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%I #17 Aug 15 2022 08:36:50
%S 0,1,6,10,86,150,1366,2390,21846,38230,349526,611670,5592406
%N Records in A269340.
%C Denote by m(n) the position in A269340 corresponding to a(n). Then m(0)=0, m(1)=1.
%C Conjecture 1. For even n>=2, m(n)=(2/3)*(4^(n-1)-1); for odd n>=3, m(n)=(2/3)*(4^(n-2)-1)+3*4^(n-2).
%C Conjecture 2. For even n>=2, a(n)=2*m(n)+2; for odd n>=3, a(n)=(7*m(n)+12)/11.
%C (Cf. with conjectures in A268866).
%C Sequence {m(n)} begins 0, 1, 2, 14, 42, 234, 682, 3754, 10922, 60074, 174762, 961194, 2796202...
%H Jeffrey Shallit, Sonja Linghui Shan, and Kai Hsiang Yang, <a href="https://arxiv.org/abs/2208.06025">Automatic Sequences in Negative Bases and Proofs of Some Conjectures of Shevelev</a>, arXiv:2208.06025 [cs.FL], 2022.
%H Vladimir Shevelev, <a href="http://arxiv.org/abs/1603.04434">Two analogs of Thue-Morse sequence</a>, arXiv:1603.04434 [math.NT], 2016.
%Y Cf. A269340, A268865, A268866.
%K nonn,more
%O 0,3
%A _Vladimir Shevelev_, Feb 24 2016
%E More terms from _Peter J. C. Moses_, Feb 24 2016
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