%I #36 Oct 13 2017 00:22:36
%S 0,2,5,7,8,10,13,14,17,19,20,22,25,27,28,31,32,34,37,39,40,42,45,46,
%T 49,51,52,55,56,58,61,62,65,67,68,70,73,75,76,79,80,82,85,87,88,90,93,
%U 94,97,99,100,102,105,107,108,111,112,114,117,118,121,123,124
%N Negabinary evil numbers (see comment).
%C Recall that a number n >= 0 is defined as an evil number (A001969) if its binary expansion contains an even number of 1's, or such n that Thue-Morse sequence A010060(n)=0.
%C Sequence A269027 is essentially Thue-Morse sequence in "negabinary", i.e., in base -2. So a number n for which A269027(n)=0 it is natural to call "negabinary evil".
%H Peter J. C. Moses, <a href="/A268272/b268272.txt">Table of n, a(n) for n = 0..1999</a>
%H Vladimir Shevelev, <a href="http://arxiv.org/abs/1603.04434">Two analogs of Thue-Morse sequence</a>, arXiv:1603.04434 [math.NT], 2016.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Negabinary.html">Negabinary</a>
%t b = 2; Select[Range[0, 125], Function[k, EvenQ@ Total@ Rest@ Reverse@ Mod[NestWhileList[(# - Mod[#, b])/-b &, k, # != 0 &], b]]] (* _Michael De Vlieger_, Mar 03 2016, after Robert Lozyniak at A039724 *)
%Y Cf. A010060, A001969, A039724, A268273, A269027.
%K nonn,base
%O 0,2
%A _Vladimir Shevelev_, Mar 02 2016
%E More terms from _Peter J. C. Moses_, Mar 02 2016