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Values of binary partition function represented by a sum of three squares
Bartosz Sobolewski, Maciej Ulas
Let be a positive integer and be the number of partitions of with parts being powers of 2, where each part can take colors. We show that if , then…
Solutions of certain meta-Fibonacci recurrences
Bartosz Sobolewski, Maciej Ulas
In this note we investigate the solutions of certain meta-Fibonacci recurrences of the form for various sets of initial conditions. In the case when $f(n)…
On -regularity of sequences of valuations and last nonzero digits
Bartosz Sobolewski
Let be an integer base with prime factors . In this paper we study sequences of "-adic valuations" and last nonzero digits in -adic expansions of…
Cyclotomic properties of polynomials associated with automatic sequences
Bartosz Sobolewski
We show that polynomials associated with automatic sequences satisfy a certain recurrence relation when evaluated at a root of unity, which generalizes a result of Brillhart, Lomon…
On the last nonzero digits of in a given base
Bartosz Sobolewski
In this paper we study the sequence of strings of last nonzero digits of in a given base . We determine for which this sequence is automatic and show how to generat…
The 2-adic valuation of generalized Fibonacci sequences with an application to certain Diophantine equations
Bartosz Sobolewski
In this paper we focus on finding all the factorials expressible as a product of a fixed number of -nacci numbers with . We derive the 2-adic valuation of the -na…