On the Wikipedia page about transcendental numbers there is a claim that for $\beta > 1$, if $\alpha = \displaystyle \sum\limits_{k=0}^{\infty }10^{-\left\lfloor \beta ^{k}\right\rfloor }$ ($\beta \mapsto \lfloor \beta \rfloor$ is the floor function), then $\alpha$ is transcendental.
The wiki page doesn't cite a source proving this and I cannot find one. I would like to cite this result in a paper I'm writing.
Any help tracking down a source would be much appreciated.