6533b7d7fe1ef96bd1268fb8
RESEARCH PRODUCT
On the Distribution ofB3-Sequences
Martin HelmMartin Helmsubject
Discrete mathematicsCombinatoricsSequenceInfinite setAlgebra and Number TheoryDistribution (number theory)Natural numberMathematicsdescription
Abstract An infinite set of natural numbers is called aB3-sequence if all sumsa1+a2+a3withaj∈Aanda1⩽a2⩽a3are distinct. LetA(n) be the number of positive elements ⩽ninA. P. Erdos conjectures that everyB3-sequenceAsatisfies lim infn→∞ A(n) n−1/3=0. In this paper we prove that no sequence satisfyingA(n)∼αn1/3can be aB3-sequence. We also give other necessary conditions for aB3-sequence.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1996-05-01 | Journal of Number Theory |