A188381 Negabinary Keith numbers.

2, 3, 4, 7, 9, 13, 16, 36, 55, 64, 162, 256, 458, 1024, 1829, 4096, 7316, 15119, 16384, 18970, 37702, 37723, 45171, 60476, 65536, 84506, 262144, 277263, 1048576, 1109052, 1722002, 2160570, 4194304, 10549178, 12699958, 15084573, 16777216, 31921069, 67108864

Offset

1,1

Comments

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).

Links

Table of n, a(n) for n=1..39.

Mathematica

(* 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]]] &]

Crossrefs

Cf. A007629, A039724, A162724.

Sequence in context: A237870 A191015 A181385 * A005576 A339592 A241131

Adjacent sequences: A188378 A188379 A188380 * A188382 A188383 A188384

Keyword

nonn,base

Author

Alonso del Arte, Mar 29 2011

Extensions

a(33)-a(39) from Amiram Eldar, Jan 29 2020

Status

approved