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%I #34 Apr 07 2020 10:41:56
%S 1,3,4,6,9,11,12,15,16,18,21,23,24,26,29,30,33,35,36,38,41,43,44,47,
%T 48,50,53,54,57,59,60,63,64,66,69,71,72,74,77,78,81,83,84,86,89,91,92,
%U 95,96,98,101,103,104,106,109,110,113,115,116,119,120,122,125
%N Negabinary odious numbers (see comment).
%C Recall that a number n>=1 is defined as odious number (A000069) if its binary expansion contains an odd number of 1's, or such n that Thue-Morse sequence A010060(n)=1. Sequence A269027 is essentially Thue-Morse sequence in "negabinary", i.e., in base -2. So a number n for which A269027(n)=1 it is natural to call "negabinary odious".
%H Peter J. C. Moses, <a href="/A268273/b268273.txt">Table of n, a(n) for n = 1..2000</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, OddQ@ 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, A000069, A039724, A268272, A269027.
%K nonn,base
%O 1,2
%A _Vladimir Shevelev_, Mar 02 2016
%E More terms from _Peter J. C. Moses_, Mar 02 2016
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