Let $X$ be a large integer. We prove that, for any fixed positive integer $k$, a suitable asymptotic formula for the number of representations of an even integer $N \in [1, X]$ as the sum of two primes and $k$ powers of $2$ holds with at most $\Odip{k}{X^{3/5} (\log X)^{10}}$ exceptions.
On the sum of two primes and k powers of two
LANGUASCO, ALESSANDRO;
2007
Abstract
Let $X$ be a large integer. We prove that, for any fixed positive integer $k$, a suitable asymptotic formula for the number of representations of an even integer $N \in [1, X]$ as the sum of two primes and $k$ powers of $2$ holds with at most $\Odip{k}{X^{3/5} (\log X)^{10}}$ exceptions.
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