Negative-Binary Numbers
We all now the definition of binary numbers (eg. 110 in binary system is equal to 6 in decimal system). Actually there is something called Negative-Binary System, in which all number is based on -2. Put it simply, 1 in NBS is 1 in decimal system, 110 in NBS is actually 2!
Specifically, say the number 100101, is actually 1 (-2)^5+1 (-2)^2+1*(-2)^0, which is -27!
Your job is to find the digital number of sum of the first 1000 positive numbers that are written in the same way in both binary system and the Negative-Binary System.
The answer is 5.
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