The generating function ln ((1 - F(x))-1)where F(x) is an ordinary generating function with the integer coefficients is considered.Some properties ot its coefficients allowing the construction of probabilistic primality testsare obtained. The connection of them with the existing primality tests is shown. Some newproperties of Lucas numbers and binomial coefficients are obtained too.
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- Title Properties of coefficients in some superpositions of generatingfunctions
- Headline Properties of coefficients in some superpositions of generatingfunctions
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Tomsk State University - Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 1(15)
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Keywords
primality test, composition of a natural number, superposition of generating functions, generating functions, тесты на простоту, композиция натурального числа, суперпозиция производящих функций, производящие функцииAuthors
References
AgrawalM., KayalN., and Saxena N. PRIMES is in P // Ann. Math. 2004. V. 160. No. 2. P. 781-793.
www.oeis.org - J. A. Sloane. The On-Line Encyclopedia of Integer Sequences. 2011.
Кручинин В. В. Комбинаторика композиций и её приложения. Томск: В-Спектр, 2010. 156с.
Properties of coefficients in some superpositions of generatingfunctions | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2012. № 1(15).
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