Displaying similar documents to “On Fibonacci-like sequences.”

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

Diego Marques, Alain Togbé (2011)

Colloquium Mathematicae

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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.

Elementary sequences.

Beslin, Scott J. (1992)

International Journal of Mathematics and Mathematical Sciences

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Increasing integer sequences and Goldbach's conjecture

Mauro Torelli (2006)

RAIRO - Theoretical Informatics and Applications

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Increasing integer sequences include many instances of interesting sequences and combinatorial structures, ranging from tournaments to addition chains, from permutations to sequences having the that any integer greater than 1 can be obtained as the sum of two elements in the sequence. The paper introduces and compares several of these classes of sequences, discussing recurrence relations, enumerative problems and questions concerning shortest sequences.