Geodesic
Arithmetic properties of polyadic series with periodic coefficients
Izvestiya. Mathematics , Tome 81 (2017) no. 2, pp. 444-461.

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We study arithmetic properties of polyadic numbers, that is, series of the form $$ \sum_{n=0}^\infty a_n n!, $$ where the numbers $a_n\in\mathbb Z$ form a periodic sequence $\{a_n\}$.
Keywords: periodic sequence, transcendence, polyadic numbers. 
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V. G. Chirskii. Arithmetic properties of polyadic series with periodic coefficients. Izvestiya. Mathematics , Tome 81 (2017) no. 2, pp. 444-461. http://geodesic.mathdoc.fr/item/IM2_2017_81_2_a7/

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