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A269341
Records in A269340.
0
0, 1, 6, 10, 86, 150, 1366, 2390, 21846, 38230, 349526, 611670, 5592406
OFFSET
0,3
COMMENTS
Denote by m(n) the position in A269340 corresponding to a(n). Then m(0)=0, m(1)=1.
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).
Conjecture 2. For even n>=2, a(n)=2*m(n)+2; for odd n>=3, a(n)=(7*m(n)+12)/11.
(Cf. with conjectures in A268866).
Sequence {m(n)} begins 0, 1, 2, 14, 42, 234, 682, 3754, 10922, 60074, 174762, 961194, 2796202...
LINKS
Jeffrey Shallit, Sonja Linghui Shan, and Kai Hsiang Yang, Automatic Sequences in Negative Bases and Proofs of Some Conjectures of Shevelev, arXiv:2208.06025 [cs.FL], 2022.
Vladimir Shevelev, Two analogs of Thue-Morse sequence, arXiv:1603.04434 [math.NT], 2016.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Vladimir Shevelev, Feb 24 2016
EXTENSIONS
More terms from Peter J. C. Moses, Feb 24 2016
STATUS
approved