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## Subsequences

Real Analysis
Grigorios Kostakos
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### Subsequences

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.
Grigorios Kostakos
Grigorios Kostakos
Founder
Articles: 0
Posts: 460
Joined: Mon Nov 09, 2015 1:36 am
Location: Ioannina, Greece

### Re: Subsequences

It seems that here we have an open problem. See
Salem numbers and uniform distribution modulo 1
Grigorios Kostakos