Problem Statement
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?
Categories:
Number Theory
Progress
Asked by Hofstadter (although in [Er77c] Erdős says this question was originally due to Ulam). The sequence begins $1,2,3,5,6,8,10,11,\ldots$ and is A005243 in the OEIS.Source: erdosproblems.com/423 | Last verified: January 15, 2026