Completeness properties of perturbed sequences

Stefan A. Burr, P. Erdős

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

If S is an arbitrary sequence of positive integers, let P(S) be the set of all integers which are representable as a sum of distinct terms of S. Call S complete if P(S) contains all large integers, and subcomplete if P(S) contains an infinite arithmetic progression. It is shown that any sequence can be perturbed in a rather moderate way into a sequence which is not subcomplete. On the other hand, it is shown that if S is any sequence satisfying a mild growth condition, then a surprisingly gentle perturbation suffices to make S complete in a strong sense. Various related questions are also considered.

Original languageEnglish
Pages (from-to)446-455
Number of pages10
JournalJournal of Number Theory
Volume13
Issue number4
DOIs
Publication statusPublished - 1981

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Completeness
Integer
Arithmetic sequence
Growth Conditions
Perturbation
Distinct
Arbitrary
Term

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Completeness properties of perturbed sequences. / Burr, Stefan A.; Erdős, P.

In: Journal of Number Theory, Vol. 13, No. 4, 1981, p. 446-455.

Research output: Contribution to journalArticle

Burr, Stefan A. ; Erdős, P. / Completeness properties of perturbed sequences. In: Journal of Number Theory. 1981 ; Vol. 13, No. 4. pp. 446-455.
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