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%I #14 Aug 27 2022 21:30:59
%S 0,1,6,0,2,0,0,1,2,0,0,3,0,1,10,0,2,0,0,3,0,1,2,0,0,1,6,0,2,0,0,1,2,0,
%T 0,3,0,1,2,0,0,1,86,0,2,0,0,3,0,1,6,0,2,0,0,1,2,0,0,3,0,1,10,0,2,0,0,
%U 3,0,1,2,0,0,1,22,0,2,0,0,3,0,1,6,0,2,0
%N A second sequence (see A268865) connected with negabinary expansions (cf. A039724) - see comments.
%C Let A_n be the Thue-Morse sequence (A010060) beginning with A010060(n). Then a(n) is defined to be the maximal number of the first terms of {1-A269027(n)} coinciding with the corresponding terms of A_n.
%H Peter J. C. Moses, <a href="/A269340/b269340.txt">Table of n, a(n) for n = 0..3999</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.
%t nn = 87; f[n_, b_] := Most@ Mod[NestWhileList[-(#1 - Mod[#1, b])/b &, n, #1 != 0 &], b]; Array[(k = 0; While[1 - Mod[Total@ f[k, 2], 2] == ThueMorse[# + k], k++]; k) &, nn - 1, 0] (* _Michael De Vlieger_, Aug 25 2022 *)
%Y Cf. A010060, A039724, A268865, A269027.
%K nonn,base
%O 0,3
%A _Vladimir Shevelev_, Feb 24 2016
%E More terms from _Peter J. C. Moses_, Feb 24 2016
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