Problem 358

Erdős Problem #358: declared status 'proved'. Formalized: yes. Let $A=\{a_1<\cdots\}$ be an infinite sequence of integers. Let $f(n)$ count the number of solutions to$$n=\sum_{u\leq i\leq v}a_i.$$Is there such an $A$ for which $f(n)\to \infty$ as $n\to \infty$? Or even where $f(n)\geq 2$ for all large $n$? Prize: no. Tags: additive basis, number theory, primes.