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15, 31, 63, 127, 255, (....)513511517523

Question

15, 31, 63, 127, 255, (....)513511517523

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Solution

The pattern in the sequence is that each number is one less than a power of 2.

15 is 2^4 - 1 31 is 2^5 - 1 63 is 2^6 - 1 127 is 2^7 - 1 255 is 2^8 - 1

So the next number in the sequence should be one less than the next power of 2, which is 2^9 - 1 = 511.

So the sequence should be: 15, 31, 63, 127, 255, 511.

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