Geodesic
On the distribution of the numbers with binary expansions of a~special type in arithmetic progressions
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 4, pp. 34-37.

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Let 2 be the primitive root $\operatorname{mod}p$. Let $N_0$ be a set of natural numbers whose binary expansions contain even numbers of 1. Numbers from $N_0$ are uniformly distributed in arithmetic progressions with the difference $p$. 
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A. P. Naumenko. On the distribution of the numbers with binary expansions of a~special type in arithmetic progressions. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 4, pp. 34-37. http://geodesic.mathdoc.fr/item/ISU_2008_8_4_a4/

[1] Gelfond A. O., “Sur les nombres qui ont des proprietes additives et multiplicatives donnies”, Acta Arith., 13 (1968), 259–265 | MR | Zbl

[2] Aierlend K., Rouzen M., Klassicheskoe vvedenie v sovremennuyu teoriyu chisel, Mir, M., 1987 | MR