Is a number whose infinite decimal part is the sequence of even numbers, transcendental? How about a number whose infinite decimal part is the odd numbers? Would the odds be more difficult to prove since they contain almost the entire sequence of primes? 



Is 0.24681012141618202224... transcendental?
In point of fact, K. Mahler proved in [this paper](https://carma.newcastle.edu.au/mahler/docs/046.pdf) that, if $p(x)$ in a non-constant polynomial such that $p(n) \in \mathbb{N}$ for every $n\in \mathbb{N}$, then the number


$$0.p(1)p(2)p(3)p(4)\ldots,$$


which is formed concatenating after the decimal point the values of $p(1), p(2), p(3), \ldots$ (in that order), is a transcendental and [non-Liouville](https://en.wikipedia.org/wiki/Liouville_number) number.


