New Transcendental Numbers from Certain Sequences

Hung Viet Chu

Published 2019-08-11Version 1

We construct three infinite decimals from certain digits of $n^n, n^m$, and $(n!)^m$ (for any fixed $m$) and show that all three are transcendental. In particular, while previous work looked at the last non-zero digit of $n^n$, we look at the digit right before its last non-zero digit. Secondly, we prove the transcendence of the infinite decimal from the last non-zero digit of $n^{4m}$. Finally, we generalize Dresden's result by showing that the decimal from $(n!)^m$ ($m$ not divisible by $4$) is also transcendental. We end with a list of questions for future research.