()

subsequences(8)


# Function returns length of the integer number x
# It tells us how many times we need to divide the number
#     to reach zero
def num_length(x):
    l = 0
    while x > 0:
        x = x // 10
        l += 1
    return l

print(num_length(4076))


# Prints the table of products
def table_products(n):
    # First line
    print("    ", end="")
    for i in range(1, n + 1):
        print(i, end=" ")
    print()

    # Second line
    print("    ", end="")
    for i in range(1, n + 1):
        print("-", end=" ")
    print()

    # Table
    for row in range(1, n + 1):
        print(row, end=" | ")
        for col in range(1, n + 1):
            print(row * col, end=" ")
        print()

table_products(15)


# Prints empty square
def empty_square(n):
    # First line
    for i in range(n):
        print("#", end=" ")
    print()

    # The middle
    for i in range(n - 2):
        print("#", end=" ")
        for j in range(n - 2):
            print(".", end=" ")
        print("#")

    # Last line
    for i in range(n):
        print("#", end=" ")
    print()

empty_square(30)


# Prints pyramid
def pyramid(n):
    width = 2*n - 1  # The width of the pyramid base
    for r in range(n):
        nr = 2*r + 1  # The width of the pyramid in row r
        empty = (width - nr) // 2  # The number of epty spaces
        for j in range(empty):
            print(".", end=" ")
        for j in range(nr):
            print("#", end=" ")
        for j in range(empty):
            print(".", end=" ")
        print()

pyramid(4)