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pro vyhledávání: '"Shevelev, Vladimir"'
Autor:
Shevelev, Vladimir
Let $E_n(x)$ be Euler polynomial, $\nu_2(n)$ be $2-$adic order of $n,$ $\{g(n)\}$ be the characteristic sequence for $\{2^{n}-1\}_{n\geq1}.$ Recently Peter Luschny asked (cf. \cite{5}, sequence A290646): is for $n\geq1$ A290646=A135517? According to
Externí odkaz:
http://arxiv.org/abs/1708.08096
Autor:
Shevelev, Vladimir
We naturally obtain some combinatorial identities finding the difference analogs of hyperbolic and trigonometric functions of order $n.$ In particular, we obtain the identities connected with the proved in the paper the addition formulas for these an
Externí odkaz:
http://arxiv.org/abs/1706.01454
Autor:
Shevelev, Vladimir, Moses, Peter J. C.
We study a special set of constellations of primes generated by twin primes.
Comment: 12 pages Addition of Corollary 3
Comment: 12 pages Addition of Corollary 3
Externí odkaz:
http://arxiv.org/abs/1610.03385
Autor:
Shevelev, Vladimir
In 1944, P. Erd\H{o}s \cite{1} proved that if $n$ is a large highly composite number (HCN) and $n_1$ is the next HCN, then $$n0$ is a constant. In this paper, using numerical results by D. A. Corneth, we show that mo
Externí odkaz:
http://arxiv.org/abs/1605.08884
Autor:
Shevelev, Vladimir
We introduce and study two analogs of one of the best known sequence in Mathematics : Thue-Morse sequence. The first analog is concerned with the parity of number of runs of 1's in the binary representation of nonnegative integers. The second one is
Externí odkaz:
http://arxiv.org/abs/1603.04434
Autor:
Shevelev, Vladimir
The author \cite{4} proved that, for every set $S$ of positive integers containing 1 (finite or infinite) there exists the density $h=h(E(S))$ of the set $E(S)$ of numbers whose prime factorizations contain exponents only from $S,$ and gave an explic
Externí odkaz:
http://arxiv.org/abs/1602.04244
Autor:
Shevelev, Vladimir
Let $\mathbf{G}$ be the set of all finite or infinite increasing sequences of positive integers beginning with 1. For a sequence $S=\{s(n)\}, n\geq1,$ from $\mathbf{G},$ a positive number $N$ is called an exponentially $S$-number $(N\in E(S)),$ if al
Externí odkaz:
http://arxiv.org/abs/1511.03860
Autor:
Shevelev, Vladimir
Let $\mathbf{S}$ be the set of all finite or infinite increasing sequences of positive integers. For a sequence $S=\{s(n)\}, n\geq1,$ from $\mathbf{S},$ let us call a positive number $N$ an exponentially $S$-number $(N\in E(S)),$ if all exponents in
Externí odkaz:
http://arxiv.org/abs/1510.05914
Autor:
Shevelev, Vladimir
We study the number $\nu(n)$ of representations of a positive integer $n$ by the form $x^3+y^3+z^3-3xyz$ in the conditions $0\leq x\leq y\leq z; z\geq x+1.$ We proved the following results: (i) for every positive $n,$ except for $n\equiv\pm3 \pmod9,$
Externí odkaz:
http://arxiv.org/abs/1508.05748
Autor:
Shevelev, Vladimir
For an arbitrary given $k\geq3,$ we consider a possibility of representation of a positive number $n$ by the form $x_1...x_k+x_1+...+x_k, 1\leq x_1\leq ... \leq x_k.$ We also study a question on the smallest value of $k\geq3$ in such a representation
Externí odkaz:
http://arxiv.org/abs/1508.03970