Frequencies of factors in Arnoux-Rauzy sequences
Nathan Wozny, Luca Q. Zamboni (2001)
Acta Arithmetica
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Nathan Wozny, Luca Q. Zamboni (2001)
Acta Arithmetica
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Mercer, A.McD. (1978)
International Journal of Mathematics and Mathematical Sciences
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Filippo Mignosi, Luca Q. Zamboni (2002)
Acta Arithmetica
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Kimberling, Clark (2007)
Journal of Integer Sequences [electronic only]
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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.
van de Bult, Fokko J., Gijswijt, Dion C., Linderman, John P., Sloane, N.J.A., Wilks, Allan R. (2007)
Journal of Integer Sequences [electronic only]
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Paquin, Geneviève, Vuillon, Laurent (2007)
The Electronic Journal of Combinatorics [electronic only]
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S. V. Astashkin, F. A. Sukochev (2008)
Banach Center Publications
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A new set of sufficient conditions under which every sequence of independent identically distributed functions from a rearrangement invariant (r.i.) space on [0,1] spans there a Hilbertian subspace are given. We apply these results to resolve open problems of N. L. Carothers and S. L. Dilworth, and of M. Sh. Braverman, concerning such sequences in concrete r.i. spaces.
Hans Carstens (1975)
Fundamenta Mathematicae
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Jovan D. Kečkić (1973)
Publications de l'Institut Mathématique
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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.
Benito, Manuel, Creyaufmüller, Wolfgang, Varona, Juan L., Zimmermann, Paul (2002)
Experimental Mathematics
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Matveev, Andrey O. (2008)
Integers
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