Problem 276

Erdős Problem #276: declared status 'open'. Formalized: yes. Is there an infinite Lucas sequence $a_0,a_1,\ldots$ where $a_{n+2}=a_{n+1}+a_n$ for $n\geq 0$ such that all $a_k$ are composite, and yet no integer has a common factor with every term of the sequence? Prize: no. Tags: covering systems, number theory.