Complete the Sequence

2, 3, 5, 9, 17, _ What is the next number in the sequence?




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I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

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In 2007, a puzzle was released and $2 million prizes were offered for the first complete solution. The competition ended at noon on 31 December 2010, with no solution being found. Wiki