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

1,2

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

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 *)

Crossrefs

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

Sequence in context: A213040 A173318 A153380 * A034027 A184795 A285412

Adjacent sequences: A268270 A268271 A268272 * A268274 A268275 A268276

Keyword

nonn,base

Author

Vladimir Shevelev, Mar 02 2016

Extensions

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

Status

approved