Výsledky vyhledávání - "Spilker, Jürgen"

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Period patterns, entry points, and orders in the Lucas sequences: theory and applications

Autor: Fiebig, Morgan, Mbirika, aBa, Spilker, Jürgen

The goal of this paper is twofold: (1) extend theory on certain statistics in the Fibonacci and Lucas sequences modulo $m$ to the Lucas sequences $U := \left(U_n(p,q)\right)_{n \geq 0}$ and $V := \left(V_n(p,q)\right)_{n \geq 0}$, and (2) apply some

Externí odkaz: http://arxiv.org/abs/2408.14632

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Pell and associated Pell braid sequences as GCDs of sums of $k$ consecutive Pell, balancing, and related numbers

Autor: Mbirika, aBa, Schrader, Janee, Spilker, Jürgen

Publikováno v: Journal of Integer Sequences, Vol. 26, Issue 6 (2023), Article 23.6.4

We consider the greatest common divisor (GCD) of all sums of $k$ consecutive terms of a sequence $(S_n)_{n\geq 0}$ where the terms $S_n$ come from exactly one of following six well-known sequences' terms: Pell $P_n$, associated Pell $Q_n$, balancing

Externí odkaz: http://arxiv.org/abs/2301.05758

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GCD of sums of $k$ consecutive squares of generalized Fibonacci numbers

Autor: Mbirika, aBa, Spilker, Jürgen

Publikováno v: Fibonacci Quarterly, Vol. 60 (2022), No. 5, 255--269

In 2021, Guyer and Mbirika gave two equivalent formulas that computed the greatest common divisor (GCD) of all sums of $k$ consecutive terms in the generalized Fibonacci sequence $\left(G_n\right)_{n \geq 0}$ given by the recurrence $G_n = G_{n-1} +

Externí odkaz: http://arxiv.org/abs/2204.12626

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