Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

On the spacing between terms of generalized Fibonacci sequences

100%

Marques D.

Colloquium Mathematicum

2014

tom 134

nr 2

267-280

For k ≥ 2, the k-generalized Fibonacci sequence $(Fₙ^{(k)})ₙ$ is defined to have the initial k terms 0,0,...,0,1 and be such that each term afterwards is the sum of the k preceding terms. We will prove that the number of solutions of the Diophantine equation $Fₘ^{(k)} - Fₙ^{(ℓ)} = c > 0$ (under some weak assumptions) is bounded by an effectively computable constant depending only on c.

On terms of linear recurrence sequences with only one distinct block of digits

63%

Marques D., Togbé A.

Colloquium Mathematicum

2011

tom 124

nr 2

145-155

In 2000, Florian Luca proved that F₁₀ = 55 and L₅ = 11 are the largest numbers with only one distinct digit in the Fibonacci and Lucas sequences, respectively. In this paper, we find terms of a linear recurrence sequence with only one block of digits in its expansion in base g ≥ 2. As an application, we generalize Luca's result by finding the Fibonacci and Lucas numbers with only one distinct block of digits of length up to 10 in its decimal expansion.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Marques D.

1 Togbé A.

1 2014

1 2011

Wyniki wyszukiwania

On the spacing between terms of generalized Fibonacci sequences

On terms of linear recurrence sequences with only one distinct block of digits