Sum of the digits of the number 2^1000 [closed]

Answer 1

How can 2^1000 be alternatively expressed?

I don't remember much from my maths days, but perhaps something like (2^(2^500))? And how can that be expressed?

Find an easy way to calculate 2^1000, put the result in a BigInteger, and the rest is perhaps trivial.

Answer 2

something like that sould do it bute force: - although there is a nice analytic solution (think pen& paper) using mathematics - that may also work for numbers greater than 1000.

    final String bignumber = BigInteger.valueOf(2).pow(1000).toString(10);
    long result = 0;
    for (int i = 0; i < bignumber.length(); i++) {
        result += Integer.valueOf(String.valueOf(bignumber.charAt(i)));
    }
    System.out.println("result: " + result);

Answer 3

In[1162] := Plus @@ IntegerDigits[2^1000]
Out[1162] = 1366

Answer 4

Create a vector of length 302, which is the length of 2^1000. Then, save 2 at index 0, then, double 1000 times. Just look at every index separetly and add 1 to the next index if the previous exeeds 10. Then just sum it up!

Answer 5

This problem is not simply asking you how to find the nearest big integer library, so I'd avoid that solution. This page has a good overview of this particular problem.

Answer 6

2^1000 is a very large value, you would have to use BigIntegers. The algorithm would be something like:

import java.math.BigInteger;
BigInteger two = new BigInteger("2");
BigInteger value = two.pow(1000);
int sum = 0;
while (value > 0) {
  sum += value.remainder(new BigInteger("10"));
  value = value.divide(new BigInteger("10"));
}