On quasi-periodicity in Proth-Gilbreath triangles
RN Bhat, C Cobeli, A Zaharescu - arXiv preprint arXiv:2307.11776, 2023 - arxiv.org
Let PG be the Proth-Gilbreath operator that transforms a sequence of integers into the
sequence of the absolute values of the differences between all pairs of neighbor terms …
sequence of the absolute values of the differences between all pairs of neighbor terms …
A lozenge triangulation of the plane with integers
RN Bhat, C Cobeli, A Zaharescu - arXiv preprint arXiv:2403.10500, 2024 - arxiv.org
We introduce and study a three-folded linear operator depending on three parameters that
has associated a triangular number tilling of the plane. As a result the set of all triples of …
has associated a triangular number tilling of the plane. As a result the set of all triples of …
Filtered rays over iterated absolute differences on layers of integers
RN Bhat, C Cobeli, A Zaharescu - Chaos, Solitons & Fractals, 2024 - Elsevier
The dynamical system generated by the iterated calculation of the high order gaps between
neighboring terms of a sequence of natural numbers is remarkable and only incidentally …
neighboring terms of a sequence of natural numbers is remarkable and only incidentally …
An extension of Lucas Theorem
Z Cinkir, A Ozturkalan - arXiv preprint arXiv:2309.00109, 2023 - arxiv.org
We give elementary proofs of some congruence criteria to compute binomial coefficients in
modulo a prime. These criteria are analogues to the symmetry property of binomial …
modulo a prime. These criteria are analogues to the symmetry property of binomial …
On the discrete trajectories of a self-propelled particle
C Cobeli, A Zaharescu - arXiv preprint arXiv:2403.14894, 2024 - arxiv.org
We introduce a double-folded operator that, upon iterative application, generates a
dynamical system with two types of trajectories: a cyclic one and, another that grows …
dynamical system with two types of trajectories: a cyclic one and, another that grows …
On the Trajectories of a Particle in a Translation Invariant Involutive Field
C Cobeli, A Zaharescu - Results in Mathematics, 2024 - Springer
We introduce a double-folded operator that, upon iterative application, generates a
dynamical system with two types of trajectories: a cyclic one and, another that grows …
dynamical system with two types of trajectories: a cyclic one and, another that grows …