Result: On the completeness of certain sequences

Title:
On the completeness of certain sequences
Authors:
Hegyvári, Norbert, Rauzy, Gerard
Source:
Publicationes Mathematicae Debrecen. 55:245-252
Publisher Information:
University of Debrecen/ Debreceni Egyetem, 1999.
Publication Year:
1999
Subject Terms:
Graham sequence, Arithmetic progressions, Other combinatorial number theory, Density, gaps, topology, sumsets, subset sum, additive number theory, infinite arithmetic progression, 0101 mathematics, 01 natural sciences
Document Type:
Academic journal Article
File Description:
application/xml
ISSN:
0033-3883
DOI:
10.5486/pmd.1999.1994
Access URL:
https://zbmath.org/1404432
Accession Number:
edsair.doi.dedup.....0a83436f98bf1a95c61ef91eec8853d4
Database:
OpenAIRE

Further Information

Let \(b_1, b_2, \dots \) be an arbitrary infinite sequence of positive integers and \(\alpha \) any positive real number. It is proved that the collection of all sums of type \(\sum \varepsilon (m,n) b_m [ 2^n \alpha ] \) with \(\varepsilon (m,n)=0\) or 1 always contains an infinite arithmetic progression (i.e. the sequence is subcomplete).