A269341 Records in A269340.

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

Table of n, a(n) for n=0..12.

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

Cf. A269340, A268865, A268866.

Sequence in context: A280881 A256246 A246800 * A348650 A201921 A117310

Adjacent sequences: A269338 A269339 A269340 * A269342 A269343 A269344

Keyword

nonn,more

Author

Vladimir Shevelev, Feb 24 2016

Extensions

More terms from Peter J. C. Moses, Feb 24 2016

Status

approved