A268865 Sequence connected with negabinary (A039724) - see comment.

2, 0, 0, 3, 0, 1, 2, 0, 0, 1, 22, 0, 2, 0, 0, 3, 0, 1, 6, 0, 2, 0, 0, 1, 2, 0, 0, 3, 0, 1, 2, 0, 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, 38, 0, 2, 0, 0, 3, 0, 1, 6, 0, 2, 0, 0, 1, 2, 0, 0, 3, 0, 1, 10, 0, 2, 0, 0, 3, 0, 1

Offset

0,1

Comments

Let b(n) be the parity of the number of 1's in the n-th term of A039724 {0,1,0,1,1,0,1,0,0,...}. 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 {b(n)} coinciding with the corresponding terms of A_n.

Links

Peter J. C. Moses, Table of n, a(n) for n = 0..2999

Vladimir Shevelev, Two analogs of Thue-Morse sequence, arXiv:1603.04434 [math.NT], 2016.

Mathematica

f[n_, b_] := Most@ Mod[NestWhileList[-(#1 - Mod[#1, b])/b &, n, #1 != 0 &], b]; Array[(k = 0; While[Mod[Total@ f[k, 2], 2] == ThueMorse[# + k], k++]; k) &, 86, 0] (* Michael De Vlieger, Aug 25 2022 *)

Crossrefs

Cf. A010060, A039724.

Sequence in context: A228926 A372727 A321414 * A024159 A029302 A263415

Adjacent sequences: A268862 A268863 A268864 * A268866 A268867 A268868

Keyword

nonn

Author

Vladimir Shevelev, Feb 15 2016

Extensions

More terms from Peter J. C. Moses, Feb 15 2016

Status

approved