A268273 Negabinary odious numbers (see comment).

1, 3, 4, 6, 9, 11, 12, 15, 16, 18, 21, 23, 24, 26, 29, 30, 33, 35, 36, 38, 41, 43, 44, 47, 48, 50, 53, 54, 57, 59, 60, 63, 64, 66, 69, 71, 72, 74, 77, 78, 81, 83, 84, 86, 89, 91, 92, 95, 96, 98, 101, 103, 104, 106, 109, 110, 113, 115, 116, 119, 120, 122, 125

Offset: 1

Author

Vladimir Shevelev, Mar 02 2016

Keywords

• nonn
• base

Comments

Recall that a number n>=1 is defined as odious number (A000069) if its binary expansion contains an odd number of 1's, or such n that Thue-Morse sequence A010060(n)=1. Sequence A269027 is essentially Thue-Morse sequence in "negabinary", i.e., in base -2. So a number n for which A269027(n)=1 it is natural to call "negabinary odious".

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..2000
• Vladimir Shevelev, Two analogs of Thue-Morse sequence, arXiv:1603.04434 [math.NT], 2016.
• Eric Weisstein's World of Mathematics, Negabinary

Crossrefs

Cf. A010060, A000069, A039724, A268272, A269027.

Programs

Mathematica

b = 2; Select[Range[0, 125], Function[k, OddQ@ Total@ Rest@ Reverse@ Mod[NestWhileList[(# - Mod[#, b])/-b &, k, # != 0 &], b]]] (* Michael De Vlieger, Mar 03 2016, after Robert Lozyniak at A039724 *)

Extensions

More terms from Peter J. C. Moses, Mar 02 2016