Problem 423

Erdős Problem #423: declared status 'open'. Formalized: no. Let $a_1=1$ and $a_2=2$ and for $k\geq 3$ we choose $a_k$ to be the least integer $>a_{k-1}$ which is the sum of at least two consecutive terms of the sequence. What is the asymptotic behaviour of this sequence? Prize: no. OEIS: A005243. Tags: number theory.