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A188381 Negabinary Keith numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
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 0s, 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..32.

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, A162724.

Sequence in context: A237870 A191015 A181385 * A005576 A241131 A129373

Adjacent sequences:  A188378 A188379 A188380 * A188382 A188383 A188384

KEYWORD

nonn,base

AUTHOR

Alonso del Arte, Mar 29 2011

STATUS

approved

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Last modified April 24 14:31 EDT 2017. Contains 285346 sequences.