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arXiv · 2607.09937

Integer Sequences which Are Closed with Respect to Multiplication and whose Sumset does not Intersect the Sequence

Georgi Demirov·Ognian Trifonov
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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.

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Georgi Demirov, Ognian Trifonov. 2026-07-10. Integer Sequences which Are Closed with Respect to Multiplication and whose Sumset does not Intersect the Sequence. https://arxiv.org/abs/2607.09937

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