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On transcendental numbers generated by certain integer sequences. (English) Zbl 1298.11070

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.

MSC:

11J81 Transcendence (general theory)

Citations:

Zbl 1165.11060

Software:

OEIS
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