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.

Welcome to mathimatikoi.org; a site of university mathematics! Enjoy your stay here!

## Subsequences

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

### Subsequences

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

Salem numbers and uniform distribution modulo 1

Grigorios Kostakos