This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A268273 #35 Feb 16 2025 08:33:30 %S A268273 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 A268273 48,50,53,54,57,59,60,63,64,66,69,71,72,74,77,78,81,83,84,86,89,91,92, %U A268273 95,96,98,101,103,104,106,109,110,113,115,116,119,120,122,125 %N A268273 Negabinary odious numbers (see comment). %C A268273 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 A268273 Peter J. C. Moses, <a href="/A268273/b268273.txt">Table of n, a(n) for n = 1..2000</a> %H A268273 Vladimir Shevelev, <a href="http://arxiv.org/abs/1603.04434">Two analogs of Thue-Morse sequence</a>, arXiv:1603.04434 [math.NT], 2016. %H A268273 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Negabinary.html">Negabinary</a> %t A268273 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 A268273 Cf. A010060, A000069, A039724, A268272, A269027. %K A268273 nonn,base %O A268273 1,2 %A A268273 _Vladimir Shevelev_, Mar 02 2016 %E A268273 More terms from _Peter J. C. Moses_, Mar 02 2016