How can I find a x such that the order of 2 mod x is n?

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Is there an algorithm which, given n, returns an integer x such that 2 has order n modulo x (i.e, 2^n = 1 mod x and n is the smallest positive solution)? Is there any such algorithm which runs faster than factoring n?
 
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How about x = 2n-1?
 
Well... this is much simpler than I expected :redface:
I guess I should have thought a bit more before posting that... I was convinced this would involve some advanced math and big time complexity.
 

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