Dispersion of ratio block sequences and asymptotic density
Ferdinánd Filip, Ladislav Mišík, János T. Tóth (2008)
Acta Arithmetica
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Ferdinánd Filip, Ladislav Mišík, János T. Tóth (2008)
Acta Arithmetica
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Václav Kijonka (2007)
Acta Mathematica Universitatis Ostraviensis
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In this paper it is discus a relation between -density and -density. A generalization of Šalát’s result concerning this relation in the case of asymptotic density is proved.
Uri Andrews, Mingzhong Cai, David Diamondstone, Carl Jockusch, Steffen Lempp (2016)
Fundamenta Mathematicae
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Let r ∈ [0,1]. A set A ⊆ ω is said to be coarsely computable at density r if there is a computable function f such that {n | f(n) = A(n)} has lower density at least r. Our main results are that A is coarsely computable at density 1/2 if A is computably traceable or truth-table reducible to a 1-random set. In the other direction, we show that if a degree a is hyperimmune or PA, then there is an a-computable set which is not coarsely computable at any positive density.
James Foran (1977)
Colloquium Mathematicae
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Rzepecka, Genowefa (2015-12-08T07:20:54Z)
Acta Universitatis Lodziensis. Folia Mathematica
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David Lubell (1971)
Acta Arithmetica
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Guillaume Bordes (2005)
Acta Arithmetica
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Jean-Marie De Koninck, Aleksandar Ivić (1984)
Publications de l'Institut Mathématique
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Aleksandar Ivić (1978)
Colloquium Mathematicae
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Pär Kurlberg, Jeffrey C. Lagarias, Carl Pomerance (2012)
Acta Arithmetica
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Thomas G. Hallam (1971)
Annales Polonici Mathematici
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Miloš Ráb (1974)
Annales Polonici Mathematici
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Vadim Komkov, Carter Waid (1973)
Annales Polonici Mathematici
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Kuo-Liang Chiou (1974)
Annales Polonici Mathematici
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Barbara Stachurska (1971)
Annales Polonici Mathematici
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Christian Ballot, Florian Luca (2013)
Acta Arithmetica
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Romanoff (1934) showed that integers that are the sum of a prime and a power of 2 have positive lower asymptotic density in the positive integers. We adapt his method by showing more generally the existence of a positive lower asymptotic density for integers that are the sum of a prime and a term of a given nonconstant nondegenerate integral linear recurrence with separable characteristic polynomial.