Prime numbers along Rudin–Shapiro sequences

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Odometers and Toeplitz systems revisited in the context of Sarnak's conjecture (2015, result): “ is known to hold for relatively few types of dynamical systems, in particular for odometers, irrational rotations, nilsequences [GT], horocycle ows [BSZ]. See also [B1], [B], [ALR], [G], [KL], [LS], [MR], for other results. We remark, that validity of Sarnak’s conjecture for odometers follows direc”
The logarithmic Sarnak conjecture for ergodic weights (2017, background): “The Sarnak conjecture has been proved for a variety of systems, for example nilsystems [34], some horocycle flows [9] and more general zero entropy systems arising from homogeneous dynamics [59], certain distal systems, in particular some extensions of a rotation by a torus [47, 51, 70], a large cla”
Equivalence of the Logarithmically Averaged Chowla and Sarnak Conjectures (2016, unknown): “CHOWLA AND SARNAK CONJECTURES 3 dynamical systems [1], [2], [3], [5], [6], [7], [8], [9], [12], [13], [14], [15], [17], [18], [25], [29], [33], [39], [40], [41], [42], [43], [48], [49], [52], [58]; for further variants of the Sarnak conjecture, see [10], [13], [37].”