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016 - Power Digit Sum

Problem 16 / Challenge #16: Power Digit Sum

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

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

ProjectEuler+ Problem Statement

The Project Euler problem is equivalent to the ProjectEuler+ challenge with $T = 1$ and $N = 1000$.