A268272 Negabinary evil numbers (see comment).

0, 2, 5, 7, 8, 10, 13, 14, 17, 19, 20, 22, 25, 27, 28, 31, 32, 34, 37, 39, 40, 42, 45, 46, 49, 51, 52, 55, 56, 58, 61, 62, 65, 67, 68, 70, 73, 75, 76, 79, 80, 82, 85, 87, 88, 90, 93, 94, 97, 99, 100, 102, 105, 107, 108, 111, 112, 114, 117, 118, 121, 123, 124

Offset

0,2

Comments

Recall that a number n >= 0 is defined as an evil number (A001969) if its binary expansion contains an even number of 1's, or such n that Thue-Morse sequence A010060(n)=0.

Sequence A269027 is essentially Thue-Morse sequence in "negabinary", i.e., in base -2. So a number n for which A269027(n)=0 it is natural to call "negabinary evil".

Links

Peter J. C. Moses, Table of n, a(n) for n = 0..1999

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, EvenQ@ 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, A001969, A039724, A268273, A269027.

Sequence in context: A184793 A343301 A034028 * A102700 A095371 A047481

Adjacent sequences: A268269 A268270 A268271 * A268273 A268274 A268275

Keyword

nonn,base

Author

Vladimir Shevelev, Mar 02 2016

Extensions

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

Status

approved