$A$ 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:
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