ON TRANSCENDENTAL NUMBERS GENERATED BY CERTAIN INTEGER SEQUENCES

Author:

Soichi IKEDA, Kaneaki MATSUOKA

2010 Mathematics Subject Classification:

11J81.

Keywords:

decimal expansion, last non-zero digits, number of trailing zeros, Roth's theorem, transcendental number.

Abstract:

By generalizing the technique of Dresden [2], 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 trailling zeros of n^j, j \in \mathbb{N}, and 10 \nmid j, as examples.

Download paper:

Iked-Mats-2013

Vol. 8 (16), 2013