Results 1 to 10 of about 2,056,400 (324)
Ternary expansions of powers of 2 [PDF]
, 2009 Paul Erdos asked how frequently the ternary expansion of 2^n omits the digit 2. He conjectured this happens only for finitely many values of n. We generalize this question to consider iterates of two discrete dynamical systems. The first is over the real
Jeffrey C. Lagarias
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Notre Dame Journal of Formal Logic, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Keremedis, Kyriakos, Herrlich, Horst
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On pairs of equations involving unlike powers of primes and powers of 2 [PDF]
Comptes Rendus. Mathématique, 2020 In this paper, it is proved that every pair of sufficiently large even integers can be represented by a pair of equations, each containing one prime, one prime square, two prime cubes and 302 powers of 2. This result constitutes a refinement upon that of
Liu, Yuhui
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Representation of a 2-power as sum of k 2-powers: A recursive formula
Journal of Number Theory, 2013 Let \(U(\ell,k)\) denote the number of distinct compositions of \(\ell\) as a sum of \(k\) powers of two (where order matters). Thus, for example, \(U(10,3) = 6\), arising from the representations \(10 = 8+1+1\) and \(10 = 4+4+2\) and their permutations. The behavior of \(U(\ell,k)\) is quite erratic; it can be regularized by defining \(W(\sigma, k) = \
A. Giorgilli, G. Molteni
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Democratic Deterrence of Middle Powers in Great Power Rivalry: The Case for Indonesia [version 2; peer review: 2 approved, 1 not approved] [PDF]
F1000ResearchShortly after the Russian invasion of Ukraine, President Biden rightly characterized the current era of great power competition as one that occurs between democracies vs autocracies; thus, democracies need a new kind of deterrence concept against ...
Aristo Purboadji
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Squares of Primes and Powers of 2, II
Journal of Number Theory, 2002 In [Monatsh. Math. 128, 283-313 (1999; Zbl 0940.11047)] the present authors established a positive lower bound of the presumably correct order of magnitude for a count of the number of representations of a large number \(N \equiv 4 \bmod 8\) as a sum of four squares of primes and \(k\) powers of 2.
Liu, J, Liu, MC, Zhan, T
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A Gauss-Kuzmin Theorem for Continued Fractions Associated with Nonpositive Integer Powers of an Integer m≥2 [PDF]
The Scientific World Journal, 2014 We consider a family {τm:m≥2} of interval maps which are generalizations of the Gauss transformation. For the continued fraction expansion arising from τm, we solve a Gauss-Kuzmin-type problem.
Dan Lascu
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Digits of powers of 2 in ternary numeral system [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 We study the digits of the powers of 2 in the ternary number system. We propose an algorithm for doubling numbers in ternary numeral system. Using this algorithm, we explain the appearance of “stairs” formed by 0s and 2s when the numbers 2ⁿ (n = 0, 1, 2,
Yagub N. Aliyev
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On pairs of equations in eight prime cubes and powers of 2
AIMS Mathematics, 2023 In this paper, it is proved that every pair of large positive even integers satisfying some necessary conditions can be represented in the form of a pair of eight cubes of primes and 287 powers of 2. This improves the previous result.
Gen Li, Liqun Hu, Xianjiu Huang
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Membranes, 2022 In this work, we report the conversion of carbon dioxide (CO2) gas into graphene on copper foil by using a thermal chemical vapor deposition (CVD) method assisted by hydrogen (H2) plasma pre-treatment.
Yotsarayuth Seekaew +5 more
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