Program to Find the nth term of the series

1, 1, 2, 3, 4, 9, 8, 27, 16, 81, 32, 243,64, 729, 128, 2187…,,

This series is a mixture of 2 series – all the odd terms in this series form a geometric series and all the even terms form yet another geometric series. Write a program to find the Nth term in the series.

• The value N in a positive integer that should be read from STDIN.
• The Nth term that is calculated by the program should be written to STDOUT.
• Other than value of n th term,no other character / string or message should be written to STDOUT.
• For example , if N=16, the 16th term in the series is 2187, so only value 2187 should be printed to STDOUT.

You can assume that N will not exceed 30.

Test Case 1

• Input- 16
• Expected Output – 2187

Test Case 2

• Input- 13
• Expected Output – 64

Explanation

1, 1, 2, 3, 4, 9, 8, 27, 16, 81, 32, 243,64, 729, 128, 2187 can represented as :

• 2⁽⁰⁾, 3⁽⁰⁾,2⁽¹⁾, 3⁽¹⁾,2⁽²⁾, 3⁽²⁾,2⁽³⁾, 3⁽³⁾,2⁽⁴⁾, 3⁽⁴⁾,2⁽⁵⁾, 3⁽⁵⁾,2⁽⁶⁾, 3⁽⁶⁾ ….

There are two consecutive sub GP’s at even and odd positions

• (GP-1) At Odd Positions (Powers of 2) – 1, 2, 4, 8, 16, 32, 64, 128
• (GP-2) At Even Positions (Powers of 3) – 1, 3, 9, 27, 81, 243, 729, 2187

Clearly, for calculating Nth position value

• If N is Even, Find (N/2) position in sub GP – 2
• If N is Odd, Find (N/2 + 1) position in sub GP – 1

num = int(input())
if(num%2==0):
  num = num // 2
  print(3**(num-1))
else:
  num = num // 2 + 1
  print(2**(num-1))