Ikeda, Soichi; Matsuoka, Kaneaki On transcendental numbers generated by certain integer sequences. (English) Zbl 1298.11070 Šiauliai Math. Semin. 8(16), 63-69 (2013). Summary: By generalizing the technique of G. P. Dresden [Math. Mag. 81, No. 2, 96–105 (2008; Zbl 1165.11060)], we prove a theorem which gives a sufficient condition for the transcendence of the numbers generated by certain integer sequences. In the last section, we consider the numbers generated by the last non-zero digits of \(n^n\), \(n^{n^n}\), \(n^{n^{n^n}}\), etc. and the number of trailing zeros of \(n^j\), \(j\in \mathbb N\) and \(10 \nmid j\), as examples. Cited in 1 Document MSC: 11J81 Transcendence (general theory) Keywords:decimal expansion; last non-zero digits; number of trailing zeros; Roth’s theorem; transcendental number Citations:Zbl 1165.11060 Software:OEIS PDFBibTeX XMLCite \textit{S. Ikeda} and \textit{K. Matsuoka}, Šiauliai Math. Semin. 8(16), 63--69 (2013; Zbl 1298.11070)