

A201992


Numbers whose binary representations are found in the ThueMorse sequence.


1



0, 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 18, 19, 20, 22, 25, 26, 37, 38, 41, 44, 45, 50, 51, 52, 75, 76, 77, 82, 83, 89, 90, 101, 102, 105, 150, 153, 154, 165, 166, 179, 180, 203, 205, 210, 211, 300, 301, 306, 308, 331, 332, 358, 361, 406, 410, 421, 422, 601
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OFFSET

0,3


COMMENTS

Interpreting A010060 as a bit string, this sequence contains the decimal equivalents of the subsequences, in order.


LINKS



EXAMPLE

The binary representation of 21 (10101) has an overlapping square sequence (1X1X1, where X is any binary sequence, in this case, X = 0), and so is not in the sequence. Compare to A063037.


MATHEMATICA

Module[{nn=10000, tm}, tm=Table[ThueMorse[n], {n, 0, nn}]; Join[{0}, Position[ Table[ If[SequenceCount[tm, IntegerDigits[k, 2]]>0, 1, 0], {k, 1000}], 1]]]// Flatten (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 03 2018 *)


PROG

(Haskell) a201992 = 0: concatMap (\n > Set.toList . Set.fromList . map binRep . filter ((==[1]).take 1) . window n . take (n*2^n) $ a010060) [1..] where
{window n = takeWhile (full . drop (n1)) . map (take n) . tails; binRep = foldl' (\a b > 2*a+b) 0}; full = not . null


CROSSREFS



KEYWORD

nonn,base,nice


AUTHOR



EXTENSIONS

Helper function added and name of value in program changed for better understanding by Walt RorieBaety, Mar 25 2012


STATUS

approved



