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 Post subject: Subsequences
PostPosted: Sat Jan 20, 2018 5:16 am 
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Prove that the sequence $\alpha_n=\lfloor{\rm{e}}^n\rfloor\,,\; n\in\mathbb{N}$, where $\lfloor{\cdot}\rfloor$ is the floor function, has a subsequence with all its terms to being odd numbers and a subsequence with all its terms to being even numbers.


Note: I don't have a solution.

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 Post subject: Re: Subsequences
PostPosted: Sun Jan 28, 2018 12:58 am 
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It seems that here we have an open problem. See
Salem numbers and uniform distribution modulo 1

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