Question

$2^{15} = 32768$ and the sum of its digits is $3 + 2 + 7 + 6 + 8 = 26$.

What is the sum of the digits of the number $2^{1000}$?

Haskell

sumDigits ::  Integer -> Integer
sumDigits n = sumDigits' n 0
    where sumDigits' 0 acc = acc
          sumDigits' n acc = sumDigits' (div n 10) (acc + (mod n 10))

main ::  IO ()
main = print $ sumDigits $ 2^1000

$ ghc -O2 -o sumExp sumExp.hs
$ time ./sumExp
real   0m0.002s
user   0m0.000s
sys    0m0.002s

Python

#!/usr/bin/env python
print(sum(int(digit) for digit in str(2**1000)))

$ time python3 sum-exp.py
real   0m0.016s
user   0m0.016s
sys    0m0.000s

Ruby

#!/usr/bin/env ruby
puts (2**1000).to_s.each_char.inject(0) {|s,v| s+v.to_i}

$ time ruby sum-exp.rb
real   0m0.038s
user   0m0.030s
sys    0m0.008s

Rust

fn main() {
    let mut decimal = vec![1];
    for _ in 0..1000 {
        let mut carry = 0;
        for i in 0..decimal.len() {
            let mut digit = decimal[i];
            digit = 2 * digit + carry;
            carry = digit / 10;
            decimal[i] = digit % 10;
        }
        if carry > 0 {
            decimal.push(carry);
        }
    }
    println!("{}", decimal.iter().sum::<u64>());
}

$ rustc -C target-cpu=native -C opt-level=3 -o digits digits.rs
$ time ./digits
real   0m0.001s
user   0m0.000s
sys    0m0.001s