There are ten positive integers less than 1000 that cannot be written as the sum of consecutive natural numbers.
For example, 9 = 4 + 5, 10 = 1 + 2 + 3 + 4,
11 = 5 + 6, and 12 = 3 + 4 + 5.

The first two numbers that cannot be written as the sum of consecutive natural numbers are 1 and 2. Can you find the other eight exceptions?

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Solution to the Problem:

The answer is all the powers of 2:
1, 2, 4, 8, 16, 32, 64, 128, 256, 512.