This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A188381 #24 Apr 07 2020 21:20:37
%S A188381 2,3,4,7,9,13,16,36,55,64,162,256,458,1024,1829,4096,7316,15119,16384,
%T A188381 18970,37702,37723,45171,60476,65536,84506,262144,277263,1048576,
%U A188381 1109052,1722002,2160570,4194304,10549178,12699958,15084573,16777216,31921069,67108864
%N A188381 Negabinary Keith numbers.
%C A188381 Keith numbers are described in A007629. All powers of 4 appear. However, 2 is the only number of the form 2^n with n odd that appears in the sequence. That's because in negabinary, such numbers are represented as 11 followed by n 0's, and that leads to the sequence 1, 1, 0, ... , 0, 2, 3, 5, 10, 20, 40, 80, 160, ... up to 5(2^(n - 2)), and 5(2^(n - 2)) > 2^(n - 1). (See A020714).
%t A188381 (* First run the program from A039724 to define ToNegaBases *) keithFromListQ[n_Integer, digits_List] := Module[{seq = digits, curr = digits[[-1]], ord = Length[digits]}, While[curr < n, curr = Plus@@Take[seq, -ord]; AppendTo[seq, curr]]; Return[seq[[-1]] == n]]; Select[Range[2, 32768], keithFromListQ[#, IntegerDigits[ToNegaBases[#, 2]]] &]
%Y A188381 Cf. A007629, A039724, A162724.
%K A188381 nonn,base
%O A188381 1,1
%A A188381 _Alonso del Arte_, Mar 29 2011
%E A188381 a(33)-a(39) from _Amiram Eldar_, Jan 29 2020