Thin Complete Subsequence

Author: Norbert Hegyvári

ABSTRACT

$A$ is said to be {\em complete} if every sufficiently large integer belongs to the sumset of $A$. $A'$ is {\em thin comlete subsequence} of $A$ if $A'$ is complete and $A'(x)=(1+o(1))\log_2x$.

It is proved that $\lim_{n\to \infty}a_{n+1}/a_n=1$ implies the existence of thin complete subsequence.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-33.ps.gz