Abstract :
An infinite set of natural numbers is called aB3-sequence if all sumsa1+a2+a3withajset membership, variantAanda1less-than-or-equals, slanta2less-than-or-equals, slanta3are distinct. LetA(n) be the number of positive elements less-than-or-equals, slantninA. P. Erdös conjectures that everyB3-sequenceAsatisfies lim infn→∞ A(n) n−1/3=0. In this paper we prove that no sequence satisfyingA(n)not, vert, similarαn1/3can be aB3-sequence. We also give other necessary conditions for aB3-sequence.
