Integer Sequences which Are Closed with Respect to Multiplication and whose Sumset does not Intersect the Sequence
Number Theory
2026-07-10 v1
Abstract
We investigate increasing sequences of integers with the property that the product of every two terms of the sequence is also a term of the sequence and the sum of every two terms is not a term of the sequence. We say that a sequence with the above properties is maximal if it is not a proper subsequence of another sequence with the above properties. We determine whether the sequences in three families are maximal or not.
Cite
@article{arxiv.2607.09937,
title = {Integer Sequences which Are Closed with Respect to Multiplication and whose Sumset does not Intersect the Sequence},
author = {Georgi Demirov and Ognian Trifonov},
journal= {arXiv preprint arXiv:2607.09937},
year = {2026}
}