Geodesic
The Goldbach problem with primes having binary expansions of a~special form
Izvestiya. Mathematics , Tome 78 (2014) no. 1, pp. 201-211

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We obtain an asymptotic formula for the number of representations of an odd number $N$ by a sum of three primes in $\mathbb{N}_{0}$, where $\mathbb{N}_{0}$ stands for the set of positive integers whose binary expansions have evenly many 1's.
Keywords: ternary Goldbach problem, Gel'fond problem, large sieve, trigonometric sums. 
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K. M. Eminyan. The Goldbach problem with primes having binary expansions of a~special form. Izvestiya. Mathematics , Tome 78 (2014) no. 1, pp. 201-211. http://geodesic.mathdoc.fr/item/IM2_2014_78_1_a8/