<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we follow our generalisation of the cancellation algorithm described in our previous paper [A. Tomski, M. Zakarczemny, <italic>On some cancellation algorithms,</italic> NNTDM. 23, 2017, p. 101–114]. for <italic>f</italic> being a natural-valued function defined on ℕ<italic>s s</italic>, ≥1 we remove the divisors of all possible values of <italic>f</italic> in the points in which the sum of coordinates is less than or equal to <italic>n</italic>. The least non-cancelled number is called the discriminator <italic>D</italic><italic>f</italic>(<italic>n</italic>). We find formulas, or at least an estimation for this discriminator, in the case of a broad class of sequences.</abstract>

In this paper, we follow our generalisation of the cancellation algorithm described in our previous paper [A. Tomski, M. Zakarczemny, On some cancellation algorithms, NNTDM. 23, 2017, p. 101–114]. for f being a natural-valued function defined on ℕs s, ≥1 we remove the divisors of all possible values of f in the points in which the sum of coordinates is less than or equal to n. The least non-cancelled number is called the discriminator Df(n). We find formulas, or at least an estimation for this discriminator, in the case of a broad class of sequences.

A Note On Browkin’s and Cao’s Cancellation Algorithm

Institute of Mathematics, Faculty of Mathematics, Physics and Chemistry

Institute of Mathematics, Faculty of Physics, Mathematics and Computer Science

Technical Transactions

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 Public License.

{"article-title":"A Note On Browkin\u2019s and Cao\u2019s Cancellation Algorithm"}

In this paper, we follow our generalisation of the cancellation algorithm described in our previous paper [A. Tomski, M. Zakarczemny, On some cancellation...

A Note On Browkin’s and Cao’s Cancellation Algorithm

Published Online: May 21, 2020

Page range: 153 - 165

Received: Apr 24, 2018

DOI: https://doi.org/10.4467/2353737XCT.18.106.8801

Keywords
discriminator, sequence, congruence, odious numbers, Thue-Morse sequence

© 2020 Andrzej Tomski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 Public License.

A Note On Browkin’s and Cao’s Cancellation Algorithm

Published Online: May 21, 2020

Page range: 153 - 165

Received: Apr 24, 2018

DOI: https://doi.org/10.4467/2353737XCT.18.106.8801

Keywordsdiscriminator, sequence, congruence, odious numbers, Thue-Morse sequence

© 2020 Andrzej Tomski et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 Public License.

Keywords
discriminator, sequence, congruence, odious numbers, Thue-Morse sequence