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We refine a result of Languasco and Zaccagnini (J Number Theory 132:3016–3028, 2012) on Diophantine approximation with two primes and powers of two. We improve the upper bound on the least value $$s_0$$ s 0 which ensures that for all $$s\ge s_0$$ s ≥ s 0 , there exists an approximation to any real number by values of the form $$\lambda _1p_1+\lambda _2p_2+\mu _1 2^{m_1}+\dots...
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