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math.NT2021
A Fibonacci type sequence with Prouhet-Thue-Morse coefficients
Eryk Lipka, Maciej Ulas
Let , where is the sum of binary digits function. The sequence is the well-known Prouhet-Thue-Morse sequence. In this note we…
math.NT2020
On two conjectures regarding generalized sequence of derangements
Eryk Lipka, Piotr Miska
The second author studied arithmetic properties of a class of sequences that generalize the sequence of derangements. The aim of the following paper is to disprove two conjectures…
math.NT2018
Automaticity of the sequence of the last nonzero digits of in a fixed base
Eryk Lipka
In 2011 Deshouillers and Ruzsa tried to argument that the sequence of the last nonzero digit of in base 12 is not automatic. This statement was proved few years later by Desho…