# Program to find last digit of the given sequence for given n in Python

PythonServer Side ProgrammingProgramming

Suppose we have a value n. We have to find the last digit of sequence S. The equation of S is given below −

$$\sum_{i=0\: 2^{^{i}}\leqslant n}^{\alpha } \sum_{j=0}^{n} 2^{2^{^{i}+2j}}$$

So, if the input is like n = 2, then the output will be 6 because: here only i = 0 and i are valid, so

• S0 = 2^(2^0 + 0) + 2^(2^0 + 2) + 2^(2^0 + 4) = 42
• S1 = 2^(2^1 + 0) + 2^(2^1 + 2) + 2^(2^1 + 4) = 84 The sum is 42+84 = 126, so last digit is 6.

To solve this, we will follow these steps −

• total:= 0
• temp := 1
• while temp <= n, do
• total := total + (2^temp mod 10)
• temp := temp * 2
• total := total * (1 +(4 when n is odd otherwise 0)) mod 10

## Example

Let us see the following implementation to get better understanding −

def solve(n):
total= 0
temp = 1
while (temp <= n):
total += pow(2, temp, 10)
temp *= 2
total = total * (1 + (4 if n %2 ==1 else 0)) % 10

n = 2
print(solve(n))

## Input

2


## Output

6
Published on 25-Oct-2021 07:24:02