Lecture Notes on 07 Mar 2014

# sum digits of a number
def sum_digits (n):
  sum = 0
  while (n > 0):
    sum += n % 10
    n = n // 10
  return sum

# reverse a number
def rev_num (n):
  r_num = 0
  while (n > 0):
    r_num = r_num * 10 + n % 10
    n = n // 10
  return r_num

# determine if a number is palindromic
def is_palindromic (n):
  return (n == rev_num(n))

# determine if a number is prime
def is_prime (n):
  limit = int (n ** 0.5) + 1
  for div in range (2, limit):
    if (n % div == 0):
      return False
  return True

# compute the nth Fibonacci term
def fib (n):
  f = 0
  if (n == 0) or (n == 1):
    f = n
  else:
    f1 = 0
    f2 = 1
    for i in range (2, n + 1):
      f = f1 + f2
      f1 = f2
      f2 = f
  return f

# determine if a number is perfect
def is_perfect (n):
  sum_div = 0
  limit = n // 2 + 1
  for div in range (1, limit):
    if (n % div == 0):
      sum_div += div
  return (n == sum_div)

def main():
  # determine a non-palindromic number whose cube is palindromic
  for n in range (1000, 10000):
    if (not is_palindromic (n)) and (is_palindromic (n * n * n)):
      n3 = n * n * n
      print (n, n3)
      break

  # determine the smallest prime that remains prime 
  # when added to its reversal
  for n in range (100, 1000):
    if (is_prime(n)) and (is_prime(n + rev_num(n))):
      rev_n = n + rev_num(n)
      print (n, rev_n)
      break

  # find sum of the even valued terms in the 
  # Fibonacci series whose values do not exceed 4 million. 
  sum_fib = 0
  f = 0
  n = 0
  while (f < 4000000):
    f = fib (n)
    if (f % 2 == 0):
      sum_fib += f
    n += 1
  print (sum_fib)
    

main()