## DIMACS TR: 98-33

## 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

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