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pro vyhledávání: '"Baruchel, Thomas"'
Autor:
Baruchel, Thomas
Some changes in a recent convolution formula are performed here in order to clean it up by using more conventional notations and by making use of more referrenced and documented components (namely Sierpi\'nski's polynomials, the Thue-Morse sequence,
Externí odkaz:
http://arxiv.org/abs/1912.00452
Autor:
Baruchel, Thomas
The sequence A268289 from the On-Line Encyclopedia of Integer Sequences, namely the cumulated differences between the number of digits 1 and the number of digits 0 in the binary expansion of consecutive integers, is studied here. This sequence happen
Externí odkaz:
http://arxiv.org/abs/1908.02250
Autor:
Baruchel, Thomas
The recursion tree resulting from Karatsuba's formula is built here by using an interleaved splitting scheme rather than the traditional left/right one. This allows an easier access to the nodes of the tree and $2n-1$ of them are initially flattened
Externí odkaz:
http://arxiv.org/abs/1902.08982
Autor:
Baruchel, Thomas
Several conjectural continued fractions found with the help of various algorithms are published in this paper.
Externí odkaz:
http://arxiv.org/abs/1704.03434
Autor:
Baruchel, Thomas, Elsner, Carsten
In this paper we consider error sums of the form \[\sum_{m=0}^{\infty} \varepsilon_m\Big( \,b_m\alpha - \frac{a_m}{c_m}\,\Big) \,,\] where $\alpha$ is a real number, $a_m$, $b_m$, $c_m$ are integers, and $\varepsilon_m=1$ or $\varepsilon_m ={(-1)}^m$
Externí odkaz:
http://arxiv.org/abs/1602.06445
Autor:
Allouche, Jean-Paul, Baruchel, Thomas
Several years ago the second author playing with different "recognizers of real constants", e.g., the LLL algorithm, the Plouffe inverter, etc. found empirically the following formula. Let $p_n/q_n$ denote the $n$th convergent of the continued fracti
Externí odkaz:
http://arxiv.org/abs/1408.2206
